hypothesis theory part

Theories, Hypotheses, and Laws: Definitions, examples, and their roles in science

by Anthony Carpi, Ph.D., Anne E. Egger, Ph.D.

Listen to this reading

Did you know that the idea of evolution had been part of Western thought for more than 2,000 years before Charles Darwin was born? Like many theories, the theory of evolution was the result of the work of many different scientists working in different disciplines over a period of time.

A scientific theory is an explanation inferred from multiple lines of evidence for some broad aspect of the natural world and is logical, testable, and predictive.

As new evidence comes to light, or new interpretations of existing data are proposed, theories may be revised and even change; however, they are not tenuous or speculative.

A scientific hypothesis is an inferred explanation of an observation or research finding; while more exploratory in nature than a theory, it is based on existing scientific knowledge.

A scientific law is an expression of a mathematical or descriptive relationship observed in nature.

Imagine yourself shopping in a grocery store with a good friend who happens to be a chemist. Struggling to choose between the many different types of tomatoes in front of you, you pick one up, turn to your friend, and ask her if she thinks the tomato is organic . Your friend simply chuckles and replies, "Of course it's organic!" without even looking at how the fruit was grown. Why the amused reaction? Your friend is highlighting a simple difference in vocabulary. To a chemist, the term organic refers to any compound in which hydrogen is bonded to carbon. Tomatoes (like all plants) are abundant in organic compounds – thus your friend's laughter. In modern agriculture, however, organic has come to mean food items grown or raised without the use of chemical fertilizers, pesticides, or other additives.

So who is correct? You both are. Both uses of the word are correct, though they mean different things in different contexts. There are, of course, lots of words that have more than one meaning (like bat , for example), but multiple meanings can be especially confusing when two meanings convey very different ideas and are specific to one field of study.

• Scientific theories

The term theory also has two meanings, and this double meaning often leads to confusion. In common language, the term theory generally refers to speculation or a hunch or guess. You might have a theory about why your favorite sports team isn't playing well, or who ate the last cookie from the cookie jar. But these theories do not fit the scientific use of the term. In science, a theory is a well-substantiated and comprehensive set of ideas that explains a phenomenon in nature. A scientific theory is based on large amounts of data and observations that have been collected over time. Scientific theories can be tested and refined by additional research , and they allow scientists to make predictions. Though you may be correct in your hunch, your cookie jar conjecture doesn't fit this more rigorous definition.

All scientific disciplines have well-established, fundamental theories . For example, atomic theory describes the nature of matter and is supported by multiple lines of evidence from the way substances behave and react in the world around us (see our series on Atomic Theory ). Plate tectonic theory describes the large scale movement of the outer layer of the Earth and is supported by evidence from studies about earthquakes , magnetic properties of the rocks that make up the seafloor , and the distribution of volcanoes on Earth (see our series on Plate Tectonic Theory ). The theory of evolution by natural selection , which describes the mechanism by which inherited traits that affect survivability or reproductive success can cause changes in living organisms over generations , is supported by extensive studies of DNA , fossils , and other types of scientific evidence (see our Charles Darwin series for more information). Each of these major theories guides and informs modern research in those fields, integrating a broad, comprehensive set of ideas.

So how are these fundamental theories developed, and why are they considered so well supported? Let's take a closer look at some of the data and research supporting the theory of natural selection to better see how a theory develops.

Comprehension Checkpoint

• The development of a scientific theory: Evolution and natural selection

The theory of evolution by natural selection is sometimes maligned as Charles Darwin 's speculation on the origin of modern life forms. However, evolutionary theory is not speculation. While Darwin is rightly credited with first articulating the theory of natural selection, his ideas built on more than a century of scientific research that came before him, and are supported by over a century and a half of research since.

• The Fixity Notion: Linnaeus

Figure 1: Cover of the 1760 edition of Systema Naturae .

Research about the origins and diversity of life proliferated in the 18th and 19th centuries. Carolus Linnaeus , a Swedish botanist and the father of modern taxonomy (see our module Taxonomy I for more information), was a devout Christian who believed in the concept of Fixity of Species , an idea based on the biblical story of creation. The Fixity of Species concept said that each species is based on an ideal form that has not changed over time. In the early stages of his career, Linnaeus traveled extensively and collected data on the structural similarities and differences between different species of plants. Noting that some very different plants had similar structures, he began to piece together his landmark work, Systema Naturae, in 1735 (Figure 1). In Systema , Linnaeus classified organisms into related groups based on similarities in their physical features. He developed a hierarchical classification system , even drawing relationships between seemingly disparate species (for example, humans, orangutans, and chimpanzees) based on the physical similarities that he observed between these organisms. Linnaeus did not explicitly discuss change in organisms or propose a reason for his hierarchy, but by grouping organisms based on physical characteristics, he suggested that species are related, unintentionally challenging the Fixity notion that each species is created in a unique, ideal form.

• The age of Earth: Leclerc and Hutton

Also in the early 1700s, Georges-Louis Leclerc, a French naturalist, and James Hutton , a Scottish geologist, began to develop new ideas about the age of the Earth. At the time, many people thought of the Earth as 6,000 years old, based on a strict interpretation of the events detailed in the Christian Old Testament by the influential Scottish Archbishop Ussher. By observing other planets and comets in the solar system , Leclerc hypothesized that Earth began as a hot, fiery ball of molten rock, mostly consisting of iron. Using the cooling rate of iron, Leclerc calculated that Earth must therefore be at least 70,000 years old in order to have reached its present temperature.

Hutton approached the same topic from a different perspective, gathering observations of the relationships between different rock formations and the rates of modern geological processes near his home in Scotland. He recognized that the relatively slow processes of erosion and sedimentation could not create all of the exposed rock layers in only a few thousand years (see our module The Rock Cycle ). Based on his extensive collection of data (just one of his many publications ran to 2,138 pages), Hutton suggested that the Earth was far older than human history – hundreds of millions of years old.

While we now know that both Leclerc and Hutton significantly underestimated the age of the Earth (by about 4 billion years), their work shattered long-held beliefs and opened a window into research on how life can change over these very long timescales.

• Fossil studies lead to the development of a theory of evolution: Cuvier

Figure 2: Illustration of an Indian elephant jaw and a mammoth jaw from Cuvier's 1796 paper.

With the age of Earth now extended by Leclerc and Hutton, more researchers began to turn their attention to studying past life. Fossils are the main way to study past life forms, and several key studies on fossils helped in the development of a theory of evolution . In 1795, Georges Cuvier began to work at the National Museum in Paris as a naturalist and anatomist. Through his work, Cuvier became interested in fossils found near Paris, which some claimed were the remains of the elephants that Hannibal rode over the Alps when he invaded Rome in 218 BCE . In studying both the fossils and living species , Cuvier documented different patterns in the dental structure and number of teeth between the fossils and modern elephants (Figure 2) (Horner, 1843). Based on these data , Cuvier hypothesized that the fossil remains were not left by Hannibal, but were from a distinct species of animal that once roamed through Europe and had gone extinct thousands of years earlier: the mammoth. The concept of species extinction had been discussed by a few individuals before Cuvier, but it was in direct opposition to the Fixity of Species concept – if every organism were based on a perfectly adapted, ideal form, how could any cease to exist? That would suggest it was no longer ideal.

While his work provided critical evidence of extinction , a key component of evolution , Cuvier was highly critical of the idea that species could change over time. As a result of his extensive studies of animal anatomy, Cuvier had developed a holistic view of organisms , stating that the

number, direction, and shape of the bones that compose each part of an animal's body are always in a necessary relation to all the other parts, in such a way that ... one can infer the whole from any one of them ...

In other words, Cuvier viewed each part of an organism as a unique, essential component of the whole organism. If one part were to change, he believed, the organism could not survive. His skepticism about the ability of organisms to change led him to criticize the whole idea of evolution , and his prominence in France as a scientist played a large role in discouraging the acceptance of the idea in the scientific community.

• Studies of invertebrates support a theory of change in species: Lamarck

Jean Baptiste Lamarck, a contemporary of Cuvier's at the National Museum in Paris, studied invertebrates like insects and worms. As Lamarck worked through the museum's large collection of invertebrates, he was impressed by the number and variety of organisms . He became convinced that organisms could, in fact, change through time, stating that

... time and favorable conditions are the two principal means which nature has employed in giving existence to all her productions. We know that for her time has no limit, and that consequently she always has it at her disposal.

This was a radical departure from both the fixity concept and Cuvier's ideas, and it built on the long timescale that geologists had recently established. Lamarck proposed that changes that occurred during an organism 's lifetime could be passed on to their offspring, suggesting, for example, that a body builder's muscles would be inherited by their children.

As it turned out, the mechanism by which Lamarck proposed that organisms change over time was wrong, and he is now often referred to disparagingly for his "inheritance of acquired characteristics" idea. Yet despite the fact that some of his ideas were discredited, Lamarck established a support for evolutionary theory that others would build on and improve.

• Rock layers as evidence for evolution: Smith

In the early 1800s, a British geologist and canal surveyor named William Smith added another component to the accumulating evidence for evolution . Smith observed that rock layers exposed in different parts of England bore similarities to one another: These layers (or strata) were arranged in a predictable order, and each layer contained distinct groups of fossils . From this series of observations , he developed a hypothesis that specific groups of animals followed one another in a definite sequence through Earth's history, and this sequence could be seen in the rock layers. Smith's hypothesis was based on his knowledge of geological principles , including the Law of Superposition.

The Law of Superposition states that sediments are deposited in a time sequence, with the oldest sediments deposited first, or at the bottom, and newer layers deposited on top. The concept was first expressed by the Persian scientist Avicenna in the 11th century, but was popularized by the Danish scientist Nicolas Steno in the 17th century. Note that the law does not state how sediments are deposited; it simply describes the relationship between the ages of deposited sediments.

Figure 3: Engraving from William Smith's 1815 monograph on identifying strata by fossils.

Smith backed up his hypothesis with extensive drawings of fossils uncovered during his research (Figure 3), thus allowing other scientists to confirm or dispute his findings. His hypothesis has, in fact, been confirmed by many other scientists and has come to be referred to as the Law of Faunal Succession. His work was critical to the formation of evolutionary theory as it not only confirmed Cuvier's work that organisms have gone extinct , but it also showed that the appearance of life does not date to the birth of the planet. Instead, the fossil record preserves a timeline of the appearance and disappearance of different organisms in the past, and in doing so offers evidence for change in organisms over time.

• The theory of evolution by natural selection: Darwin and Wallace

It was into this world that Charles Darwin entered: Linnaeus had developed a taxonomy of organisms based on their physical relationships, Leclerc and Hutton demonstrated that there was sufficient time in Earth's history for organisms to change, Cuvier showed that species of organisms have gone extinct , Lamarck proposed that organisms change over time, and Smith established a timeline of the appearance and disappearance of different organisms in the geological record .

Figure 4: Title page of the 1859 Murray edition of the Origin of Species by Charles Darwin.

Charles Darwin collected data during his work as a naturalist on the HMS Beagle starting in 1831. He took extensive notes on the geology of the places he visited; he made a major find of fossils of extinct animals in Patagonia and identified an extinct giant ground sloth named Megatherium . He experienced an earthquake in Chile that stranded beds of living mussels above water, where they would be preserved for years to come.

Perhaps most famously, he conducted extensive studies of animals on the Galápagos Islands, noting subtle differences in species of mockingbird, tortoise, and finch that were isolated on different islands with different environmental conditions. These subtle differences made the animals highly adapted to their environments .

This broad spectrum of data led Darwin to propose an idea about how organisms change "by means of natural selection" (Figure 4). But this idea was not based only on his work, it was also based on the accumulation of evidence and ideas of many others before him. Because his proposal encompassed and explained many different lines of evidence and previous work, they formed the basis of a new and robust scientific theory regarding change in organisms – the theory of evolution by natural selection .

Darwin's ideas were grounded in evidence and data so compelling that if he had not conceived them, someone else would have. In fact, someone else did. Between 1858 and 1859, Alfred Russel Wallace , a British naturalist, wrote a series of letters to Darwin that independently proposed natural selection as the means for evolutionary change. The letters were presented to the Linnean Society of London, a prominent scientific society at the time (see our module on Scientific Institutions and Societies ). This long chain of research highlights that theories are not just the work of one individual. At the same time, however, it often takes the insight and creativity of individuals to put together all of the pieces and propose a new theory . Both Darwin and Wallace were experienced naturalists who were familiar with the work of others. While all of the work leading up to 1830 contributed to the theory of evolution , Darwin's and Wallace's theory changed the way that future research was focused by presenting a comprehensive, well-substantiated set of ideas, thus becoming a fundamental theory of biological research.

• Expanding, testing, and refining scientific theories
• Genetics and evolution: Mendel and Dobzhansky

Since Darwin and Wallace first published their ideas, extensive research has tested and expanded the theory of evolution by natural selection . Darwin had no concept of genes or DNA or the mechanism by which characteristics were inherited within a species . A contemporary of Darwin's, the Austrian monk Gregor Mendel , first presented his own landmark study, Experiments in Plant Hybridization, in 1865 in which he provided the basic patterns of genetic inheritance , describing which characteristics (and evolutionary changes) can be passed on in organisms (see our Genetics I module for more information). Still, it wasn't until much later that a "gene" was defined as the heritable unit.

In 1937, the Ukrainian born geneticist Theodosius Dobzhansky published Genetics and the Origin of Species , a seminal work in which he described genes themselves and demonstrated that it is through mutations in genes that change occurs. The work defined evolution as "a change in the frequency of an allele within a gene pool" ( Dobzhansky, 1982 ). These studies and others in the field of genetics have added to Darwin's work, expanding the scope of the theory .

• Evolution under a microscope: Lenski

More recently, Dr. Richard Lenski, a scientist at Michigan State University, isolated a single Escherichia coli bacterium in 1989 as the first step of the longest running experimental test of evolutionary theory to date – a true test meant to replicate evolution and natural selection in the lab.

After the single microbe had multiplied, Lenski isolated the offspring into 12 different strains , each in their own glucose-supplied culture, predicting that the genetic make-up of each strain would change over time to become more adapted to their specific culture as predicted by evolutionary theory . These 12 lines have been nurtured for over 40,000 bacterial generations (luckily bacterial generations are much shorter than human generations) and exposed to different selective pressures such as heat , cold, antibiotics, and infection with other microorganisms. Lenski and colleagues have studied dozens of aspects of evolutionary theory with these genetically isolated populations . In 1999, they published a paper that demonstrated that random genetic mutations were common within the populations and highly diverse across different individual bacteria . However, "pivotal" mutations that are associated with beneficial changes in the group are shared by all descendants in a population and are much rarer than random mutations, as predicted by the theory of evolution by natural selection (Papadopoulos et al., 1999).

• Punctuated equilibrium: Gould and Eldredge

While established scientific theories like evolution have a wealth of research and evidence supporting them, this does not mean that they cannot be refined as new information or new perspectives on existing data become available. For example, in 1972, biologist Stephen Jay Gould and paleontologist Niles Eldredge took a fresh look at the existing data regarding the timing by which evolutionary change takes place. Gould and Eldredge did not set out to challenge the theory of evolution; rather they used it as a guiding principle and asked more specific questions to add detail and nuance to the theory. This is true of all theories in science: they provide a framework for additional research. At the time, many biologists viewed evolution as occurring gradually, causing small incremental changes in organisms at a relatively steady rate. The idea is referred to as phyletic gradualism , and is rooted in the geological concept of uniformitarianism . After reexamining the available data, Gould and Eldredge came to a different explanation, suggesting that evolution consists of long periods of stability that are punctuated by occasional instances of dramatic change – a process they called punctuated equilibrium .

Like Darwin before them, their proposal is rooted in evidence and research on evolutionary change, and has been supported by multiple lines of evidence. In fact, punctuated equilibrium is now considered its own theory in evolutionary biology. Punctuated equilibrium is not as broad of a theory as natural selection . In science, some theories are broad and overarching of many concepts, such as the theory of evolution by natural selection; others focus on concepts at a smaller, or more targeted, scale such as punctuated equilibrium. And punctuated equilibrium does not challenge or weaken the concept of natural selection; rather, it represents a change in our understanding of the timing by which change occurs in organisms , and a theory within a theory. The theory of evolution by natural selection now includes both gradualism and punctuated equilibrium to describe the rate at which change proceeds.

• Hypotheses and laws: Other scientific concepts

One of the challenges in understanding scientific terms like theory is that there is not a precise definition even within the scientific community. Some scientists debate over whether certain proposals merit designation as a hypothesis or theory , and others mistakenly use the terms interchangeably. But there are differences in these terms. A hypothesis is a proposed explanation for an observable phenomenon. Hypotheses , just like theories , are based on observations from research . For example, LeClerc did not hypothesize that Earth had cooled from a molten ball of iron as a random guess; rather, he developed this hypothesis based on his observations of information from meteorites.

A scientist often proposes a hypothesis before research confirms it as a way of predicting the outcome of study to help better define the parameters of the research. LeClerc's hypothesis allowed him to use known parameters (the cooling rate of iron) to do additional work. A key component of a formal scientific hypothesis is that it is testable and falsifiable. For example, when Richard Lenski first isolated his 12 strains of bacteria , he likely hypothesized that random mutations would cause differences to appear within a period of time in the different strains of bacteria. But when a hypothesis is generated in science, a scientist will also make an alternative hypothesis , an explanation that explains a study if the data do not support the original hypothesis. If the different strains of bacteria in Lenski's work did not diverge over the indicated period of time, perhaps the rate of mutation was slower than first thought.

So you might ask, if theories are so well supported, do they eventually become laws? The answer is no – not because they aren't well-supported, but because theories and laws are two very different things. Laws describe phenomena, often mathematically. Theories, however, explain phenomena. For example, in 1687 Isaac Newton proposed a Theory of Gravitation, describing gravity as a force of attraction between two objects. As part of this theory, Newton developed a Law of Universal Gravitation that explains how this force operates. This law states that the force of gravity between two objects is inversely proportional to the square of the distance between those objects. Newton 's Law does not explain why this is true, but it describes how gravity functions (see our Gravity: Newtonian Relationships module for more detail). In 1916, Albert Einstein developed his theory of general relativity to explain the mechanism by which gravity has its effect. Einstein's work challenges Newton's theory, and has been found after extensive testing and research to more accurately describe the phenomenon of gravity. While Einstein's work has replaced Newton's as the dominant explanation of gravity in modern science, Newton's Law of Universal Gravitation is still used as it reasonably (and more simply) describes the force of gravity under many conditions. Similarly, the Law of Faunal Succession developed by William Smith does not explain why organisms follow each other in distinct, predictable ways in the rock layers, but it accurately describes the phenomenon.

Theories, hypotheses , and laws drive scientific progress

Theories, hypotheses , and laws are not simply important components of science, they drive scientific progress. For example, evolutionary biology now stands as a distinct field of science that focuses on the origins and descent of species . Geologists now rely on plate tectonics as a conceptual model and guiding theory when they are studying processes at work in Earth's crust . And physicists refer to atomic theory when they are predicting the existence of subatomic particles yet to be discovered. This does not mean that science is "finished," or that all of the important theories have been discovered already. Like evolution , progress in science happens both gradually and in short, dramatic bursts. Both types of progress are critical for creating a robust knowledge base with data as the foundation and scientific theories giving structure to that knowledge.

Table of Contents

• Theories, hypotheses, and laws drive scientific progress

Activate glossary term highlighting to easily identify key terms within the module. Once highlighted, you can click on these terms to view their definitions.

Activate NGSS annotations to easily identify NGSS standards within the module. Once highlighted, you can click on them to view these standards.

• Table of Contents
• Random Entry
• Chronological
• Editorial Information
• About the SEP
• Editorial Board
• How to Cite the SEP
• Special Characters
• Advanced Tools
• Support the SEP
• PDFs for SEP Friends
• Make a Donation
• SEPIA for Libraries
• Entry Contents

Bibliography

Academic tools.

• Friends PDF Preview
• Author and Citation Info
• Back to Top

The Structure of Scientific Theories

Scientific inquiry has led to immense explanatory and technological successes, partly as a result of the pervasiveness of scientific theories. Relativity theory, evolutionary theory, and plate tectonics were, and continue to be, wildly successful families of theories within physics, biology, and geology. Other powerful theory clusters inhabit comparatively recent disciplines such as cognitive science, climate science, molecular biology, microeconomics, and Geographic Information Science (GIS). Effective scientific theories magnify understanding, help supply legitimate explanations, and assist in formulating predictions. Moving from their knowledge-producing representational functions to their interventional roles (Hacking 1983), theories are integral to building technologies used within consumer, industrial, and scientific milieus.

This entry explores the structure of scientific theories from the perspective of the Syntactic, Semantic, and Pragmatic Views. Each of these answers questions such as the following in unique ways. What is the best characterization of the composition and function of scientific theory? How is theory linked with world? Which philosophical tools can and should be employed in describing and reconstructing scientific theory? Is an understanding of practice and application necessary for a comprehension of the core structure of a scientific theory? Finally, and most generally, how are these three views ultimately related?

1.1 Syntactic, Semantic, and Pragmatic Views: The Basics

1.2 two examples: newtonian mechanics and population genetics, 2.1 theory structure per the syntactic view, 2.2 a running example: newtonian mechanics, 2.3 interpreting theory structure per the syntactic view, 2.4 taking stock: syntactic view, 3.1 theory structure per the semantic view, 3.2 a running example: newtonian mechanics, 3.3 interpreting theory structure per the semantic view, 3.4 taking stock: semantic view, 4.1 theory structure per the pragmatic view, 4.2 a running example: newtonian mechanics, 4.3 interpreting theory structure per the pragmatic view, 4.4 taking stock: pragmatic view, 5. population genetics, 6. conclusion, other internet resources, related entries, 1. introduction.

In philosophy, three families of perspectives on scientific theory are operative: the Syntactic View , the Semantic View , and the Pragmatic View. Savage distills these philosophical perspectives thus:

The syntactic view that a theory is an axiomatized collection of sentences has been challenged by the semantic view that a theory is a collection of nonlinguistic models, and both are challenged by the view that a theory is an amorphous entity consisting perhaps of sentences and models, but just as importantly of exemplars, problems, standards, skills, practices and tendencies. (Savage 1990, vii–viii)

Mormann (2007) characterizes the Syntactic and Semantic Views in similar terms, and is among the first to use the term “Pragmatic View” to capture the third view (137). The three views are baptized via a trichotomy from linguistics deriving from the work of Charles Morris, following Charles S. Peirce. In a classic exposition, the logical positivist Carnap writes:

If in an investigation explicit reference is made to the speaker, or, to put it in more general terms, to the user of a language, then we assign it to the field of pragmatics . (Whether in this case reference to designata is made or not makes no difference for this classification.) If we abstract from the user of the language and analyze only the expressions and their designata, we are in the field of semantics . And if, finally, we abstract from the designata also and analyze only the relations between the expressions, we are in (logical) syntax . The whole science of language, consisting of the three parts mentioned, is called semiotic . (1942, 9; see also Carnap 1939, 3–5, 16)

To summarize, syntax concerns grammar and abstract structures; semantics investigates meaning and representation; and pragmatics explores use. Importantly, while no view is oblivious to the syntax, semantics, or pragmatics of theory, the baptism of each is a product of how one of the three aspects of language is perceived to be dominant: theory as syntactic logical reconstruction (Syntactic View); theory as semantically meaningful mathematical modeling (Semantic View); or theory structure as complex and as closely tied to theory pragmatics, i.e., function and context (Pragmatic View). Each of these philosophical perspectives on scientific theory will be reviewed in this entry. Their relations will be briefly considered in the Conclusion.

It will be helpful to pare each perspective down to its essence. Each endorses a substantive thesis about the structure of scientific theories.

For the Syntactic View, the structure of a scientific theory is its reconstruction in terms of sentences cast in a metamathematical language. Metamathematics is the axiomatic machinery for building clear foundations of mathematics, and includes predicate logic, set theory, and model theory (e.g., Zach 2009; Hacking 2014). A central question of the Syntactic View is: in which logical language should we recast scientific theory?

Some defenders of the Semantic View keep important aspects of this reconstructive agenda, moving the metamathematical apparatus from predicate logic to set theory. Other advocates of the Semantic View insist that the structure of scientific theory is solely mathematical. They argue that we should remain at the mathematical level, rather than move up (or down) a level, into foundations of mathematics. A central question for the Semantic View is: which mathematical models are actually used in science?

Finally, for the Pragmatic View, scientific theory is internally and externally complex. Mathematical components, while often present, are neither necessary nor sufficient for characterizing the core structure of scientific theories. Theory also consists of a rich variety of nonformal components (e.g., analogies and natural kinds). Thus, the Pragmatic View argues, a proper analysis of the grammar (syntax) and meaning (semantics) of theory must pay heed to scientific theory complexity, as well as to the multifarious assumptions, purposes, values, and practices informing theory. A central question the Pragmatic View poses is: which theory components and which modes of theorizing are present in scientific theories found across a variety of disciplines?

In adopting a descriptive perspective on the structure of scientific theories, each view also deploys, at least implicitly, a prescriptive characterization of our central topic. In other words, postulating that scientific theory is \(X\) (e.g., \(X\) = a set-theoretic structure, as per Suppes 1960, 1962, 1967, 1968, 2002) also implies that what is not \(X\) (or could not be recast as \(X\)) is not (or could not possibly be) a scientific theory, and would not help us in providing scientific understanding, explanation, prediction, and intervention. For the Syntactic View, what is not (or cannot be) reconstructed axiomatically is not theoretical, while for the Semantic View, what is not (or cannot be) modeled mathematically is not theoretical. In contrast, in part due to its pluralism about what a scientific theory actually (and possibly) is, and because it interprets theory structure as distributed in practices, the Pragmatic View resists the definitional and normative terms set by the other two views. As a result, the Pragmatic View ultimately reforms the very concepts of “theory” and “theory structure.”

This encyclopedia entry will be organized as follows. After presenting this piece’s two sustained examples, immediately below, the three views are reviewed in as many substantive sections. Each section starts with a brief overview before characterizing that perspective’s account of theory structure. Newtonian mechanics is used as a running example within each section. The interpretation of theory structure—viz., how theory “hooks up” with phenomena, experiment, and the world—is also reviewed in each section. In the final section of this entry, we turn to population genetics and an analysis of the Hardy-Weinberg Principle (HWP) to compare and contrast each view. The Conclusion suggests, and remains non-committal about, three kinds of relations among the views: identity , combat , and complementarity . Theory is not a single, static entity that we are seeing from three different perspectives, as we might represent the Earth using three distinct mathematical map projections. Rather, theory itself changes as a consequence of perspective adopted.

Two examples will be used to illustrate differences between the three views: Newtonian mechanics and population genetics. While relativity theory is the preferred theory of the Syntactic View, Newtonian mechanics is more straightforward. Somewhat permissively construed, the theory of Newtonian mechanics employs the basic conceptual machinery of inertial reference frames, centers of mass, Newton’s laws of motion, etc., to describe the dynamics and kinematics of, among other phenomena, point masses acting vis-à-vis gravitational forces (e.g. the solar system) or with respect to forces involved in collisions (e.g., pool balls on a pool table; a closed container filled with gas). Newtonian mechanics is explored in each section.

Population genetics investigates the genetic composition of populations of natural and domesticated species, including the dynamics and causes of changes in gene frequencies in such populations (for overviews, see Lloyd 1994 [1988]; Gould 2002; Pigliucci and Müller 2010; Okasha 2012). Population genetics emerged as a discipline with the early 20 th century work of R.A. Fisher, Sewall Wright, and J.B.S. Haldane, who synthesized Darwinian evolutionary theory and Mendelian genetics. One important part of population genetic theory is the Hardy-Weinberg Principle. HWP is a null model mathematically stating that gene frequencies remain unchanged across generations when there is no selection, migration, random genetic drift, or other evolutionary forces acting in a given population. HWP peppers early chapters of many introductory textbooks (e.g., Crow and Kimura 1970; Hartl and Clark 1989; Bergstrom and Dugatkin 2012). We return to HWP in Section 5 and here merely state questions each view might ask about population genetics.

The Syntactic View focuses on questions regarding the highest axiomatic level of population genetics (e.g., Williams 1970, 1973; Van Valen 1976; Lewis 1980; Tuomi 1981, 1992). Examples of such queries are:

• What would be the most convenient metamathematical axiomatization of evolutionary processes (e.g., natural selection, drift, migration, speciation, competition)? In which formal language(s) would and could such axiomatizations be articulated (e.g., first-order predicate logic, set theory, and category theory)?
• Which single grammars could contain a variety of deep evolutionary principles and concepts, such as HWP, “heritability,” and “competitive exclusion”?
• Which formal and methodological tools would permit a smooth flow from the metamathematical axiomatization to the mathematical theory of population genetics?

Investigations of the axiomatized rational reconstruction of theory shed light on the power and promises, and weaknesses and incompleteness, of the highest-level theoretical edifice of population genetics.

Secondly, the Semantic View primarily examines questions regarding the mathematical structure of population genetics (Lewontin 1974, Beatty 1981; López Beltrán 1987; Thompson 1989, 2007; Lloyd 1994 [1988]). Very generally, this exploration involves the following questions:

• What is the form and content of the directly presented class of mathematical models of evolutionary theory (e.g., HWP)? How could and should we organize the cluster of mathematical models (sensu Levins 1966) of population genetics?
• Which additional models (e.g., diagrammatic, narrative, scale) might be used to enrich our understanding of evolutionary theory?
• What are the relations among theoretical mathematical models, data models, and experimental models? How does theory explain and shape data? How do the data constrain and confirm theory?

The main subject of investigation is mathematical structure, rather than metamathematics or even alternative model types or modeling methods.

Finally, the Pragmatic View asks about the internal complexity of population genetic theory, as well as about the development and context of population genetics. In so doing, it inquires into how purposes and values have influenced the theoretical structure of evolutionary theory, selecting and shaping current population genetics from a wide variety of possible alternative theoretical articulations. The following questions about the structure of population genetic theory might be here addressed:

• What role did R.A. Fisher’s interest in animal husbandry, and his tenure at Rothamsted Experimental Station, play in shaping his influential methodologies of Analysis of Variance (ANOVA) and experimental design involving randomization, blocking, and factorial designs?
• How did the development of computers and computational practices, statistical techniques, and the molecularization of genetics, shape theory and theorizing in population genetics, especially from the 1980s to today?
• How might normative context surrounding the concept of “race” impact the way concepts such as “heritability” and “lineage,” or principles such as HWP, are deployed in population genetics?

As when studying an organism, the structure of theory cannot be understood independently of its history and function.

2. The Syntactic View

According to the Syntactic View, which emerged mainly out of work of the Vienna Circle and Logical Empiricism (see Coffa 1991; Friedman 1999; Creath 2014; Uebel 2014), philosophy most generally practiced is, and should be, the study of the logic of natural science, or Wissenschaftslogik (Carnap 1937, 1966; Hempel 1966). Robust and clear logical languages allow us to axiomatically reconstruct theories, which—by the Syntacticists’ definition—are sets of sentences in a given logical domain language (e.g., Campbell 1920, 122; Hempel 1958, 46; cf. Carnap 1967 [1928], §156, “Theses about the Constructional System”). Domain languages include “the language of physics, the language of anthropology” (Carnap 1966, 58).

This view has been variously baptized as the Received View (Putnam 1962; Hempel 1970), the Syntactic Approach (van Fraassen 1970, 1989), the Syntactic View (Wessels 1976), the Standard Conception (Hempel 1970), the Orthodox View (Feigl 1970), the Statement View (Moulines 1976, 2002; Stegmüller 1976), the Axiomatic Approach (van Fraassen 1989), and the Once Received View (Craver 2002). For historical reasons, and because of the linguistic trichotomy discussed above, the “Syntactic View” shall be the name of choice in this entry.

Some conceptual taxonomy is required in order to understand the logical framework of the structure of scientific theories for the Syntactic View. We shall distinguish terms , sentences , and languages (see Table 1).

2.1.1 Terms

Building upwards from the bottom, let us start with the three kinds of terms or vocabularies contained in a scientific language: theoretical, logical, and observational. Examples of theoretical terms are “molecule,” “atom,” “proton,” and “protein,” and perhaps even macro-level objects and properties such as “proletariat” and “aggregate demand.” Theoretical terms or concepts can be classificatory (e.g., “cat” or “proton”), comparative (e.g., “warmer”), or quantitative (e.g., “temperature”) (Hempel 1952; Carnap 1966, Chapter 5). Moreover, theoretical terms are “theoretical constructs” introduced “jointly” as a “theoretical system” (Hempel 1952, 32). Logical terms include quantifiers (e.g., \(\forall, \exists\)) and connectives (e.g., \(\wedge, \rightarrow\)). Predicates such as “hard,” “blue,” and “hot,” and relations such as “to the left of” and “smoother than,” are observational terms.

2.1.2 Sentences

Terms can be strung together into three kinds of sentences: theoretical, correspondence, and observational. \(T_S\) is the set of theoretical sentences that are the axioms, theorems, and laws of the theory. Theoretical sentences include the laws of Newtonian mechanics and of the Kinetic Theory of Gases, all suitably axiomatized (e.g., Carnap 1966; Hempel 1966). Primitive theoretical sentences (e.g., axioms) can be distinguished from derivative theoretical sentences (e.g., theorems; see Reichenbach 1969 [1924]; Hempel 1958; Feigl 1970). \(C_S\) is the set of correspondence sentences tying theoretical sentences to observable phenomena or “to a ‘piece of reality’” (Reichenbach 1969 [1924], 8; cf. Einstein 1934, 1936 [1936], 351). To simplify, they provide the theoretical syntax with an interpretation and an application, i.e., a semantics. Suitably axiomatized version of the following sentences provide semantics to Boyle’s law, \(PV = nRT\): “\(V\) in Boyle’s law is equivalent to the measurable volume \(xyz\) of a physical container such as a glass cube that is \(x\), \(y\), and \(z\) centimeters in length, width, and height, and in which the gas measured is contained” and “\(T\) in Boyle’s law is equivalent to the temperature indicated on a reliable thermometer or other relevant measuring device properly calibrated, attached to the physical system, and read.” Carnap (1987 [1932], 466) presents two examples of observational sentences, \(O_S\): “Here (in a laboratory on the surface of the earth) is a pendulum of such and such a kind,” and “the length of the pendulum is 245.3 cm.” Importantly, theoretical sentences can only contain theoretical and logical terms; correspondence sentences involve all three kinds of terms; and observational sentences comprise only logical and observational terms.

2.1.3 Languages

The total domain language of science consists of two languages: the theoretical language, \(L_T\), and the observational language, \(L_O\) (e.g., Hempel 1966, Chapter 6; Carnap 1966, Chapter 23; the index entry for “Language,” of Feigl, Scriven, and Maxwell 1958, 548 has three subheadings: “observation,” “theoretical,” and “ordinary”). The theoretical language includes theoretical vocabulary, while the observational language involves observational terms. Both languages contain logical terms. Finally, the theoretical language includes, and is constrained by, the logical calculus, Calc , of the axiomatic system adopted (e.g., Hempel 1958, 46; Suppe 1977, 50-53). This calculus specifies sentence grammaticality as well as appropriate deductive and non-ampliative inference rules (e.g., modus ponens) pertinent to, especially, theoretical sentences. Calc can itself be written in theoretical sentences.

2.1.4 Theory Structure, in General

Table 1 summarizes the Syntactic View’s account of theory structure:

The salient divide is between theory and observation. Building on Table 1, there are three different levels of scientific knowledge, according to the Syntactic View:

\(\{T_S\} =\) The uninterpreted syntactic system of the scientific theory. \(\{T_S, C_S\} =\) The scientific theory structure of a particular domain (e.g., physics, anthropology). \(\{T_S,C_S,O_S\} =\) All of the science of a particular domain.

Scientific theory is thus taken to be a syntactically formulated set of theoretical sentences (axioms, theorems, and laws) together with their interpretation via correspondence sentences. As we have seen, theoretical sentences and correspondence sentences are cleanly distinct, even if both are included in the structure of a scientific theory.

Open questions remain. Is the observation language a sub-language of the theoretical language, or are they both parts of a fuller language including all the vocabulary? Can the theoretical vocabulary or language be eliminated in favor of a purely observational vocabulary or language? Are there other ways of carving up kinds of languages? First, a “dialectical opposition” between “logic and experience,” “form and content,” “constitutive principles and empirical laws,” and “‘from above’… [and] ‘from below’” pervades the work of the syntacticists (Friedman 1999, 34, 63). Whether syntacticists believe that a synthesis or unification of this general opposition between the theoretical (i.e., logic, form) and the observational (i.e., experience, content) is desirable remains a topic of ongoing discussion. Regarding the second question, Hempel 1958 deflates what he calls “the theoretician’s dilemma”—i.e., the putative reduction without remainder of theoretical concepts and sentences to observational concepts and sentences. Finally, other language divisions are possible, as Carnap 1937 argues (see Friedman 1999, Chapter 7). Returning to the main thread of this section, the distinction toolkit of theoretical and observational terms, sentences, and languages (Table 1) permit the syntacticists to render theoretical structure sharply, thereby aiming at the reconstructive “logic of science” ( Wissenschafstlogik ) that they so desire.

Reichenbach 1969 [1924] stands as a canonical attempt by a central developer of the Syntactic View of axiomatizing a physical theory, viz., relativity theory (cf. Friedman 1983, 1999; see also Reichenbach 1965 [1920]). For the purposes of this encyclopedia entry, it is preferable to turn to another syntactic axiomatization effort. In axiomatizing Newtonian mechanics, the mid-20 th century mathematical logician Hans Hermes spent significant energy defining the concept of mass (Hermes 1938, 1959; Jammer 1961). More precisely, he defines the theoretical concept of “mass ratio” of two particles colliding inelastically in an inertial reference frame \(S\). Here is his full definition of mass ratio (1959, 287):

One paraphrase of this definition is, “‘the mass of \(x\) is α times that of \(x_0\)’ is equivalent to ‘there exists a system \(S\), an instant \(t\), momentary mass points \(y\) and \(y_0\), and initial velocities \(v\) and \(v_0\), such that \(y\) and \(y_0\) are genidentical, respectively, with \(x\) and \(x_0\); the joined mass points move with a velocity of 0 with respect to frame \(S\) immediately upon colliding at time \(t\); and \(y\) and \(y_0\) have determinate velocities \(v\) and \(v_0\) before the collision in the ratio α, which could also be 1 if \(x\) and \(x_0\) are themselves genidentical.’” Hermes employs the notion of “genidentical” to describe the relation between two temporal sections of a given particle’s world line (Jammer 1961, 113). Set aside the worry that two distinct particles cannot be genidentical per Hermes’ definition, though they can have identical properties. In short, this definition is syntactically complete and is written in first-order predicate logic, as are the other axioms and definitions in Hermes (1938, 1959). Correspondence rules connecting a postulated mass \(x\) with an actual mass were not articulated by Hermes.

The link between theory structure and the world, under the Syntactic View, is contained in the theory itself: \(C_S\), the set of correspondence rules. The term “correspondence rules” (Margenau 1950; Nagel 1961, 97–105; Carnap 1966, Chapter 24) has a variety of near-synonyms:

• Dictionary (Campbell 1920)
• Operational rules (Bridgman 1927)
• Coordinative definitions (Reichenbach 1969 [1924], 1938)
• Reduction sentences (Carnap 1936/1937; Hempel 1952)
• Correspondence postulates (Carnap 1963)
• Bridge principles (Hempel 1966; Kitcher 1984)
• Reduction functions (Schaffner 1969, 1976)
• Bridge laws (Sarkar 1998)

Important differences among these terms cannot be mapped out here. However, in order to better understand correspondence rules, two of their functions will be considered: (i) theory interpretation (Carnap, Hempel) and (ii) theory reduction (Nagel, Schaffner). The dominant perspective on correspondence rules is that they interpret theoretical terms. Unlike “mathematical theories,” the axiomatic system of physics “cannot have… a splendid isolation from the world” (Carnap 1966, 237). Instead, scientific theories require observational interpretation through correspondence rules. Even so, surplus meaning always remains in the theoretical structure (Hempel 1958, 87; Carnap 1966). Second, correspondence rules are seen as necessary for inter-theoretic reduction (van Riel and Van Gulick 2014). For instance, they connect observation terms such as “temperature” in phenomenological thermodynamics (the reduced theory) to theoretical concepts such as “mean kinetic energy” in statistical mechanics (the reducing theory). Correspondence rules unleash the reducing theory’s epistemic power. Notably, Nagel (1961, Chapter 11; 1979) and Schaffner (1969, 1976, 1993) allow for multiple kinds of correspondence rules, between terms of either vocabulary, in the reducing and the reduced theory (cf. Callender 1999; Winther 2009; Dizadji-Bahmani, Frigg, and Hartmann 2010). Correspondence rules are a core part of the structure of scientific theories and serve as glue between theory and observation.

Finally, while they are not part of the theory structure, and although we saw some examples above, observation sentences are worth briefly reviewing. Correspondence rules attach to the content of observational sentences. Observational sentences were analyzed as (i) protocol sentences or Protokollsätze (e.g., Schlick 1934; Carnap 1987 [1932], 1937, cf. 1963; Neurath 1983 [1932]), and as (ii) experimental laws (e.g., Campbell 1920; Nagel 1961; Carnap 1966; cf. Duhem 1954 [1906]). Although constrained by Calc , the grammar of these sentences is determined primarily by the order of nature, as it were. In general, syntacticists do not consider methods of data acquisition, experiment, and measurement to be philosophically interesting. In contrast, the confirmation relation between (collected) data and theory, especially as developed in inductive logic (e.g., Reichenbach 1938, 1978; Carnap 1962 [1950], 1952), as well as questions about the conventionality, grammaticality, foundationalism, atomism, and content of sense-data and synthetic statements, are considered philosophically important (e.g., Carnap 1987 [1932], 1937, 1966; Neurath 1983 [1932]; Reichenbach 1951; Schlick 1925 [1918], 1934; for contemporary commentary, see, e.g., Creath 1987, 2014; Rutte 1991; Friedman 1999).

To summarize, the Syntactic View holds that there are three kinds of terms or vocabularies: logical, theoretical, and observational; three kinds of sentences: \(T_S\), \(C_S\), and \(O_S\); and two languages: \(L_T\) and \(L_O\). Moreover, the structure of scientific theories could be analyzed using the logical tools of metamathematics. The goal is to reconstruct the logic of science, viz. to articulate an axiomatic system.

Interestingly, this perspective has able and active defenders today, who discuss constitutive and axiomatized principles of the historical “relativized a priori” (Friedman 2001, cf. 2013), argue that “the semantic view, if plausible, is syntactic” (Halvorson 2013), and explore “logicism” for, and in, the philosophy of science (Demopulous 2003, 2013; van Benthem 2012). Furthermore, for purposes of the syntactic reconstruction of scientific theories, some continue espousing—or perhaps plea for the resurrection of—predicate logic (e.g., Lutz 2012, 2014), while other contemporary syntacticists (e.g., Halvorson 2012, 2013, 2019) endorse more recently developed metamathematical and mathematical equipment, such as category theory, which “turns out to be a kind of universal mathematical language like set theory” (Awodey 2006, 2; see Eilenberg and MacLane 1945). Importantly, Halvorson (2019) urges that interlocutors adopt “structured” rather than “flat” views of theories. For the case of the syntactic view this would mean that rather than accept the usual formulation that a theory is a set of sentences, “… [we] might say that a theory consists of both sentences and inferential relations between those sentences” (Halvorson 2019, 277–8). Classical syntacticists such as Rudolf Carnap (Friedman 1999, 2011; Carus 2007; Blatti and Lapointe 2016; Koellner ms. in Other Internet Resources) and Joseph Henry Woodger (Nicholson and Gawne 2014) have recently received increasing attention.

3. The Semantic View

An overarching theme of the Semantic View is that analyzing theory structure requires employing mathematical tools rather than predicate logic. After all, defining scientific concepts within a specific formal language makes any axiomatizing effort dependent on the choice, nature, and idiosyncrasies of that narrowly-defined language. For instance, Suppes understands first-order predicate logic, with its “linguistic” rather than “set-theoretical” entities, as “utterly impractical” for the formalization of “theories with more complicated structures like probability theory” (Suppes 1957, 232, 248–9; cf. Suppes 2002). Van Fraassen, another influential defender of the Semantic View, believes that the logical apparatus of the Syntactic View “had moved us mille milles de toute habitation scientifique , isolated in our own abstract dreams” (van Fraassen 1989, 225). Indeed, what would the appropriate logical language for specific mathematical structures be, especially when such structures could be reconstructed in a variety of formal languages? Why should we imprison mathematics and mathematical scientific theory in syntactically defined language(s) when we could, instead, directly investigate the mathematical objects, relations, and functions of scientific theory?

Consistent with the combat strategy (discussed in the Conclusion), here is a list of grievances against the Syntactic View discussed at length in the work of some semanticists.

• First-Order Predicate Logic Objection . Theoretical structure is intrinsically and invariably tied to the specific choice of a language, \(L_T\), expressed in first-order predicate logic. This places heavy explanatory and representational responsibility on relatively inflexible and limited languages.
• Theory Individuation Objection . Since theories are individuated by their linguistic formulations, every change in high-level syntactic formulations will bring forth a distinct theory. This produces a reductio: if \(T_1 = p \rightarrow q\) and \(T_2 = \neg p \vee q\) then \(T_1\) and \(T_2\), though logically equivalent, have different syntactic formulations and would be distinct theories.
• Theoretical/Observational Languages Objection . Drawing the theoretical/observational distinction in terms of language is inappropriate, as observability pertains to entities rather than to concepts.
• Unintended Models Objection . There is no clear way of distinguishing between intended and unintended models for syntactically characterized theories (e.g., the Löwenheim-Skolem theorem, Bays 2014).
• Confused Correspondence Rules Objection . Correspondence rules are a confused medley of direct meaning relationships between terms and world, means of inter-theoretic reduction, causal relationship claims, and manners of theoretical concept testing.
• Trivially True yet Non-Useful Objection . Presenting scientific theory in a limited axiomatic system, while clearly syntactically correct, is neither useful nor honest, since scientific theories are mathematical structures.
• Practice and History Ignored Objection . Syntactic approaches do not pay sufficient attention to the actual practice and history of scientific theorizing and experimenting.

What, then, does the Semantic View propose to put in the Syntactic View’s place?

Even a minimal description of the Semantic View must acknowledge two distinct strategies of characterizing and comprehending theory structure: the state-space and the set-/model-theoretic approaches.

3.1.1 The State-Space Approach

The state-space approach emphasizes the mathematical models of actual science, and draws a clear line between mathematics and metamathematics. The structure of a scientific theory is identified with the “class,” “family” or “cluster” of mathematical models constituting it, rather than with any metamathematical axioms “yoked to a particular syntax” (van Fraassen 1989, 366). Under this analysis, “the correct tool for philosophy of science is mathematics, not metamathematics”—this is Suppes’ slogan, per van Fraassen (1989, 221; 1980, 65). In particular, a state space or phase space is an \(N\)-dimensional space, where each of the relevant variables of a theory correspond to a single dimension and each point in that space represents a possible state of a real system. An actual, real system can take on, and change, states according to different kinds of laws, viz., laws of succession determining possible trajectories through that space (e.g., Newtonian kinematic laws); laws of co-existence specifying the permitted regions of the total space (e.g., Boyle’s law); and laws of interaction combining multiple laws of succession or co-existence, or both (e.g., population genetic models combining laws of succession for selection and genetic drift, Wright 1969; Lloyd 1994 [1988]; Rice 2004; Clatterbuck, Sober, and Lewontin 2013). Different models of a given theory will share some dimensions of their state space while differing in others. Such models will also partially overlap in laws (for further discussion of state spaces, laws, and models pertinent to the Semantic View, see Suppe 1977, 224–8; Lloyd 1994, Chapter 2; Nolte 2010; Weisberg 2013, 26–9).

Historically, the state-space approach emerged from work by Evert Beth, John von Neumann, and Hermann Weyl, and has important parallels with Przełęcki (1969) and Dalla Chiara Scabia and Toraldo di Francia (1973) (on the history of the approach see: Suppe 1977; van Fraassen 1980, 65–67; Lorenzano 2013; advocates of the approach include: Beatty 1981; Giere 1988, 2004; Giere, Bickle, and Mauldin 2006; Lloyd 1983, 1994 [1988], 2013 In Press; Suppe 1977, 1989; Thompson, 1989, 2007; van Fraassen 1980, 1989, 2008; for alternative early analyses of models see, e.g., Braithwaite 1962; Hesse 1966, 1967). Interestingly, van Fraassen (1967, 1970) provides a potential reconstruction of state spaces via an analysis of “semi-interpreted languages.” Weisberg (2013), building on many insights from Giere’s work, presents a broad view of modeling that includes mathematical structures that are “trajectories in state spaces” (29), but also permits concrete objects and computational structures such as algorithms to be deemed models. Lorenzano (2013) calls Giere’s (and, by extension, Weisberg’s and even Godfrey-Smith’s 2006) approach “model-based,” separating it out from the state-space approach. A more fine-grained classification of the state-space approach is desirable, particularly if we wish to understand important lessons stemming from the Pragmatic View of Theories, as we shall see below.

As an example of a state-space analysis of modeling, consider a capsule traveling in outer space. An empirically and dynamically adequate mathematical model of the capsule’s behavior would capture the position of the capsule (i.e., three dimensions of the formal state space), as well as the velocity and acceleration vectors for each of the three standard spatial dimensions (i.e., six more dimensions in the formal state space). If the mass were unknown or permitted to vary, we would have to add one more dimension. Possible and actual trajectories of our capsule, with known mass, within this abstract 9-dimensional state space could be inferred via Newtonian dynamical laws of motion (example in Lewontin 1974, 6–8; consult Suppe 1989, 4). Importantly, under the state-space approach, the interesting philosophical work of characterizing theory structure (e.g., as classes of models), theory meaning (e.g., data models mapped to theoretical models), and theory function (e.g., explaining and predicting) happens at the level of mathematical models.

3.1.2 The Set-/Model-Theoretic Approach

Lurking in the background of the state-space conception is the fact that mathematics actually includes set theory and model theory—i.e., mathematical logic. Indeed, according to some interlocutors, “metamathematics is part of mathematics” (Halvorson 2012, 204). Historically, a set-/model-theoretic approach emerged from Tarski’s work and was extensively articulated by Suppes and his associates (van Fraassen 1980, 67). Set theory is a general language for formalizing mathematical structures as collections—i.e., sets—of abstract objects (which can themselves be relations or functions; see Krivine 2013 [1971]). Model theory investigates the relations between, on the one hand, the formal axioms, theorems, and laws of a particular theory and, on the other hand, the mathematical structures—the models—that provide an interpretation of that theory, or put differently, that make the theory’s axioms, theorems, and laws true (Hodges 1997, Chapter 2; Jones 2005). Interestingly, model theory often uses set theory (e.g., Marker 2002); set theory can, in turn, be extended to link axiomatic theories and semantic models via “set-theoretical predicates” (e.g., Suppes 1957, 2002). Finally, there are certain hybrids of these two branches of mathematical logic, including “partial structures” (e.g., da Costa and French 1990, 2003; Bueno 1997; French 2017; French and Ladyman 1999, 2003; Vickers 2009; Bueno, French, and Ladyman 2012). Lorenzano (2013) provides a more complex taxonomy of the intellectual landscape of the Semantic View, including a discussion of Structuralism, a kind of set-/model-theoretic perspective. Structuralism involves theses about “theory-nets,” theory-relative theoretical vs. non-theoretical terms, a diversity of intra- and inter-theoretic laws with different degrees of generality, a typology of inter-theoretic relations, and a rich account of correspondence rules in scientific practice (see Moulines 2002; Pereda 2013; Schmidt 2014; Ladyman 2014). On the whole, the set-/model-theoretic approach of the Semantic View insists on the inseparability of metamathematics and mathematics. In preferring to characterize a theory axiomatically in terms of its intension rather than its extension, it shares the Syntactic View’s aims of reconstructive axiomatization (e.g., Sneed 1979; Stegmüller 1979; Frigg and Votsis 2011; Halvorson 2013, 2019; Lutz 2012, 2014, 2017).

An example will help motivate the relation between theory and model. Two qualifications are required: (i) we return to a more standard set-/model-theoretic illustration below, viz., McKinsey, Sugar, and Suppes’ (1953) axiomatization of particle mechanics, and (ii) this motivational example is not from the heartland of model theory (see Hodges 2013). Following van Fraassen’s intuitive case of “seven-point geometry” (1980, 41–44; 1989, 218–220), also known as “the Fano plane” we see how a particular geometric figure, the model , interprets and makes true a set of axioms and theorems, the theory . In topology and geometry there is rich background theory regarding how to close Euclidean planes and spaces to make finite geometries by, for instance, eliminating parallel lines. Consider the axioms of a projective plane:

• For any two points, exactly one line lies on both.
• For any two lines, exactly one point lies on both.
• There exists a set of four points such that no line has more than two of them.

A figure of a geometric model that makes this theory true is:

This is the smallest geometrical model satisfying the three axioms of the projective plane theory. Indeed, this example fits van Fraassen’s succinct characterization of the theory-model relation:

A model is called a model of a theory exactly if the theory is entirely true if considered with respect to this model alone. (Figuratively: the theory would be true if this model was the whole world.) (1989, 218)

That is, if the entire universe consisted solely of these seven points and seven lines, the projective plane theory would be true. Of course, our universe is bigger. Because Euclidean geometry includes parallel lines, the Fano plane is not a model of Euclidean geometry. Even so, by drawing the plane, we have shown it to be isomorphic to parts of the Euclidean plane. In other words, the Fano plane has been embedded in a Euclidean plane. Below we return to the concepts of embedding and isomorphism, but this example shall suffice for now to indicate how a geometric model can provide a semantics for the axioms of a theory.

In short, for the Semantic View the structure of a scientific theory is its class of mathematical models. According to some advocates of this view, the family of models can itself be axiomatized, with those very models (or other models) serving as axiom truth-makers.

Returning to our running example, consider Suppes’ 1957 model-theoretic articulation of particle mechanics, which builds on his 1953 article with J.C.C. McKinsey and A.C. Sugar. Under this analysis, there is a domain of set-theoretic objects of the form \(\{ P, T, s, m, f, g \}\), where \(P\) and \(T\) are themselves sets, \(s\) and \(g\) are binary functions, \(m\) is a unary and \(f\) a ternary function. \(P\) is the set of particles; \(T\) is a set of real numbers measuring elapsed times; \(s(p, t)\) is the position of particle \(p\) at time \(t\); \(m(p)\) is the mass of particle \(p\); \(f(p, q, t)\) is the force particle \(q\) exerts on \(p\) at time \(t\); and \(g(p, t)\) is the total resultant force (by all other particles) on \(p\) at time \(t\). Suppes and his collaborators defined seven axioms—three kinematical and four dynamical—characterizing Newtonian particle mechanics (see also Simon 1954, 1970). Such axioms include Newton’s third law reconstructed in set-theoretic formulation thus (Suppes 1957, 294):

Importantly, the set-theoretic objects are found in more than one of the axioms of the theory, and Newton’s calculus is reconstructed in a novel, set-theoretic form. Set-theoretic predicates such as “is a binary relation” and “is a function” are also involved in axiomatizing particle mechanics (Suppes 1957, 249). Once these axioms are made explicit, their models can be specified and these can, in turn, be applied to actual systems, thereby providing a semantics for the axioms (e.g., as described in Section 3.3.1 below). A particular system satisfying these seven axioms is a particle mechanics system. (For an example of Newtonian mechanics from the state-space approach, recall the space capsule of Section 3.1.1.)

How is the theory structure, described in Section 3.1, applied to empirical phenomena? How do we connect theory and data via observation and experimental and measuring techniques? The Semantic View distinguishes theory individuation from both theory-phenomena and theory-world relations. Three types of analysis of theory interpretation are worth investigating: (i) a hierarchy of models (e.g., Suppes; Suppe), (ii) similarity (e.g., Giere; Weisberg), and (iii) isomorphism (e.g., van Fraassen; French and Ladyman).

3.3.1 A Hierarchy of Models

One way of analyzing theory structure interpretation is through a series of models falling under the highest-level axiomatizations. This series has been called “a hierarchy of models,” though it need not be considered a nested hierarchy. These models include models of theory, models of experiment, and models of data (Suppes 1962, 2002). Here is a summary of important parts of the hierarchy (Suppes 1962, Table 1, 259; cf. Giere 2010, Figure 1, 270):

• Axioms of Theory . Axioms define set-theoretic predicates, and constitute the core structure of scientific theories, as reviewed in Section 3.1.2.
• Models of Theory. “Representation Theorems,” permit us “to discover if an interesting subset of models for the theory may be found such that any model for the theory is isomorphic to some member of this subset” (Suppes 1957, 263). Representation theorem methodology can be extended (i) down the hierarchy, both to models of experiment and models of data, and (ii) from isomorphism to homomorphism (Suppes 2002, p. 57 ff.; Suppe 2000; Cartwright 2008).
• Models of Experiment . Criteria of experimental design motivate choices for how to set up and analyze experiments. There are complex mappings between models of experiment thus specified, and (i) models of theory, (ii) theories of measurement, and (iii) models of data.
• Models of Data . In building models of data, phenomena are organized with respect to statistical goodness-of-fit tests and parameter estimation, in the context of models of theory. Choices about which parameters to represent must be made.

The temptation to place phenomena at the bottom of the hierarchy must be resisted because phenomena permeate all levels. Indeed, the “class of phenomena” pertinent to a scientific theory is its “intended scope” (Suppe 1977, 223; Weisberg 2013, 40). Furthermore, this temptation raises fundamental questions about scientific representation: “there is the more profound issue of the relationship between the lower most representation in the hierarchy—the data model perhaps—and reality itself, but of course this is hardly something that the semantic approach alone can be expected to address” (French and Ladyman 1999, 113; cf. van Fraassen 2008, 257–258, “The ‘link’ to reality”). Borrowing from David Chalmers, the “hard problem” of philosophy of science remains connecting abstract structures to concrete phenomena, data, and world.

3.3.2 Similarity

The similarity analysis of theory interpretation combines semantic and pragmatic dimensions (Giere 1988, 2004, 2010; Giere, Bickle, and Mauldin 2006; Weisberg 2013). According to Giere, interpretation is mediated by theoretical hypotheses positing representational relations between a model and relevant parts of the world. Such relations may be stated as follows:

Here \(S\) is a scientist, research group or community, \(W\) is a part of the world, and \(X\) is, broadly speaking, any one of a variety of models (Giere 2004, 743, 747, 2010). Model-world similarity judgments are conventional and intentional:

Note that I am not saying that the model itself represents an aspect of the world because it is similar to that aspect. …Anything is similar to anything else in countless respects, but not anything represents anything else. It is not the model that is doing the representing; it is the scientist using the model who is doing the representing. (2004, 747)

Relatedly, Weisberg (2013) draws upon Tversky (1977) to develop a similarity metric for model interpretation (equation 8.10, 148). This metric combines (i) model-target semantics (90–97), and (ii) the pragmatics of “context, conceptualization of the target, and the theoretical goals of the scientist” (149). Giere and Weisberg thus endorse an abundance of adequate mapping relations between a given model and the world. From this diversity, scientists and scientific communities must select particularly useful similarity relationships for contextual modeling purposes. Because of semantic pluralism and irreducible intentionality, this similarity analysis of theory interpretation cannot be accommodated within a hierarchy of models approach, interpreted as a neat model nesting based on pre-given semantic relations among models at different levels.

3.3.3 Isomorphism

The term “isomorphism” is a composite of the Greek words for “equal” and “shape” or “form.” Indeed, in mathematics, isomorphism is a perfect one-to-one, bijective mapping between two structures or sets. Figure (2) literally and figuratively captures the term:

Especially in set theory, category theory, algebra, and topology, there are various kinds of “-morphisms,” viz., of mapping relations between two structures or models. Figure (3) indicates five different kinds of homomorphism, arranged in a Venn diagram.

Although philosophers have focused on isomorphism, other morphisms such as monomorphism (i.e., an injective homomorphism where some elements in the co-domain remain unmapped from the domain) might also be interesting to investigate, especially for embedding data (i.e., the domain) into rich theoretical structures (i.e., the co-domain). To complete the visualization above, an epimorphism is a surjective homomorphism, and an endomorphism is a mapping from a structure to itself, although it need not be a symmetrical—i.e., invertible—mapping, which would be an automorph.

Perhaps the most avid supporter of isomorphism and embedding as the way to understand theory interpretation is van Fraassen. In a nutshell, if we distinguish (i) theoretical models, (ii) “empirical substructures” (van Fraassen 1980, 64, 1989, 227; alternatively: “surface models” 2008, 168), and (iii) “observable phenomena” (1989, 227, 2008, 168), then, van Fraassen argues, theory interpretation is a relation of isomorphism between observable phenomena and empirical substructures, which are themselves isomorphic with one or more theoretical models. Moreover, if a relation of isomorphism holds between \(X\) and a richer \(Y\), we say that we have embedded \(X\) in \(Y\). For instance, with respect to the seven-point geometry above (Figure 1), van Fraassen contends that isomorphism gives embeddability, and that the relation of isomorphism “is important because it is also the exact relation a phenomenon bears to some model or theory, if that theory is empirically adequate” (1989, 219–20; this kind of statement seems to be simultaneously descriptive and prescriptive about scientific representation, see Section 1.1 above). In The Scientific Image he is even clearer about fleshing out the empirical adequacy of a theory (with its theoretical models) in terms of isomorphism between “appearances” (i.e., “the structures which can be described in experimental and measurement reports,” 1980, 64, italics removed) and empirical substructures. Speaking metaphorically,

the phenomena are, from a theoretical point of view, small, arbitrary, and chaotic—even nasty, brutish, and short…—but can be understood as embeddable in beautifully simple but much larger mathematical models. (2008, 247; see also van Fraassen 1981, 666 and 1989, 230)

Interestingly, and as a defender of an identity strategy (see Conclusion), Friedman also appeals to embedding and subsumption relations between theory and phenomena in his analyses of theory interpretation (Friedman 1981, 1983). Bueno, da Costa, French, and Ladyman also employ embedding and (partial) isomorphism in the empirical interpretation of partial structures (Bueno 1997; Bueno, French, and Ladyman 2012; da Costa and French 1990, 2003; French 2017; French and Ladyman 1997, 1999, 2003; Ladyman 2004). Suárez discusses complexities in van Fraassen’s analyses of scientific representation and theory interpretation (Suárez 1999, 2011). On the one hand, representation is structural identity between the theoretical and the empirical. On the other hand, “There is no representation except in the sense that some things are used, made, or taken, to represent some things as thus or so” (van Fraassen 2008, 23, italics removed). The reader interested in learning how van Fraassen simultaneously endorses acontextually structural and contextually pragmatic aspects of representation and interpretation should refer to van Fraassen’s (2008) investigations of maps and “the essential indexical.” [To complement the structure vs. function distinction, see van Fraassen 2008, 309–311 for a structure (“structural relations”) vs. history (“the intellectual processes that lead to those models”) distinction; cf. Ladyman et al. 2011] In all of this, embedding via isomorphism is a clear contender for theory interpretation under the Semantic View.

In short, committing to either a state-space or a set-/model-theoretic view on theory structure does not imply any particular perspective on theory interpretation (e.g., hierarchy of models, similarity, embedding). Instead, commitments to the former are logically and actually separable from positions on the latter (e.g., Suppes and Suppe endorse different accounts of theory structure, but share an understanding of theory interpretation in terms of a hierarchy of models). The Semantic View is alive and well as a family of analyses of theory structure, and continues to be developed in interesting ways both in its state-space and set-/model-theoretic approaches.

4. The Pragmatic View

The Pragmatic View recognizes that a number of assumptions about scientific theory seem to be shared by the Syntactic and Semantic Views. Both perspectives agree, very roughly, that theory is (1) explicit, (2) mathematical, (3) abstract, (4) systematic, (5) readily individualizable, (6) distinct from data and experiment, and (7) highly explanatory and predictive (see Flyvbjerg 2001, 38–39; cf. Dreyfus 1986). The Pragmatic View imagines the structure of scientific theories rather differently, arguing for a variety of theses:

• Limitations . Idealized theory structure might be too weak to ground the predictive and explanatory work syntacticists and semanticists expect of it (e.g., Cartwright 1983, 1999a, b, 2019; Morgan and Morrison 1999; Suárez and Cartwright 2008).
• Pluralism . Theory structure is plural and complex both in the sense of internal variegation and of existing in many types. In other words, there is an internal pluralism of theory (and model) components (e.g., mathematical concepts, metaphors, analogies, ontological assumptions, values, natural kinds and classifications, distinctions, and policy views, e.g., Kuhn 1970; Boumans 1999), as well as a broad external pluralism of different types of theory (and models) operative in science (e.g., mechanistic, historical, and mathematical models, e.g., Hacking 2009, Longino 2013). Indeed, it may be better to speak of the structures of scientific theories, in the double-plural.
• Nonformal aspects. The internal pluralism of theory structure (thesis #2) includes many nonformal aspects deserving attention. That is, many components of theory structure, such as metaphors, analogies, values, and policy views have a non-mathematical and “informal” nature, and they lie implicit or hidden (e.g., Bailer-Jones 2002; Craver 2002; Contessa 2006; Morgan 2012). Interestingly, the common understanding of “formal,” which identifies formalization with mathematization, may itself be a conceptual straightjacket; the term could be broadened to include “diagram abstraction” and “principle extraction” (e.g., Griesemer 2013, who explicitly endorses what he also calls a “Pragmatic View of Theories”).
• Function. Characterizations of the nature and dynamics of theory structure should pay attention to the user as well as to purposes and values (e.g., Apostel 1960; Minsky 1965; Morrison 2007; Winther 2012a).
• Practice . Theory structure is continuous with practice and “the experimental life,” making it difficult to neatly dichotomize theory and practice (e.g., Hacking 1983, 2009; Shapin and Schaffer 1985; Galison 1987, 1988, 1997; Suárez and Cartwright 2008, Cartwright 2019).

These are core commitments of the Pragmatic View.

It is important to note at the outset that the Pragmatic View takes its name from the linguistic trichotomy discussed above, in the Introduction. This perspective need not imply commitment to, or association with, American Pragmatism (e.g. the work of Charles S. Peirce, William James, or John Dewey; cf. Hookway 2013; Richardson 2002). For instance, Hacking (2007a) distinguishes his pragmatic attitudes from the school of Pragmatism. He maps out alternative historical routes of influence, in general and on him, vis-à-vis fallibilism (via Imre Lakatos, Karl Popper; Hacking 2007a, §1), historically conditioned truthfulness (via Bernard Williams; Hacking 2007a, §3), and realism as intervening (via Francis Everitt, Melissa Franklin; Hacking 2007a, §4). To borrow a term from phylogenetics, the Pragmatic View is “polyphyletic.” The components of its analytical framework have multiple, independent origins, some of which circumnavigate American Pragmatism.

With this qualification and the five theses above in mind, let us now turn to the Pragmatic View’s analysis of theory structure and theory interpretation.

We should distinguish two strands of the Pragmatic View: the Pragmatic View of Models and a proper Pragmatic View of Theories .

4.1.1 The Pragmatic View of Models

Nancy Cartwright’s How the Laws of Physics Lie crystallized the Pragmatic View of Models. Under Cartwright’s analysis, models are the appropriate level of investigation for philosophers trying to understand science. She argues for significant limitations of theory (thesis #1), claiming that laws of nature are rarely true, and are epistemically weak. Theory as a collection of laws cannot, therefore, support the many kinds of inferences and explanations that we have come to expect it to license. Cartwright urges us to turn to models and modeling, which are central to scientific practice. Moreover, models “lie”—figuratively and literally—between theory and the world (cf. Derman 2011). That is, “to explain a phenomenon is to find a model that fits it into the basic framework of the theory and that thus allows us to derive analogues for the messy and complicated phenomenological laws which are true of it.” A plurality of models exist, and models “serve a variety of purposes” (Cartwright 1983, 152; cf. Suppes 1978). Cartwright is interested in the practices and purposes of scientific models, and asks us to focus on models rather than theories.

Cartwright’s insights into model pluralism and model practices stand as a significant contribution of “The Stanford School” (cf. Cat 2014), and were further developed by the “models as mediators” group, with participants at LSE, University of Amsterdam, and University of Toronto (Morgan and Morrison 1999; Chang 2011; cf. Martínez 2003). This group insisted on the internal pluralism of model components (thesis #2). According to Morgan and Morrison, building a model involves “fitting together… bits which come from disparate sources,” including “stories” (Morgan and Morrison 1999, 15). Boumans (1999) writes:

model building is like baking a cake without a recipe. The ingredients are theoretical ideas, policy views, mathematisations of the cycle, metaphors and empirical facts. (67) Mathematical moulding is shaping the ingredients in such a mathematical form that integration is possible… (90)

In an instructive diagram, Boumans suggests that a variety of factors besides theory and data feed into a model: metaphors, analogies, policy views, stylised facts, mathematical techniques, and mathematical concepts (93). The full range of components involved in a model will likely vary according to discipline, and with respect to explanations and interventions sought (e.g., analogies but not policy views will be important in theoretical physics). In short, model building involves a complex variety of internal nonformal aspects, some of which are implicit (theses #2 and #3).

As one example of a nonformal component of model construction and model structure, consider metaphors and analogies (e.g., Bailer-Jones 2002). Geary (2011) states the “simplest equation” of metaphor thus: “\(X = Y\)” (8, following Aristotle: “Metaphor consists in giving the thing a name that belongs to something else… ,” Poetics , 1457b). The line between metaphor and analogy in science is blurry. Some interlocutors synonymize them (e.g., Hoffman 1980; Brown 2003), others reduce one to the other (analogy is a form of metaphor, Geary 2011; metaphor is a kind of analogy, Gentner 1982, 2003), and yet others bracket one to focus on the other (e.g., Oppenheimer 1956 sets aside metaphor). One way to distinguish them is to reserve “analogy” for concrete comparisons, with clearly identifiable and demarcated source and target domains, and with specific histories, and use “metaphor” for much broader and indeterminate comparisons, with diffuse trajectories across discourses. Analogies include the “lines of force” of electricity and magnetism (Maxwell and Faraday), the atom as a planetary system (Rutherford and Bohr), the benzene ring as a snake biting its own tail (Kekulé), Darwin’s “natural selection” and “entangled bank,” and behavioral “drives” (Tinbergen) (e.g., Hesse 1966, 1967; Bartha 2010). Examples of metaphor are genetic information, superorganism, and networks (e.g., Keller 1995). More could be said about other informal model components, but this discussion of metaphors and analogies shall suffice to hint at how models do not merely lie between theory and world. Models express a rich internal pluralism (see also de Chadarevian and Hopwood 2004; Morgan 2012).

Model complexity can also be seen in the external plurality of models (thesis #2). Not all models are mathematical, or even ideally recast as mathematical. Non-formalized (i.e., non–state-space, non-set-/model-theoretic) models such as physical, diagrammatic, material, historical, “remnant,” and fictional models are ubiquitous across the sciences (e.g., Frigg and Hartmann 2012; for the biological sciences, see Hull 1975; Beatty 1980; Griesemer 1990, 1991 a, b, 2013; Downes 1992; Richards 1992; Winther 2006a; Leonelli 2008; Weisberg 2013). Moreover, computer simulations differ in important respects from more standard analytical mathematical models (e.g., Smith 1996; Winsberg 2010; Weisberg 2013). According to some (e.g., Griesemer 2013; Downes 1992; Godfrey-Smith 2006; Thomson-Jones 2012), this diversity belies claims by semanticists that models can always be cast “into set theoretic terms” (Lloyd 2013 In Press), are “always a mathematical structure” (van Fraassen 1970, 327), or that “formalisation of a theory is an abstract representation of the theory expressed in a formal deductive framework… in first-order predicate logic with identity, in set theory, in matrix algebra and indeed, any branch of mathematics...” (Thompson 2007, 485–6). Even so, internal pluralism has been interpreted as supporting a “deflationary semantic view,” which is minimally committed to the perspective that “model construction is an important part of scientific theorizing” (Downes 1992, 151). Given the formal and mathematical framework of the Semantic View (see above), however, the broad plurality of kinds of models seems to properly belong under a Pragmatic View of Models.

4.1.2 The Pragmatic View of Theories

Interestingly, while critiquing the Syntactic and Semantic Views on most matters, the Pragmatic View of Models construed theory, the process of theorizing, and the structure of scientific theories, according to terms set by the two earlier views. For instance, Cartwright tends to conceive of theory as explicit, mathematical, abstract, and so forth (see the first paragraph of Section 4). She always resisted “the traditional syntactic/semantic view of theory” for its “vending machine” view, in which a theory is a deductive and automated machine that upon receiving empirical input “gurgitates” and then “drops out the sought-for representation” (1999a, 184–5). Rather than reform Syntactic and Semantic accounts of theory and theory structure, however, she invites us, as we just saw, to think of science as modeling, “with theory as one small component” (Cartwright, Shomar, and Suárez 1995, 138; Suárez and Cartwright 2008). Many have followed her. Kitcher’s predilection is also to accept the terms of the Syntactic and Semantic Views. For instance, he defines theories as “axiomatic deductive systems” (1993, 93). In a strategy complementary to Cartwright’s modeling turn, Kitcher encourages us to focus on practice, including practices of modeling and even practices of theorizing. In The Advancement of Science , practice is analyzed as a 7-tuple, with the following highly abbreviated components: (i) a language; (ii) questions; (iii) statements (pictures, diagrams); (iv) explanatory patterns; (v) standard examples; (vi) paradigms of experimentation and observation, plus instruments and tools; and (vii) methodology (Kitcher 1993, 74). Scientific practice is also center stage for those singing the praises of “the experimental life” (e.g., Hacking 1983; Shapin and Schaffer 1985; Galison 1987), and those highlighting the cognitive grounds of science (e.g., Giere 1988; Martínez 2014) and science’s social and normative context (e.g., Kitcher 1993, 2001; Longino 1995, 2002; Ziman 2000; cf. Simon 1957). Indeed, the modeling and practice turns in the philosophy of science were reasonable reactions to the power of axiomatic reconstructive and mathematical modeling analyses of the structure of scientific theories.

Yet, a Pragmatic View of Theories is also afoot, one resisting orthodox characterizations of theory often embraced, at least early on, by Pragmatic View philosophers such as Cartwright, Hacking, Kitcher, and Longino. For instance, Craver (2002) accepts both the Syntactic and Semantic Views, which he humorously and not inaccurately calls “the Once Received View” and the “Model Model View.” But he also observes:

While these analyses have advanced our understanding of some formal aspects of theories and their uses, they have neglected or obscured those aspects dependent upon nonformal patterns in theories. Progress can be made in understanding scientific theories by attending to their diverse nonformal patterns and by identifying the axes along which such patterns might differ from one another. (55)

Craver then turns to mechanistic theory as a third theory type (and a third philosophical analysis of theory structure) that highlights nonformal patterns:

Different types of mechanisms can be distinguished on the basis of recurrent patterns in their organization. Mechanisms may be organized in series, in parallel, or in cycles. They may contain branches and joins, and they often include feedback and feedforward subcomponents. (71)

Consistent with theses #2 and #3 of the Pragmatic View, we must recognize the internal pluralism of theories as including nonformal components. Some of these are used to represent organizational and compositional relations of complex systems (Craver 2007; Wimsatt 2007; Winther 2011; Walsh 2015). While mechanistic analyses such as Craver’s may not wish to follow every aspect of the Pragmatic View of Theories, there are important and deep resonances between the two.

In a review of da Costa and French (2003), Contessa (2006) writes:

Philosophers of science are increasingly realizing that the differences between the syntactic and the semantic view are less significant than semanticists would have it and that, ultimately, neither is a suitable framework within which to think about scientific theories and models. The crucial divide in philosophy of science, I think, is not the one between advocates of the syntactic view and advocates of the semantic view, but the one between those who think that philosophy of science needs a formal framework or other and those who think otherwise. (376)

Again, we are invited to develop a non-formal framework of science and presumably also of scientific theory. (Halvorson 2012, 203 takes Contessa 2006 to task for advocating “informal philosophy of science.”) Moreover, in asking “what should the content of a given theory be taken to be on a given occasion?”, Vickers (2009) answers:

It seems clear that, in addition to theories being vague objects in the way that ‘heaps’ of sand are, there will be fundamentally different ways to put together theoretical assumptions depending on the particular investigation one is undertaking. For example, sometimes it will be more appropriate to focus on the assumptions which were used by scientists, rather than the ones that were believed to be true. (247, footnote suppressed)

A Pragmatic View of Theories helps make explicit nonformal internal components of theory structure.

Key early defenders of the modeling and practice turns have also recently begun to envision theory in a way distinct from the terms set by the Syntactic and Semantic Views. Suárez and Cartwright (2008) extend and distribute theory by arguing that “What we know ‘theoretically’ is recorded in a vast number of places in a vast number of different ways—not just in words and formulae but in machines, techniques, experiments and applications as well” (79). And while her influence lies primarily in the modeling turn, even in characterizing the “vending machine” view, Cartwright calls for a “reasonable philosophical account of theories” that is “much more textured, and… much more laborious” than that adopted by the Syntactic and Semantic Views (1999a, 185). The theory-data and theory-world axes need to be rethought. In her 2019 book on “artful modeling”, Cartwright emphasizes the importance of know-how and creativity in scientific practice, and “praise[s] engineers and cooks and inventors, as well as experimental physicists like Millikan and Melissa Franklin” (Cartwright 2019, 76). Kitcher wishes to transform talk of theories into discussion of “significance graphs” (2001, 78 ff.). These are network diagrams illustrating which (and how) questions are considered significant in the context of particular scientific communities and norms (cf. Brown 2010). Consistently with a Pragmatic View of Theories, Morrison (2007) reconsiders and reforms canonical conceptualizations of “theory.” Finally, Longino (2013) proposes an archaeology of assumptions behind and under different research programs and theories of human behavior such as neurobiological, molecular behavioral genetic, and social-environmental approaches (e.g., Oyama 2000). For instance, two shared or recurring assumptions across programs and theories are:

(1) that the approach in question has methods of measuring both the behavioral outcome that is the object of investigation and the factors whose association with it are the topic of investigation and (2) that the resulting measurements are exportable beyond the confines of the approach within which they are made. (Longino 2013, 117)

A Pragmatic View of Theories expands the notion of theory to include nonformal aspects, which surely must include elements from Boumans’ list above (e.g., metaphors, analogies, policy views), as well as more standard components such as ontological assumptions (e.g., Kuhn 1970; Levins and Lewontin 1985; Winther 2006b), natural kinds (e.g., Hacking 2007b), and conditions of application or scope (e.g., Longino 2013).

In addition to exploring internal theory diversity and in parallel with plurality of modeling, a Pragmatic View of Theories could also explore pluralism of modes of theorizing, and of philosophically analyzing theoretical structure (thesis #2). Craver (2002) provides a start in this direction in that he accepts three kinds of scientific theory and of philosophical analysis of scientific theory. A more synoptic view of the broader pragmatic context in which theories are embedded can be found in the literature on different “styles” of scientific reasoning and theorizing (e.g., Crombie 1994, 1996; Vicedo 1995; Pickstone 2000; Davidson 2001; Hacking 2002, 2009; Winther 2012b; Elwick 2007; Mancosu 2010). While there is no univocal or dominant classification of styles, two lessons are important. First, a rough consensus exists that theoretical investigations of especially historical, mechanistic, and mathematical structures and relations will involve different styles. Second, each style integrates theoretical products and theorizing processes in unique ways, thus inviting an irreducible pragmatic methodological pluralism in our philosophical analysis of the structure of scientific theories. For instance, the structure of theories of mechanisms in molecular biology or neuroscience involves flow charts, and is distinct from the structure of theories of historical processes and patterns as found in systematics and phylogenetics, which involves phylogenetic trees. As Crombie suggests, we need a “comparative historical anthropology of thinking.” (1996, 71; see Hacking 2009) Mathematical theory hardly remains regnant. It gives way to a pluralism of theory forms and theory processes. Indeed, even mathematical theorizing is a pluralistic motley, as Hacking (2014) argues. Although a “deflationary” Semantic View could account for pluralism of theory forms, the Pragmatic View of Theories, drawing on styles, is required to do justice to the immense variety of theorizing processes, and of philosophical accounts of theory and theory structure.

Finally, outstanding work remains in sorting out the philosophical utility of a variety of proposed units in addition to styles, such as Kuhn’s (1970) paradigms, Lakatos’ (1980) research programmes, Laudan’s (1977) research traditions, and Holton’s (1988) themata. A rational comparative historical anthropology of both theorizing and philosophical analyses of theorizing remains mostly unmapped (cf. Matheson and Dallmann 2014). Such a comparative meta-philosophical analysis should also address Davidson’s (1974) worries about “conceptual schemes” and Popper’s (1996 [1976]) critique of “the myth of the framework” (see Hacking 2002; Godfrey-Smith 2003).

Cartwright has done much to develop a Pragmatic View. Start by considering Newton’s second law:

Here \(F\) is the resultant force on a mass \(m\), and \(a\) is the net acceleration of \(m\); both \(F\) and \(a\) are vectors. This law is considered a “general” (Cartwright 1999a, 187) law expressed with “abstract quantities” (Cartwright 1999b, 249). Newton’s second law can be complemented with other laws, such as (i) Hooke’s law for an ideal spring:

Here \(k\) is the force constant of the spring, and \(x\) the distance along the x-axis from the equilibrium position, and (ii) Coulomb’s law modeling the force between two charged particles:

Here \(K\) is Coulomb’s electrical constant, \(q\) and \(q'\) are the charges of the two objects, and \(r\) the distance between the two objects. The picture Cartwright draws for us is that Newton’s, Hooke’s, and Coulomb’s laws are abstract, leaving out many details. They can be used to derive mathematical models of concrete systems. For instance, by combining (1) and (2), the law of gravitation (a “fundamental” law, Cartwright 1983, 58–59), other source laws, and various simplifying assumptions, we might create a model for the orbit of Mars, treating the Sun and Mars as a 2-body system, ignoring the other planets, asteroids, and Mars’ moons. Indeed, the Solar System is a powerful “nomological machine” (Cartwright 1999a, 50–53), which “is a fixed (enough) arrangement of components, or factors, with stable (enough) capacities that in the right sort of stable (enough) environment will, with repeated operation, give rise to the kind of regular behaviour that we represent in our scientific laws” (Cartwright 1999a, 50). Importantly, most natural systems are complex and irregular, and cannot be neatly characterized as nomological machines. For these cases, abstract laws “run out” (Cartwright 1983) and are rarely smoothly “deidealised” (Suárez 1999). In general, abstract laws predict and explain only within a given domain of application, and only under ideal conditions. More concrete laws or models are not directly deduced from them (e.g., Suárez 1999, Suárez and Cartwright 2008), and they can rarely be combined to form effective “super-laws” (Cartwright 1983, 70–73). In short, the move from (1) and (2) or from (1) and (3) to appropriate phenomenological models, is not fully specified by either abstract law pairing. Indeed, Cartwright developed her notion of “capacities” to discuss how “the principles of physics” “are far better rendered as claims about capacities, capacities that can be assembled and reassembled in different nomological machines, unending in their variety, to give rise to different laws” (1999a, 52). Articulating concrete models requires integrating a mix of mathematical and nonformal components. Laws (1), (2), and (3) remain only one component, among many, of the models useful for, e.g., exploring the behavior of the Solar System, balls on a pool table, or the behavior of charges in electrical fields.

Shifting examples but not philosophical research program, Suárez and Cartwright (2008) explains how analogies such as superconductors as diamagnets (as opposed to ferromagnets) were an integral part of the mathematical model of superconductivity developed by Fritz and Heinz London in the 1930s (63; cf. London and London 1935). Suárez and Cartwright gladly accept that this model “is uncontroversially grounded in classic electromagnetic theory” (64). However, contra Semantic View Structuralists such as Bueno, da Costa, French, and Ladyman, they view nonformal aspects as essential to practices of scientific modeling and theorizing: “The analogy [of diamagnets] helps us to understand how the Londons work with their model… which assumptions they add and which not… a formal reconstruction of the model on its own cannot help us to understand that” (69). In short, the running example of Newtonian mechanics, in conjunction with a glimpse into the use of analogies in mathematical modeling, illustrates the Pragmatic View’s account of theory syntax: theory is constituted by a plurality of formal and informal components.

As we have explored throughout this section, models and theories have informal internal components, and there are distinct modes of modeling and theorizing. Because of the Pragmatic View’s attention to practice, function, and application, distinguishing structure from interpretation is more difficult here than under the Syntactic and Semantic Views. Any synchronic analysis of the structure of models and theories must respect intentional diachronic processes of interpreting and using, as we shall now see.

Regarding the import of function in models and theories (thesis #4), already the Belgian philosopher of science Apostel defined modeling thus: “Let then \(R(S,P,M,T)\) indicate the main variables of the modelling relationship. The subject \(S\) takes, in view of the purpose \(P\), the entity \(M\) as a model for the prototype \(T\)” (1960, 128, see also Apostel 1970). Purposes took center-stage in his article title: “Towards the Formal Study of Models in the Non-Formal Sciences.” MIT Artificial Intelligence trailblazer Minsky also provided a pragmatic analysis:

We use the term “model” in the following sense: To an observer \(B\), an object \(A^*\) is a model of an object \(A\) to the extent that \(B\) can use \(A^*\) to answer questions that interest him about \(A\). The model relation is inherently ternary. Any attempt to suppress the role of the intentions of the investigator \(B\) leads to circular definitions or to ambiguities about “essential features” and the like. (1965, 45)

This account is thoroughly intentionalist and anti-essentialist. That is, mapping relations between model and world are left open and overdetermined. Specifying the relevant relations depends on contextual factors such as questions asked, and the kinds of similarities and isomorphisms deemed to be of interest. The appropriate relations are selected from an infinite (or, at least, near-infinite) variety of possible relations (e.g., Rosenblueth and Wiener 1945; Lowry 1965).

Regarding practice (thesis #5), in addition to ample work on the experimental life mentioned above, consider a small example. A full understanding of the content and structure of the London brothers’ model of superconductivity requires attention to informal aspects such as analogies. Even London and London (1935) state in the summary of their paper that “the current [”in a supraconductor“] is characterized as a kind of diamagnetic volume current” (88). They too saw the diamagnetic analogy as central to their theoretical practices. Criteria and practices of theory confirmation also differ from the ones typical of the Syntactic and Semantic Views. While predictive and explanatory power as well as empirical adequacy remain important, the Pragmatic View also insists on a variety of other justificatory criteria, including pragmatic virtues (sensu Kuhn 1977; Longino 1995) such as fruitfulness and utility. In a nutshell, the Pragmatic View argues that scientific theory structure is deeply shaped and constrained by functions and practices, and that theory can be interpreted and applied validly according to many different criteria.

The analytical framework of the Pragmatic View remains under construction. The emphasis is on internal diversity, and on the external pluralism of models and theories, of modeling and theorizing, and of philosophical analyses of scientific theories. The Pragmatic View acknowledges that scientists use and need different kinds of theories for a variety of purposes. There is no one-size-fits-all structure of scientific theories. Notably, although the Pragmatic View does not necessarily endorse the views of the tradition of American Pragmatism, it has important resonances with the latter school’s emphasis on truth and knowledge as processual, purposive, pluralist, and context-dependent, and on the social and cognitive structure of scientific inquiry.

A further qualification in addition to the one above regarding American Pragmatism is in order. The Pragmatic View has important precursors in the historicist or “world view” perspectives of Feyerabend, Hanson, Kuhn, and Toulmin, which were an influential set of critiques of the Syntactic View utterly distinct from the Semantic View. This philosophical tradition focused on themes such as meaning change and incommensurability of terms across world views (e.g., paradigms), scientific change (e.g., revolutionary: Kuhn 1970; evolutionary: Toulmin 1972), the interweaving of context of discovery and context of justification, and scientific rationality (Preston 2012; Bird 2013; Swoyer 2014). The historicists also opposed the idea that theories can secure meaning and empirical support from a theory-neutral and purely observational source, as the Syntactic View had insisted on with its strong distinction between theoretical and observational vocabularies (cf. Galison 1988). Kuhn’s paradigms or, more precisely, “disciplinary matrices” even had an internal anatomy with four components: (i) laws or symbolic generalizations, (ii) ontological assumptions, (iii) values, and (iv) exemplars (Kuhn 1970, postscript; Godfrey-Smith 2003; Hacking 2012). This work was concerned more with theory change than with theory structure and had fewer conceptual resources from sociology of science and history of science than contemporary Pragmatic View work. Moreover, paradigms never quite caught on the way analyses of models and modeling have. Even so, this work did much to convince later scholars, including many of the Pragmatic View, of certain weaknesses in understanding theories as deductive axiomatic structures.

As a final way to contrast the three views, we return to population genetics and, especially, to the Hardy-Weinberg Principle (HWP). Both Woodger (1937, 1959) and Williams (1970, 1973) provide detailed axiomatizations of certain parts of biology, especially genetics, developmental biology, and phylogenetics. For instance, Woodger (1937) constructs an axiomatic system based on ten logical predicates or relations, including \(\bP\) ( part of ), \(\bT\) ( before in time ), \(\bU\) ( reproduced by cell division or cell fusion ), \(\bm\) ( male gamete ), \(\bff\) ( female gamete ), and \(\bgenet\) ( genetic property ) (cf. Nicholson and Gawne 2014). Woodger (1959) elaborates these logical predicates or relations to produce a careful reconstruction of Mendelian genetics. Here are two axioms in his system (which are rewritten in contemporary notation, since Woodger used Russell and Whitehead’s Principia Mathematica notation):

The first axiom should be read thus: “no gamete is both male and female” (1959, 416). In the second axiom, given that \(DLZxyz\) is a primitive relation defined as “\(x\) is a zygote which develops in the environment \(y\) into the life \(z\)” (1959, 415), the translation is “every life develops in one and only one environment from one and only one zygote” (416). Woodger claims that “the whole of Mendel’s work can be expressed…” via this axiomatic system. Woodger briefly mentions that if one assumes that the entire system or population is random with respect to gamete fusions, “then the Pearson-Hardy law is derivable” (1959, 427). This was a reference to HWP. In her explorations of various axiomatizations of Darwinian lineages and “subclans,” and the process of the “expansion of the fitter,” Williams (1970, 1973) also carefully defines concepts, and axiomatizes basic biological principles of reproduction, natural selection, fitness, and so forth. However, she does not address HWP. Of interest is the lack of axiomatization of HWP or other mathematical principles of population genetics in Woodger’s and Williams’ work. Were such principles considered secondary or uninteresting by Woodger and Williams? Might Woodger’s and Williams’ respective axiomatic systems simply lack the power and conceptual resources to axiomatically reconstruct a mathematical edifice actually cast in terms of probability theory? Finally, other friends of the Syntactic View, such as the early Michael Ruse, do not provide an axiomatization of HWP (Ruse 1975, 241).

Proponents of the Semantic View claim that their perspective on scientific theory accurately portrays the theoretical structure of population genetics. Thompson (2007) provides both set-theoretical and state-space renditions of Mendelian genetics. The first involves defining a set-theoretic predicate for the system, viz., \(\{P, A, f, g\}\), where \(P\) and \(A\) are sets representing, respectively, the total collection of alleles and loci in the population, while \(f\) and \(g\) are functions assigning an allele to a specific location in, respectively, the diploid cells of an individual or the haploid gametic cells. Axioms in this set-theoretic formalization include “The sets \(P\) and \(A\) are finite and non empty” (2007, 498). In contrast, the state-space approach of the Semantic View articulates a phase space with each dimension representing allelic (or genotypic) frequencies (e.g., cover and Chapter 3 of Lloyd 1994 [1988]). As an example, “for population genetic theory, a central law of succession is the Hardy-Weinberg law” (Thompson 2007, 499). Mathematically, the diploid version of HWP is written thus:

Here \(p\) and \(q\) are the frequencies of two distinct alleles at a biallelic locus. The left-hand side represents the allele frequencies in the parental generation and a random mating pattern, while the right-hand side captures genotype frequencies in the offspring generation, as predicted from the parental generation. This is a null theoretical model—actual genotypic and allelic frequencies of the offspring generation often deviate from predicted frequencies (e.g., a lethal homozygote recessive would make the \(q^2_{\text{off}}\) term = 0). Indeed, HWP holds strictly only in abstracted and idealized populations with very specific properties (e.g., infinitely large, individuals reproduce randomly) and only when there are no evolutionary forces operating in the population (e.g., no selection, mutation, migration, or drift) (e.g., Hartl and Clark 1989; Winther et al. 2015). HWP is useful also in the way it interacts with laws of succession for selection, mutation, and so forth (e.g., Okasha 2012). This powerful population genetic principle is central to Semantic View analyses of the mathematical articulation of the theoretical structure of population genetics (see also Lorenzano 2014, Ginnobili 2016).

Recall that the Pragmatic View highlights the internal and external pluralism—as well as the purposiveness—of model and theory structure. Consider recent uses of population genetic theory to specify the kinds and amounts of population structure existing in Homo sapiens . In particular, different measures and mathematical modeling methodologies are employed in investigating human genomic diversity (e.g., Jobling et al. 2004; Barbujani et al. 2013; Kaplan and Winther 2013). It is possible to distinguish at least two different research projects, each of which has a unique pragmatic content (e.g., aims, values, and methods). Diversity partitioning assesses genetic variation within and among pre-determined groups using Analysis of Variance (also crucial to estimating heritability, Downes 2014). Clustering analysis uses Bayesian modeling techniques to simultaneously produce clusters and assign individuals to these “unsupervised” cluster classifications. The robust result of the first modeling project is that (approximately) 85% of all genetic variance is found within human subpopulations (e.g., Han Chinese or Sami), 10% across subpopulations within a continental region, and only 5% is found across continents (i.e., “African,” “Asian,” and “European” – Lewontin 1972, 1974). (Recall also that we are all already identical at, on average, 999 out of 1000 nucleotides.) To calculate diversity partitions at these three nested levels, Lewontin (1972) used a Shannon information-theoretic measure closely related to Sewall Wright’s \(F\)-statistic:

Here \(H_T\) is the total heterozygosity of the population assessed, and \(\bar{H}_S\) is the heterozygosity of each subpopulation (group) of the relevant population, averaged across all the subpopulations. \(F_{ST}\) is bounded by 0 and 1, and is a measure of population structure, with higher \(F_{ST}\) values suggesting more structure, viz., more group differentiation. HWP appears implicitly in both \(H_T\) and \(\bar{H}_S\), which take heterozygosity (\(2pq\)) to be equal to the expected proportion of heterozygotes under HWP rather than the actual frequency of heterozygotes. \(H_T\) is computed by using the grand population average of \(p\) and \(q\), whereas calculating \(\bar{H}_S\) involves averaging across the expected heterozygosities of each subpopulation. If random mating occurs—and thus HWP applies—across the entire population without respecting subpopulation borders, then \(H_T\) and \(\bar{H}_S\) will be equal (i.e., \(p\) of the total population and of each individual subpopulation will be the same; likewise for \(q\)). If, instead, HWP applies only within subpopulations but not across the population as a whole, then \(\bar{H}_S\) will be smaller than \(H_T\), and \(F_{ST}\) will be positive (i.e., there will be “excess homozygosity” across subpopulations, which is known as the “Wahlund Principle” in population genetics). This is one way among many to deploy the population-genetic principle of HWP. Thus, the Lewontin-style diversity partitioning result that only roughly 5% of the total genetic variance is among races is equivalent to saying that \(F_{ST}\) across the big three continental populations in Lewontin’s three-level model is 0.05 (e.g., Barbujani et al. 1997). The basic philosophical tendency is to associate the diversity partitioning research project’s (approximately) 85%-10%-5% result with an anti-realist interpretation of biological race.

In contrast, clustering analysis (e.g., Pritchard et al. 2000; Rosenberg et al. 2002; cf. Edwards 2003) can be readily performed even with the small amount of among-continent genetic variance in Homo sapiens . For instance, when the Bayesian modeling computer program STRUCTURE is asked to produce 5 clusters, continental “races” appear—African, Amerindian, Asian, European, and Pacific Islanders. Interestingly, this modeling technique is also intimately linked to HWP: “Our main modeling assumptions are Hardy-Weinberg equilibrium within populations and complete linkage equilibrium between loci within populations” (Pritchard et al. 2000, 946). That is, for a cluster to eventually be robust in the modeling runs, it should meet HWP expectations. Clustering analysis has sometimes been interpreted as a justification for a realist stance towards biological race (see discussions in Hochman 2013; Winther and Kaplan 2013; Edge and Rosenberg 2015; Spencer 2015).

This example of the mathematical modeling of human genomic diversity teaches that basic and simple formal components can be used in different ways to develop and apply theory, both inside and outside of science. In contrast to the Syntactic and Semantic Views, the Pragmatic View foregrounds tensions vis-à-vis ontological assumptions and political consequences regarding the existence (or not) of biological race between diversity partitioning (Lewontin 1972) and clustering analysis (Pritchard et al. 2000) research packages. These ontological ruptures can be identified despite the fact that both research projects assess population structure by examining departures from HWP (i.e., they measure excess homozygosity), and are completely consistent (e.g., Winther 2014; Ludwig 2015; Edge and Rosenberg 2015).

This exploration of how the three views on the structure of scientific theory address population genetics, and in particular HWP, invites a certain meta-pluralism. That is, the Syntactic View carefully breaks down fundamental concepts and principles in genetics and population genetics, articulating definitions and relations among terms. The Semantic View insightfully decomposes and interweaves the complex mathematical edifice of population genetics. The Pragmatic View sheds light on modeling choices and on distinct interpretations and applications of the same theory or model, both within and without science. The three perspectives are hardly mutually exclusive. (N.B., the two running examples concern theory structure in Newtonian mechanics and population genetics, independently considered. While interesting, debates about “evolutionary forces” are beyond the scope of the current entry; see, e.g., Hitchcock and Velasco 2014.)

The structure of scientific theories is a rich topic. Theorizing and modeling are core activities across the sciences, whether old (e.g., relativity theory, evolutionary theory) or new (e.g., climate modeling, cognitive science, and systems biology). Furthermore, theory remains essential to developing multipurpose tools such as statistical models and procedures (e.g., Bayesian models for data analysis, agent-based models for simulation, network theory for systems analysis). Given the strength and relevance of theory and theorizing to the natural sciences, and even to the social sciences (e.g., microeconomics, physical, if not cultural, anthropology), philosophical attention to the structure of scientific theories could and should increase. This piece has focused on a comparison of three major perspectives: Syntactic View, Semantic View, and Pragmatic View. In order to handle these complex debates effectively, we have sidestepped certain key philosophical questions, including questions about scientific realism; scientific explanation and prediction; theoretical and ontological reductionism; knowledge-production and epistemic inference; the distinction between science and technology; and the relationship between science and society. Each of these topics bears further philosophical investigation in light of the three perspectives here explored.

A table helps summarize general aspects of the three views’ analyses of the structure of scientific theories:

Table 2. General aspects of each view’s analysis of the structure of scientific theories.

The Syntactic, Semantic, and Pragmatic views are often taken to be mutually exclusive and, thus, to be in competition with one another. They indeed make distinct claims about the anatomy of scientific theories. But one can also imagine them to be complementary, focusing on different aspects and questions of the structure of scientific theories and the process of scientific theorizing. For instance, in exploring nonformal and implicit components of theory, the Pragmatic View accepts that scientific theories often include mathematical parts, but tends to be less interested in these components. Moreover, there is overlap in questions—e.g., Syntactic and Semantic Views share an interest in formalizing theory; the Semantic and Pragmatic Views both exhibit concern for scientific practice.

How are these three views ultimately related? A standard philosophical move is to generalize and abstract, understanding a situation from a higher level. One “meta” hypothesis is that a given philosophical analysis of theory structure tends to be associated with a perceived relationship among the three views here discussed. The Syntactic View is inclined to interpret the Semantic View’s formal machinery as continuous with its own generalizing axiomatic strategy, and hence diagnoses many standard Semantic View critiques (Section 3) as missing their mark (the strategy of identity ; e.g., Friedman 1982; Worrall 1984; Halvorson 2012, 2013, 2019; Lutz 2012, 2017; cf. Chakravartty 2001). The Semantic View explicitly contrasts its characterization of theory structure with the “linguistic” or “metamathematical” apparatus of the Syntactic View (the strategy of combat ; e.g., Suppe 1977; van Fraassen 1980, 1989; Lloyd 1994 [1988]). Finally, the Pragmatic View, which did not exist as a perspective until relatively recently, imagines theory as pluralistic and can thus ground a holistic philosophical investigation. It envisions a meta-pluralism in which reconstructive axiomatization and mathematical modeling remain important, though not necessary for all theories. This third view endorses a panoply of theoretical structures and theorizing styles, negotiating continuity both between theorizing and “the experimental life,” and among philosophical analyses of the structure of scientific theories (the strategy of complementarity ; e.g., Hacking 1983, 2009; Galison 1988, 1997; Craver 2002; Suárez and Cartwright 2008; Griesemer 2013). Interestingly, Suárez and Pero (2019) explicitly concur with the Pragmatic View as described in this article, but believe that “the semantic conception in its bare minimal expression” is compatible with, if not sufficient for, capturing “pragmatic elements and themes involved in a more flexible and open-ended approach to scientific theory” (Suárez and Pero 2019, 348). By design, the ecumenical meta-pluralism sanctioned by the Pragmatic View does not completely offset identity and combat strategies. Moreover, only “partial acceptance” of the respective views may ultimately be possible. Even so, the complementarity strategy might be worth developing further. Compared to identity and combat meta-perspectives, it provides broader—or at least different—insights into the structure of scientific theories. More generally, exploring the relations among these views is itself a rich topic for future philosophical work, as is investigating their role in, and interpretation of, active scientific fields ripe for further philosophical analysis such as climate change (e.g., Winsberg 2018), model organisms (e.g., Ankeny and Leonelli 2020), and cartography and GIS (e.g., Winther 2020).

• Ankeny, R. and S. Leonelli, 2020, Model Organisms , Cambridge: Cambridge University Press.
• Apostel, L., 1960, “Towards the Formal Study of Models in the Non-Formal Sciences,” Synthese , 12 (23): 125–161.
• –––, 1970, “The Justification of Formalisation,” Quality and Quantity , 4 (1): 3–38.
• Awodey, S., 2006, Category Theory , Oxford: Oxford University Press.
• Bailer-Jones, D.M., 2002, “Models, Metaphors and Analogies,” in Blackwell Guide to the Philosophy of Science , P.K. Machamer and M. Silberstein (eds.), Oxford: Blackwell, pp. 108–127.
• Barbujani, G., S. Ghirotto, and F. Tassi, 2013, “Nine Things to Remember about Human Genome Diversity,” Tissue Antigens , 82 (3): 155–164.
• Barbujani, G.A., Magagni, E. Minch, and L.L. Cavalli-Sforza, 1997, “An Apportionment of Human DNA Diversity,” Proceedings of the National Academy of Sciences , 94 (9): 4516–4519.
• Bartha, P.F.A., 2010, By Parallel Reasoning: The Construction and Evaluation of Analogical Arguments , New York: Oxford University Press
• Bays, T., 2014, “Skolem’s Paradox”, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/spr2014/entries/paradox-skolem/ >.
• Beatty, J., 1981, “What’s Wrong with the Received View of Evolutionary Theory?” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980 , (2): 397–426.
• Bergstrom, C. and L. Dugatkin, 2012, Evolution , New York: Norton.
• Bird, A., 2013, “Thomas Kuhn”, The Stanford Encyclopedia of Philosophy (Fall 2013 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/fall2013/entries/thomas-kuhn/ >.
• Blatti, S. and S. Lapointe (eds.), 2016, Ontology After Carnap , Oxford: Oxford University Press.
• Boumans, M., 1999, “Built-In Justification,” in Models as Mediators: Perspectives on Natural and Social Science , M.S. Morgan and M. Morrison (eds.), Cambridge: Cambridge University Press, pp. 66–96.
• Braithwaite, R., 1962, “Models in the Empirical Sciences,” in Logic, Methodology and Philosophy of Science: Proceedings of the 1960 International Congress , E. Nagel, P. Suppes, and A. Tarski (eds.), Stanford, CA: Stanford University Press, pp. 224–231.
• Bridgman, P.W., 1927, The Logic of Modern Physics , New York: Macmillan.
• Bueno, O., 1997, “Empirical Adequacy: A Partial Structures Approach,” Studies in History and Philosophy of Science (Part A) , 28 (4): 585–610.
• Bueno, O., S. French, and J. Ladyman, 2012, “Models and Structures: Phenomenological and Partial,” Studies in History and Philosophy of Science (Part B) , 43 (1): 43–46.
• Brown, T., 2003, Making Truth: Metaphor in Science , Urbana: University of Illinois Press.
• Brown, M.J., 2010, “Genuine Problems and the Significance of Science,” Contemporary Pragmatism , 7 (2): 131–153.
• Callender, C., 1999, “Reducing Thermodynamics to Statistical Mechanics: The Case of Entropy,” The Journal of Philosophy , 96 (7): 348–373.
• Campbell, N.R., 1920, Physics: The Elements , Cambridge: Cambridge University Press.
• Carnap, R., 1967 [1928], The Logical Structure of the World , translated by R.A. George, Berkeley, CA: University of California Press. Original: Der logische Aufbau der Welt , Leipzig: Felix Meiner.
• –––, 1932, “Über Protokollsätze”, Erkenntnis , 3: 215–228; transl. by R. Creath and R. Nollan, “On Protocol Sentences,” Noûs , 21 (4) (1987): 457–470.
• –––, 1936/1937, “Testability and Meaning,” Philosophy of Science , 1936, 3 (4): 419–471; 1937, 4 (1): 1–40.
• –––, 1937, The Logical Syntax of Language , London: Kegan Paul, Trench, & Trübner.
• –––, 1939, Foundations of Logic and Mathematics (International Encyclopedia of Unified Science, Volume 1, Number 3), Chicago: University of Chicago Press.
• –––, 1942, Introduction to Semantics , Cambridge, MA: Harvard University Press.
• –––, 1952, The Continuum of Inductive Methods , Chicago: University of Chicago Press.
• –––, 1962 [1950], Logical Foundations of Probability , Chicago: University of Chicago Press, 2 nd edition.
• –––, 1963, “Philosopher Replies,” in The Philosophy of Rudolf Carnap (Library of Living Philosophers, Volume 11), P. Schilpp (ed.), La Salle: Open Court, pp. 889–999.
• –––, 1966, Philosophical Foundations of Science , New York: Basic Books; repr. as An Introduction to the Philosophy of Science , 1972; repr. New York: Dover, 1996.
• Cartwright, N., 1983, How the Laws of Physics Lie , New York: Oxford University Press.
• –––, 1989, Nature’s Capacities and Their Measurement , New York: Oxford University Press.
• –––, 1999a, The Dappled World: A Study of the Boundaries of Science , Cambridge: Cambridge University Press.
• –––, 1999b, “Models and the Limits of Theories: Quantum Hamiltonians and the BCS Model of Superconductivity,” in Models as Mediators: Perspectives on Natural and Social Science , M. Morgan and M. Morrison (eds.), (Perspectives on Natural and Social Sciences), Cambridge: Cambridge University Press, pp. 241–281.
• –––, 2008, “In Praise of the Representation Theorem,” in Representation, Evidence, and Justification: Themes from Suppes , W.K. Essler and M. Frauchiger (eds.), Ontos Verlag, pp. 83–90.
• –––, 2019, Nature, the Artful Modeler: Lectures on Laws, Science, How Nature Arranges the World and How We Can Arrange It Better , Chicago, IL: Open Court.
• Cartwright, N., T. Shomar, and M. Suárez, 1995, “The Tool Box of Science: Tools for the Building of Models with a Superconductivity Example,” in Theories and Models in Scientific Processes (Poznan Studies in the Philosophy of the Sciences and the Humanities, Volume 44), W. Herfel, W. Krajewski, I. Niiniluoto, and R. Wojcicki (eds.), Amsterdam: Rodopi, pp. 137–149.
• Carus, A.W., 2007, Carnap and Twentieth-Century Thought: Explication as Enlightenment , Cambridge: Cambridge University Press.
• Cat, J., 2014, “The Unity of Science”, The Stanford Encyclopedia of Philosophy (Winter 2014 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/win2014/entries/scientific-unity/ >.
• Chakravartty, A., 2001, “The Semantic or Model-Theoretic View of Theories and Scientific Realism,” Synthese , 127 (3): 325–345.
• Chang, H., 2011, “The Philosophical Grammar of Scientific Practice” in International Studies in the Philosophy of Science , 25 (3): 205–221.
• Clatterbuck, H., E. Sober, and R. Lewontin, 2013, “Selection Never Dominates Drift (Nor Vice Versa),” Biology & Philosophy , 28 (4): 577–592.
• Coffa, A. J., 1991, The Semantic Tradition From Kant to Carnap: To the Vienna Station , Cambridge: Cambridge University Press.
• Contessa, G., 2006, “Scientific Models, Partial Structures and the New Received View of Theories,” Studies in History and Philosophy of Science (Part A) , 37 (2): 370–377.
• Craver, C.F., 2002, “Structures of Scientific Theories,” in Blackwell Guide to the Philosophy of Science , P.K. Machamer and M. Silberstein (eds.), Oxford: Blackwell, pp. 55–79.
• –––, 2007, Explaining the Brain: Mechanisms and the Mosaic Unity of Neuroscience , New York: Oxford University Press.
• Creath, R., 1987, “The Initial Reception of Carnap’s Doctrine of Analyticity,” Noûs , 21 (4): 477–499.
• –––, 2014, “Logical Empiricism”, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/spr2014/entries/logical-empiricism/ >.
• Crombie, A.C., 1994, Styles of Scientific Thinking in the European Tradition (Volumes 1–3), London: Duckworth.
• –––, 1996, “Commitments and Styles of European Scientific Thinking,” Theoria , 11 (25): 65–76.
• Crow J. and M. Kimura, 1970, An Introduction to Population Genetics Theory , Edina, MN: Burgess International Group Incorporated.
• da Costa, N.C.A. and S. French, 1990, “The Model-Theoretic Approach in the Philosophy of Science,” Philosophy of Science , 57 (2): 248–65.
• –––, 2003. Science and Partial Truth: A Unitary Approach to Models and Scientific Reasoning , Oxford: Oxford University Press.
• Dalla Chiara Scabia, M.L. and G. Toraldo di Francia, 1973, “A Logical Analysis of Physical Theories,” La Rivista del Nuovo Cimento , 3 (1): 1–20.
• Davidson, A., 2001, The emergence of sexuality: Historical epistemology and the formation of concepts , Cambridge, MA: Harvard University Press.
• Davidson, D., 1974, “On the Very Idea of a Conceptual Scheme,” Proceedings and Addresses of the American Philosophical Association , 47: 5–20.
• de Chadarevian, S. and N. Hopwood, 2004, Models: The Third Dimension of Science , Stanford, CA: Stanford University Press.
• Demopoulos, W., 2003, “On the Rational Reconstruction of our Theoretical Knowledge,” The British Journal for the Philosophy of Science , 54 (3): 371–403.
• –––, 2013, Logicism and Its Philosophical Legacy , Cambridge: Cambridge University Press.
• Derman, E., 2011, Models Behaving Badly: Why Confusing Illusion with Reality Can Lead to Disaster, on Wall Street and in Life , New York: Free Press.
• Dizadji-Bahmani, F., R. Frigg, and S. Hartmann, 2010, “Who’s Afraid of Nagelian Reduction?,” Erkenntnis , 73 (3): 393–412.
• Döring, A. and R.G. Winther, forthcoming, “The Human Condition is an Ocean: Philosophy and the Mediterranean Sea,” in Words and Worlds: Use and Abuse of Analogies and Metaphors within Sciences and Humanities , S. Wuppuluri and A.C. Grayling (eds.), Synthese Library Series.
• Downes, S., 1992, “The Importance of Models in Theorizing: A Deflationary Semantic View,” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1992 , (1): 142–153.
• –––, “Heritability,” The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/spr2014/entries/heredity/ >.
• Dreyfus, H., 1986, “Why Studies of Human Capacities Modeled on Ideal Natural Science Can Never Achieve their Goal,” in Rationality, Relativism, and the Human Sciences , J. Margolis, M. Krausz, and R. Burian (eds.), Dordrecht: Martinus Nijhoff, pp. 3–22.
• Duhem, P., 1906, La théorie physique: Son objet et sa structure , Paris: Chevalier et Rivière; transl. by P.W. Wiener, The Aim and Structure of Physical Theory , Princeton, NJ: Princeton University Press (1954).
• Edge, M.D. and N. Rosenberg, 2015, “Implications of the Apportionment of Human Genetic Diversity for the Apportionment of Human Phenotypic Diversity,” Studies in History and Philosophy of Biological and Biomedical Sciences , 52: 32–45.
• Edwards, A.W.F., 2003, “Human Genetic Diversity: Lewontin‘s Fallacy” BioEssays , 25 (8): 798–801.
• Eilenberg, S. and S. MacLane, 1945, “General Theory of Natural Equivalences,” Transactions of the American Mathematical Society , 58 (2): 231–294.
• Einstein, A., 1934, “On the Method of Theoretical Physics,” Philosophy of Science , 1 (2): 163–169.
• –––, 1936, “Physik und Realität,” Journal of The Franklin Institute , 221 (3): 313–347; transl. by J. Piccard, “Physics and Reality,” Journal of the Franklin Institute , 221 (3) (1936): 349–382.
• Elwick, J., 2007, Styles of Reasoning in British Life Sciences: Shared Assumptions, 1820–1858 , London: Pickering & Chatto.
• Feigl, H., 1970, “The ‘Orthodox’ View of Theories: Remarks in Defense as Well as Critique,” in Analyses of Theories and Methods of Physics and Psychology (Minnesota Studies in the Philosophy of Science, Volume 4), M. Radner and S. Winokur (eds.), Minneapolis: University of Minnesota Press, pp. 3–16.
• Feigl, H., M. Scriven, and G. Maxwell (eds.), 1958, Minnesota Studies in the Philosophy of Science (Volume 2), Minneapolis: University of Minnesota Press.
• Flyvbjerg, B., 2001, Making Social Science Matter: Why Social Inquiry Fails and How it Can Succeed Again , Cambridge: Cambridge University Press.
• French, S., 2017, “Identity Conditions, Idealisations and Isomorphisms: a Defence of the Semantic Approach,” first online 19 September 2017, Synthese . doi:10.1007/s11229-017-1564-z
• French, S. and J. Ladyman, 1997, “Superconductivity and Structures: Revisiting the London Account,” Studies in History and Philosophy of Modern Physics , 28 (3): 363–393.
• –––, 1999, “Reinflating the Semantic Approach,” International Studies in the Philosophy of Science , 13 (2): 103–121.
• –––, 2003. “Remodelling Structural Realism: Quantum Physics and the Metaphysics of Structure,” Synthese , 136 (1): 31–56.
• Friedman, M., 1981, “Theoretical Explanation,” in Reduction, Time, and Reality: Studies in the Philosophy of the Natural Sciences , R. Healey (ed.), New York: Cambridge University Press, pp. 1–16.
• –––, 1982, “ The Scientific Image , by B. van Fraassen,” The Journal of Philosophy , 79 (5): 274–283.
• –––, 1983, Foundations of Space-Time Theories: Relativistic Physics and Philosophy of Science , Princeton: Princeton University Press.
• –––, 1999, Reconsidering Logical Positivism , New York: Cambridge University Press.
• –––, 2001, Dynamics of Reason , Stanford, CA: CSLI Publications.
• –––, 2011, “Carnap on Theoretical Terms: Structuralism without Metaphysics,” Synthese , 180 (2): 249–263.
• –––, 2013, Kant’s Construction of Nature: A Reading of the Metaphysical Foundations of Natural Science , Cambridge: Cambridge University Press.
• Frigg, R. and S. Hartmann, 2012, “Models in Science”, The Stanford Encyclopedia of Philosophy (Fall 2012 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/fall2012/entries/models-science/ >.
• Frigg, R. and I. Votsis, 2011, “Everything You Always Wanted to Know about Structural Realism but Were Afraid to Ask,” European Journal for Philosophy of Science , 1 (2): 227–276.
• Galison, P., 1987, How Experiments End , Chicago: University of Chicago Press.
• –––, 1988, “History, Philosophy, and the Central Metaphor,” Science in Context , 2 (1): 197–212.
• –––, 1997, Image and Logic: A Material Culture of Microphysics , Chicago: University of Chicago Press.
• Geary, J., 2011, I Is an Other: The Secret Life of Metaphor and How It Shapes the Way We See The World , New York: Harper Perennial.
• Gentner, D., 1982, “Are Scientific Analogies Metaphors?” in Metaphor: Problems and Perspectives , D. Miall (ed.), Brighton: Harvester Press, pp. 106–132.
• –––, 2003, “Analogical Reasoning, Psychology of,” in Encyclopedia of Cognitive Science , L. Nadel (ed.), London: Nature Publishing Group, pp. 106–112.
• Giere, R., 1988, Explaining Science: A Cognitive Approach , Chicago: University of Chicago Press.
• –––, 2004, “How Models Are Used to Represent Reality,” Philosophy of Science , 71 (5): 742–752.
• –––, 2010, “An Agent-based Conception of Models and Scientific Representation,” Synthese , 172 (2): 269–281.
• Giere, R., B. Bickle, and R. Mauldin, 2006, Understanding Scientific Reasoning , Belmont, CA: Thomson/Wadsworth, 5 th edition.
• Ginnobili, S., 2016, “Missing Concepts in Natural Selection Theory Reconstructions,” History and Philosophy of the Life Sciences , 38 (Article 8). doi:10.1007/s40656-016-0109-y
• Godfrey-Smith, P., 2003, Theory and Reality: An Introduction to the Philosophy of Science , Chicago: University of Chicago Press.
• –––, 2006, “The Strategy of Model-Based Science,” Biology and Philosophy , 21 (5): 725–740.
• Gould, S.J., 2002, The Structure of Evolutionary Theory , Cambridge, MA: Harvard University Press.
• Griesemer, J., 1990, “Modeling in the Museum: On the Role of Remnant Models in the Work of Joseph Grinnell,” Biology and Philosophy , 5 (1): 3–36.
• –––, 1991a, “Material Models in Biology,” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990 , (2): 79–94.
• –––, 1991b, “Must Scientific Diagrams Be Eliminable? The Case of Path Analysis,” Biology and Philosophy , 6 (2): 155–180.
• –––, 2013, “Formalization and the Meaning of Theory in the Inexact Biological Sciences,” Biological Theory , 7 (4): 298–310.
• Hacking, I., 1983, Representing and Intervening: Introductory Topics in the Philosophy of Natural Science , Cambridge: Cambridge University Press.
• –––, 2002, Historical Ontology , Cambridge, MA: Harvard University Press.
• –––, 2007a, “On Not Being a Pragmatist: Eight Reasons and a Cause,” in New Pragmatists , C. Misak (ed.), New York: Oxford University Press, pp. 32–49.
• –––, 2007b, “Natural Kinds: Rosy Dawn, Scholastic Twilight,” Royal Institute of Philosophy Supplements , 61: 203–240.
• –––, 2009, Scientific Reason , Taipei: National Taiwan University Press.
• –––, 2012, “Introduction,” in T.S. Kuhn, The Structure of Scientific Revolutions , 50 th Anniversary ed. (4 th ed.), Chicago: University of Chicago Press, pp. vii–xxxvii.
• –––, 2014, Why Is There Philosophy of Mathematics At All? , Cambridge: Cambridge University Press.
• Halvorson, H., 2012, “What Scientific Theories Could Not Be,” Philosophy of Science , 79 (2): 183–206.
• –––, 2013, “The Semantic View, if Plausible, is Syntactic,” Philosophy of Science , 80 (3): 475–478.
• –––, 2019, The Logic in Philosophy of Science , Cambridge: Cambridge University Press.
• Hartl, D. and A. Clark, 1989, Principles of Population Genetics , Sunderland, MA: Sinauer Associates.
• Hempel, C., 1952, Fundamentals of Concept Formation in Empirical Science , Chicago: University of Chicago Press.
• –––, 1958, “The Theoretician’s Dilemma,” in Minnesota Studies in the Philosophy of Science (Volume 2), H. Feigl, M. Scriven, and G. Maxwell (eds.), Minneapolis: University of Minnesota Press, pp. 37–98.
• –––, 1966, Philosophy of Natural Science , Englewood Cliffs, N.J.: Prentice-Hall.
• –––, 1970, “On the ‘Standard Conception’ of Scientific Theories,” in Minnesota Studies in the Philosophy of Science (Volume 4), M. Radner and S. Winokur (eds.), Minneapolis: University of Minnesota Press, pp. 142–163.
• Hermes, H. 1938, Eine Axiomatisierung der allgemeinen Mechanik (Forschungen zur Logik und zur Grundlegung der exacten Wissenschaften, Heft 3), Leipzig: S. Hirzel.
• –––, 1959, “Zur Axiomatisierung der Mechanik,” in The Axiomatic Method with Special Reference to Geometry and Physics: Proceedings of an International Symposium Held at the University of California, Berkeley, December 26, 1957–January 4, 1958 , L. Henkin, P. Suppes, and A. Tarski (eds.), Amsterdam: North Holland, pp. 282–290.
• Hesse, M., 1966, Models and Analogies in Science , Notre Dame: University of Notre Dame Press.
• –––, 1967, “Models and Analogy in Science,” in The Encyclopedia of Philosophy (Volume 5), P. Edwards (ed.), New York: Macmillan, pp. 354–359.
• Hitchcock, C. and J.D. Velasco, 2014, “Newtonian and Evolutionary Forces,” Ergo , 1 (2): 39–77.
• Hochman, A., 2013, “Against the New Racial Naturalism,” The Journal of Philosophy 110 (6): 331–351.
• Hodges, W., 1997, A Shorter Model Theory , New York: Cambridge University Press.
• –––, 2013, “Model Theory”, The Stanford Encyclopedia of Philosophy (Fall 2013 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/fall2013/entries/model-theory/ >.
• Hoffman, R., 1980, “Metaphor in Science,” in Cognition and Figurative Language , R. Honeck (ed.), Hillsdale: Lawrence Erlbaum Associates, pp. 393–423.
• Holton, G., 1988, Thematic Origins of Scientific Thought: Kepler to Einstein , Cambridge, MA: Harvard University Press, 2 nd edition.
• Hookway, C., 2013, “Pragmatism”, The Stanford Encyclopedia of Philosophy (Winter 2013 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/win2013/entries/pragmatism/ >.
• Hull, D., 1975, “Central Subjects and Historical Narratives,” History & Theory , 14 (3): 253–274.
• Jammer, M., 1961, Concepts of Mass in Classical and Modern Physics , Cambridge, MA: Harvard University Press; reprinted unabridged by Dover in 1997.
• Jobling, M.A., M. Hurles, C. Tyler-Smith, 2004, Human Evolutionary Genetics. Origins, Peoples and Diseases , New York: Garland Science.
• Jones, M., 2005, “Idealization and Abstraction: A Framework,” in Idealization XII: Correcting the Model – Idealization and Abstraction in the Sciences (Poznan Studies in the Philosophy of the Sciences and the Humanities, Volume 86), M. Jones and N. Cartwright (eds.), Amsterdam: Rodopi, pp. 173–217. (Same individual as Thomson-Jones 2012.)
• Kaplan, J.M. and R.G. Winther, 2013, “Prisoners of Abstraction? The Theory and Measure of Genetic Variation, and the Very Concept of ‘Race’,” Biological Theory , 7 (4): 401–412.
• Keller, E.F., 1995, Reconfiguring Life: Metaphors of Twentieth-Century Biology , New York: Columbia University Press.
• Kitcher P., 1984, “1953 and All That. A Tale of Two Sciences,” Philosophical Review , 93 (3): 335–373.
• –––, 1993, The Advancement of Science: Science Without Legend, Objectivity Without Illusion , New York: Oxford University Press.
• –––, 2001, Science, Truth, and Democracy , New York: Oxford University Press.
• Krivine, J., 2013 [1971], Introduction to Axiomatic Set Theory (Synthese Library, Volume 34), Dordrecht: D. Reidel.
• Kuhn, T.S., 1970, The Structure of Scientific Revolutions , Chicago: University of Chicago Press, 2 nd edition.
• –––, 1977, “Objectivity, Value Judgment, and Theory Choice,” in The Essential Tension: Selected Studies in Scientific Tradition and Change , T.S. Kuhn (ed.), Chicago: University of Chicago Press, pp. 320–339.
• Ladyman, J., 2014, “Structural Realism”, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/spr2014/entries/structural-realism/ >.
• Ladyman, J., O. Bueno, M. Suárez, and B. van Fraassen, 2011, “Scientific Representation: A Long Journey from Pragmatics to Pragmatics,” Metascience , 20 (3): 417–442.
• Lakatos, I., 1980, The Methodology of Scientific Research Programmes (Philosophical Papers: Volume 1), Cambridge: Cambridge University Press.
• Laudan, L., 1977, Progress and Its Problems: Towards a Theory of Scientific Growth , Berkeley, CA: University of California Press.
• Leonelli, S., 2008, “Performing Abstraction: Two Ways of Modelling Arabidopsis thaliana ,” Biology and Philosophy , 23 (4): 509–528.
• Levins, R., 1966, “The Strategy of Model Building in Population Biology,” American Scientist , 54 (4): 421–431.
• Levins, R. and R. Lewontin, 1985, The Dialectical Biologist , Cambridge, MA: Harvard University Press.
• Lewis, R.W., 1980, “Evolution: A System of Theories,” Perspectives in Biology and Medicine , 23 (4): 551–572.
• Lewontin, R.C., 1972, “Apportionment of Human Diversity,” Evolutionary Biology , 6: 381–398.
• –––, 1974, The Genetic Basis of Evolutionary Change , New York: Columbia University Press.
• Lloyd, E., 1983, “The Nature of Darwin’s Support for the Theory of Natural Selection,” Philosophy of Science , 50 (1): 112–129.
• –––, 1994 [1988], The Structure and Confirmation of Evolutionary Theory , Princeton: Princeton University Press.
• –––, 2013 In Press, “Structure of Evolutionary Theory,” in International Encyclopedia of Social and Behavioral Sciences , W. Durham (ed.), 2 nd edition, Amsterdam: Elsevier.
• London, F. and H. London, 1935, “The Electromagnetic Equations of the Supraconductor,” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences , 149 (866): 71–88.
• Longino, H.E., 1995, “Gender, Politics, and the Theoretical Virtues,” Synthese 104 (3): 383–397.
• –––, 2002, The Fate of Knowledge , Princeton: Princeton University Press.
• –––, 2013, Studying Human Behavior: How Scientists Investigate Aggression & Sexuality , Chicago: University of Chicago Press.
• López Beltrán, C., 1987, “La Explicación Evolucionista y el Uso de Modelos,” Masters Thesis, Posgrado en Filosofía de la Ciencia, Universidad Autónoma Metropolitana (Iztapalapa).
• Lorenzano, P., 2013, “The Semantic Conception and the Structuralist View of Theories: A Critique of Suppe’s Criticisms,” Studies in History and Philosophy of Science (Part A) , 44: 600–607.
• –––, 2014, “What is the Status of the Hardy-Weinberg Law within Population Genetics?,” in European Philosophy of Science: Philosophy of Science in Europe and the Viennese Heritage (Vienna Circle Institute Yearbook: Volume 17), M.C. Galavotti, E. Nemeth, F.L. Stadler F. (eds.), Cham, Switzerland: Springer, pp. 159–172.
• Lowry, I., 1965, “A Short Course in Model Design,” Journal of the American Institute of Planners , 31 (2): 158–166.
• Ludwig, D., 2015. “Against the New Metaphysics of Race,” Philosophy of Science 82: 1–21.
• Lutz, S., 2012, “On a Straw Man in the Philosophy of Science: A Defense of the Received View,” HOPOS: The Journal of the International Society for the History of Philosophy of Science , 2 (1): 77–120.
• –––, 2014, “What’s Right with a Syntactic Approach to Theories and Models?” Erkenntnis , 79 (8 supplement): 1475–1492.
• –––, 2017, What “Was the Syntax-Semantics Debate in the Philosophy of Science About?,” Philosophy and Phenomenological Research , 95 (2): 319–352.
• Mancosu, P., 2010, “Mathematical Style”, The Stanford Encyclopedia of Philosophy (Spring 2010 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/spr2010/entries/mathematical-style/ >.
• Margenau, H., 1950, The Nature of Physical Reality: A Philosophy of Modern Physics , New York: McGraw-Hill.
• Marker, D., 2002, Model Theory: An Introduction , New York: Springer.
• Martínez, S., 2003, Geografía de las prácticas científicas: Racionalidad, heurística y normatividad , Mexico City: UNAM Press.
• –––, 2014, “Technological Scaffolds for Culture and Cognition,” in Developing Scaffolds in Evolution, Culture and Cognition , L. Caporael, J. Griesemer, and W. Wimsatt (eds.), Cambridge, MA: MIT Press, pp. 249–264.
• Matheson, C. and J. Dallmann, 2014, “Historicist Theories of Scientific Rationality”, The Stanford Encyclopedia of Philosophy (Fall 2014 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/fall2014/entries/rationality-historicist/ >.
• McKinsey, J.C.C., A.C. Sugar, and P. Suppes, 1953, “Axiomatic Foundations of Classical Particle Mechanics,” Journal of Rational Mechanics and Analysis , 2 (2): 253–272.
• Minsky, M., 1965, “Matter, Mind, and Models,” in Proceedings of the International Federation for Information Processing Congress (Volume 1), W. Kalenich (ed.), Washington D.C.: Spartan Books, pp. 45–49.
• Morgan, M., 2012, The World in the Model: How Economists Work and Think , New York: Cambridge University Press.
• Morgan, M.S. and M. Morrison (eds.), 1999, Models as Mediators: Perspectives on Natural and Social Science , Cambridge: Cambridge University Press.
• Mormann, T., 2007, “The Structure of Scientific Theories in Logical Empiricism,” The Cambridge Companion to Logical Empiricism , in A. Richardson and T. Uebel (eds.), Cambridge: Cambridge University Press, pp. 136–162.
• Morrison, M., 2007, “Where Have All the Theories Gone?,” Philosophy of Science , 74 (2): 195–228.
• Moulines, C., 1976, “Approximate Application of Empirical Theories: A General Explication,” Erkenntnis , 10 (2): 201–227.
• –––, 2002, “Introduction: Structuralism as a Program for Modelling Theoretical Science,” Synthese , 130 (1): 1–11.
• Nagel, E., 1961, The Structure of Science: Problems in the Logic of Scientific Explanation , New York: Harcourt, Brace & World.
• –––, 1979, “Issues in the Logic of Reductive Explanations,” in Teleology Revisited and Other Essays in the Philosophy and History of Science , New York: Columbia University Press, pp. 95–117.
• Neurath, O., 1932, “Protokollsätze”, Erkenntnis , 3: 204–214; “Protocol Statements,” in Philosophical Papers 1913-1946 , R.S. Cohen and M. Neurath (eds.), Dordrecht: Reidel (1983), pp. 91–99.
• Nicholson, D. and R. Gawne, 2014, “Rethinking Woodger’s Legacy in the Philosophy of Biology,” Journal of the History of Biology , 47 (2): 243–292.
• Nolte, D.D., 2010, “The Tangled Tale of Phase Space,” Physics Today , April: 33–38.
• Okasha, S., 2012, “Population Genetics”, The Stanford Encyclopedia of Philosophy (Fall 2012 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/fall2012/entries/population-genetics/ >.
• Oppenheimer, J.R., 1956, “Analogy in Science,” American Psychologist , 11 (3): 127–135.
• Oyama, S., 2000, The Ontogeny of Information: Developmental Systems and Evolution , 2 nd ed., Durham: Duke University Press.
• Pereda, C., 2013, “Ulises Moulines y la concepción estructural de las teorías científicas,” in La filosofía en México en el siglo XX: Apuntes de un participante , C. Pereda, Mexico City: CONACULTA (Consejo Nacional para la Cultura y las Artes), pp. 200–212.
• Pickstone, J.V., 2000, Ways of Knowing: A New History of Science, Technology and Medicine , Chicago: University of Chicago Press.
• Pigliucci, M. and G.B. Müller, 2010, Evolution: The Extended Synthesis , Cambridge, MA: MIT Press.
• Popper, K., 1996 [1976], “The Myth of the Framework,” In The Myth of the Framework: In Defence of Science and Rationality , M. A. Notturno (ed), Abingdon: Routledge, pp. 33–64.
• Pritchard J.K., M. Stephens, and P. Donnelly, 2000, “Inference of Population Structure Using Multilocus Genotype Data,” Genetics , 155 (2): 945–959.
• Preston, J., 2012, “Paul Feyerabend”, The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/win2012/entries/feyerabend/ >.
• Przełęcki, M., 1969, The Logic of Empirical Theories , London: Routledge & Kegan Paul.
• Putnam, H., 1962, “What Theories Are Not,” in Logic, Methodology, and Philosophy of Science: Proceedings of the 1960 International Congress , E. Nagel, P. Suppes, and A. Tarski (eds.), Stanford, CA: Stanford University Press, pp. 240–251.
• Reichenbach, H., 1938, Experience and Prediction: An Analysis of the Foundations and the Structure of Knowledge , Chicago: University of Chicago Press.
• –––, 1965 [1920], The Theory of Relativity and A Priori Knowledge , with an introduction by M. Reichenbach, Berkeley: University of California Press. Original: Relativitätstheorie und Erkenntnis apriori , Berlin: Springer.
• –––, 1969 [1924], The Axiomatization of the Theory of Relativity , with an introduction by W.C. Salmon. Berkeley-Los Angeles: University of California Press. Original: Axiomatik der relativistischen Raum-Zeit-Lehre , Braunschweig: F. Vieweg & Sohn.
• –––, 1978, Selected Writings, 1909–1953: With a Selection of Biographical and Autobiographical Sketches (Volumes 1–2), Dordrecht: Reidel.
• Rice, S., 2004, Evolutionary Theory: Mathematical and Conceptual Foundations , Sunderland, MA: Sinauer Associates.
• Richards, R., 1992, “The Structure of Narrative Explanation in History and Biology,” in History and Evolution , M. Nitecki and D. Nitecki (eds.), Albany: State University of New York Press, pp. 19–53.
• Richardson, A., 2002, “Engineering Philosophy of Science: American Pragmatism and Logical Empiricism in the 1930s,” Philosophy of Science , 69 (S3): S36–S47.
• Rosenberg N.A., J.K. Pritchard, J.L. Weber, H.M. Cann, K.K. Kidd, L.A. Zhivotovsky, and M.A. Feldman, 2002, “Genetic Structure of Human Populations,” Science , 298 (5602): 2381–2385.
• Rosenblueth, A. and N. Wiener, 1945, “The Role of Models in Science,” Philosophy of Science , 12 (4): 316–321.
• Ruse, M., 1975, “Charles Darwin’s Theory of Evolution: An Analysis,” Journal of the History of Biology , 8 (2): 219–241.
• Rutte, H., 1991, “Neurath contra Schlick. On the Discussion of Truth in the Vienna Circle,” in Rediscovering the Forgotten Vienna Circle: Austrian studies on Otto Neurath and the Vienna Circle , T. Uebel (ed.), Dordrecht: Kluwer, pp. 169–174.
• Sarkar, S., 1998, Genetics and Reductionism , Cambridge: Cambridge University Press.
• Savage, C.W., 1990, “Preface,” in Scientific Theories. Minnesota Studies in the Philosophy of Science. Volume 14, C.W. Savage (ed.), Minneapolis: University of Minnesota Press, pp. vii–ix.
• Schaffner K., 1969, “Correspondence Rules,” Philosophy of Science , 36 (3): 280–290.
• –––, 1976, “Reductionism in Biology: Prospects and Problems,” in PSA : Proceedings of the Biennial Meeting of the Philosophy of Science Association 1974 : 613–632.
• –––, 1993, Discovery and Explanation in Biology and Medicine , Chicago: University of Chicago Press.
• Schlick, M., 1925 [1918], General Theory of Knowledge , LaSalle, IL: Open Court.
• –––, 1934, “Über das Fundament der Erkenntnis,” Erkenntnis , 4 (1): 79–99.
• Schmidt, H.-J., 2014, “Structuralism in Physics”, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/spr2014/entries/physics-structuralism/ >.
• Shapin, S. and S. Schaffer, 1985, Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life , Princeton: Princeton University Press.
• Simon, H., 1954, “The Axiomatization of Classical Mechanics,” Philosophy of Science , 21 (4): 340–343.
• –––, 1957, Models of Man , New York: Wiley.
• –––, 1970, “The Axiomatization of Physical Theories,” Philosophy of Science , 37 (1): 16–26.
• Smith, B.C., 1996, On the Origin of Objects , Cambridge, MA: MIT Press.
• Sneed, J., 1979, The Logical Structure of Mathematical Physics , Dordrecht: D. Reidel, 2 nd edition.
• Spencer, Q., 2015, “Philosophy of Race Meets Population Genetics,” Studies in History and Philosophy of Biological and Biomedical Sciences 52: 46–55.
• Stegmüller, W., 1976, The Structure and Dynamics of Theories , New York: Springer.
• –––, 1979, “The Structuralist View: Survey, Recent Developments and Answers to Some Criticisms”, in The Logic and Epistemology of Scientific Change , I. Niiniluoto and R. Tuomela (eds.), Amsterdam: North Holland.
• Suárez, M., 1999, “The Role of Models in the Application of Scientific Theories; Epistemological Implications,” in Models as Mediators. Perspectives on Natural and Social Science , M.S. Morgan and M. Morrison (eds.), Cambridge: Cambridge University Press, pp. 168–196.
• –––, 2011, Comment on van Fraassen Scientific Representation: Paradoxes of Perspective , in Ladyman, J., O. Bueno, M. Suárez, and B. van Fraassen, “Scientific Representation: A Long Journey from Pragmatics to Pragmatics,” Metascience , 20 (3): 428–433.
• Suárez, M. and N. Cartwright, 2008, “Theories: Tools versus Models,” Studies in History and Philosophy of Modern Physics , 39 (1): 62–81.
• Suárez, M. and F. Pero, 2019, “The Representational Semantic Conception,” Philosophy of Science , 86 (2): 344–365.
• Suppe, F., 1977, The Structure of Scientific Theories , Urbana, IL: University of Illinois Press.
• –––, 1989, The Semantic Conception of Theories and Scientific Realism , Chicago: University of Illinois Press.
• –––, 2000, “Understanding Scientific Theories: An Assessment of Developments,” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1998 , (2): S102–S115.
• Suppes, P., 1957, Introduction to Logic , Princeton: D. Van Nostrand Co.
• –––, 1960, “A Comparison of the Meaning and Uses of Models in Mathematics and the Empirical Sciences,” Synthese , 12 (2-3): 287–301.
• –––, 1962, “Models of Data,” in Logic, Methodology, and Philosophy of Science: Proceedings of the 1960 International Congress , E. Nagel, P. Suppes, and A. Tarski (eds.), Stanford, CA: Stanford University Press, pp. 252–261.
• –––, 1967, “What is a Scientific Theory?,” In Philosophy of Science Today , S. Morgenbesser (ed.), New York: Basic Books, pp. 55–67.
• –––, 1968, “The Desirability of Formalization in Science,” The Journal of Philosophy , 65 (20): 651–664.
• –––, 1978, “The Plurality of Science,” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978 , (2): 3–16.
• –––, 2002, Representation and Invariance of Scientific Structures , Stanford, CA: CSLI Publications.
• Swoyer, C., 2014, “Relativism”, The Stanford Encyclopedia of Philosophy (Winter 2014 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/win2014/entries/relativism/ >.
• Thompson, P., 1989, The Structure of Biological Theories , Albany: SUNY Press.
• –––, 2007, “Formalisations of Evolutionary Biology,” in Philosophy of Biology , M. Matthen and C. Stephens (eds.), Elsevier, Amsterdam, pp. 485–523
• Thomson-Jones, M., 2012, “Modelling without Mathematics,” Philosophy of Science , 79 (5): 761–772. (Same individual as Jones 2005.)
• Toulmin, S., 1972, Human Understanding: The Collective Use and Evolution of Concepts , Princeton: Princeton University Press.
• Tuomi, J., 1981, “Structure and Dynamics of Darwinian Evolutionary Theory,” Systematic Zoology , 30 (1): 22–31.
• –––, 1992, “Evolutionary Synthesis: A Search for the Strategy,” Philosophy of Science , 59 (3): 429–438.
• Tversky, A., 1977, “Features of Similarity,” Psychological Review , 84 (4): 327–352.
• Uebel, T., 2014, “Vienna Circle”, The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/spr2014/entries/vienna-circle/ >.
• van Benthem J., 2012, “The Logic of Empirical Theories Revisited,” Synthese , 186 (3): 775–792.
• van Fraassen, B., 1967, “Meaning Relations among Predicates,” Noûs , 1 (2): 161–179.
• –––, 1970, “On the Extension of Beth’s Semantics of Physical Theories,” Philosophy of Science , 37 (3): 325–339.
• –––, 1980, The Scientific Image , Oxford: Oxford University Press.
• –––, 1981, “Theory Construction and Experiment: An Empiricist View,” PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980 , (2): 663–678.
• –––, 1989, Laws and Symmetry , New York: Oxford University Press.
• –––, 2008, Scientific Representation: Paradoxes of Perspective , New York: Oxford University Press.
• van Riel, R. and R. Van Gulick, 2014, “Scientific Reduction”, The Stanford Encyclopedia of Philosophy (Summer 2014 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/sum2014/entries/scientific-reduction/ >.
• Van Valen, L., 1976, “Domains, Deduction, the Predictive Method, and Darwin,” Evolutionary Theory , 1: 231–245.
• Vicedo, M., 1995, “Scientific Styles: Toward Some Common Ground in the History, Philosophy, and Sociology of Science,” Perspectives on Science , 3: 231–254.
• Vickers, P., 2009, “Can Partial Structures Accommodate Inconsistent Science?” Principia , 13 (2): 233–250.
• Walsh, D., 2015, Organisms, Agency, and Evolution, Cambridge: Cambridge University Press.
• Weisberg, M., 2013, Simulation and Similarity: Using Models to Understand the World , New York: Oxford University Press.
• Wessels, L., 1976, “Laws and Meaning Postulates in van Fraassen’s View of Theories,” in PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1974 : 215–234.
• Williams, M., 1970, “Deducing the Consequences of Selection: A Mathematical Model,” Journal of Theoretical Biology , 48: 343–385.
• –––, 1973, “The Logical Status of Natural Selection and other Evolutionary Controversies: Resolution by Axiomatization,” in M. Bunge (ed.), The Methodological Unity of Science , Dordrecht: D. Reidel, pp. 84–102.
• Wimsatt, W.C., 2007, Re-Engineering Philosophy for Limited Beings: Piecewise Approximations to Reality , Cambridge, MA: Harvard University Press.
• Winsberg, E., 2010, Science in the Age of Computer Simulation , Chicago: University of Chicago Press.
• –––, 2018, Philosophy and Climate Science , Cambridge: Cambridge University Press.
• Winther, R.G., 2006a, “Parts and Theories in Compositional Biology,” Biology and Philosophy , 21 (4): 471–499.
• –––, 2006b, “Fisherian and Wrightian Perspectives in Evolutionary Genetics and Model-Mediated Imposition of Theoretical Assumptions,” Journal of Theoretical Biology , 240 (2): 218–232.
• –––, 2009, “Schaffner’s Model of Theory Reduction: Critique and Reconstruction,” Philosophy of Science , 76 (2): 119–142.
• –––, 2011, “Part-Whole Science,” Synthese , 178 (3): 397–427.
• –––, 2012a, “Mathematical Modeling in Biology: Philosophy and Pragmatics,” Frontiers in Plant Evolution and Development , 3: 102, doi:10.3389/fpls.2012.00102
• –––, 2012b, “Interweaving Categories: Styles, Paradigms, and Models,” Studies in History and Philosophy of Science (Part A) , 43 (4): 628–639.
• –––, 2014, “The Genetic Reification of ‘Race’? A Story of Two Mathematical Methods,” Critical Philosophy of Race , 2 (2): 204–223.
• –––, 2020, When Maps Become the World , Chicago, IL: University of Chicago Press.
• Winther, R.G., R. Giordano, M.D. Edge, and R. Nielsen, 2015, “The Mind, the Lab, and the Field: Three Kinds of Populations in Scientific Practice,” Studies in History and Philosophy of Biological and Biomedical Sciences , 52: 12–21.
• Winther, R.G. and J.M. Kaplan, 2013, “Ontologies and Politics of Biogenomic ‘Race’,” Theoria. A Journal of Social and Political Theory (South Africa) , 60 (3): 54–80.
• Woodger J.H., 1937, The Axiomatic Method in Biology , Cambridge: Cambridge University Press.
• –––, 1959, “Studies in the Foundations of Genetics,” in The Axiomatic Method with Special Reference to Geometry and Physics: Proceedings of an International Symposium Held at the University of California, Berkeley, December 26, 1957 – January 4, 1958 , L. Henkin, P. Suppes, and A. Tarski (eds.), Amsterdam: North Holland, pp. 408–428.
• Worrall, J., 1984, “An Unreal Image,” The British Journal for the Philosophy of Science , 35 (1): 65–80.
• Wright, S., 1969, Evolution and the Genetics of Populations: A Treatise in Four Volumes (Volume 2: The Theory of Gene Frequencies), Chicago: University of Chicago Press.
• Zach, R., 2009, “Hilbert’s Program”, The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), E. N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/spr2009/entries/hilbert-program/ >.
• Ziman, J., 2000, Real Science: What It Is, and What It Means , Cambridge: Cambridge University Press.

How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Koellner, P., ms., “ Carnap on the Foundations of Logic and Mathematics ,” unpublished.
• Browse Philpapers on The Nature of Theories
• Browse Philpapers on Theoretical Virtues
• Browser Philpapers on Models and Idealization
• Evolution Resources from the National Academies
• Definitions of Fact, Theory, and Law in Scientific Work , National Center for Science Education (NCSE).

Carnap, Rudolf | cognitive science | confirmation | Darwinism | empiricism: logical | feminist philosophy, interventions: epistemology and philosophy of science | Feyerabend, Paul | genetics: population | incommensurability: of scientific theories | Kuhn, Thomas | models in science | model theory | paradox: Skolem’s | physics: structuralism in | pragmatism | rationality: historicist theories of | reduction, scientific | science: theory and observation in | scientific explanation | scientific realism | scientific representation | simulations in science | statistical physics: philosophy of statistical mechanics | structural realism | style: in mathematics | theoretical terms in science | underdetermination, of scientific theories | Vienna Circle

Acknowledgments

The following provided helpful feedback or conversation, or both, Jácome Armas, Nancy Cartwright, Mario Casanueva, Carl Craver, Eugene Earnshaw, Doc Edge, Michael Friedman, Sari Friedman, Fermín Fulda, Ryan Giordano, Ian Hacking, Hervé Kieffel, Elisabeth A. Lloyd, Helen Longino, Carlos López Beltrán, Greg Lusk, Sebastian Lutz, Sergio Martínez, Amir Najmi, Thomas Ryckman, Mette Bannergaard Johansen, Mette Smølz Skau, Bas van Fraassen, Denis Walsh, Ole Wæver, and two anonymous reviewers. Alex Dor, Cory Knudson, and Lucas McGranahan offered expert research assistance.

Copyright © 2020 by Rasmus Grønfeldt Winther < rgwinther @ gmail . com >

• Accessibility

Support SEP

Mirror sites.

View this site from another server:

• Info about mirror sites

The Stanford Encyclopedia of Philosophy is copyright © 2023 by The Metaphysics Research Lab , Department of Philosophy, Stanford University

Library of Congress Catalog Data: ISSN 1095-5054

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons

Margin Size

• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

1.3: Hypothesis, Theories, and Laws

• Last updated
• Save as PDF
• Page ID 97964

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\id}{\mathrm{id}}\)

\( \newcommand{\kernel}{\mathrm{null}\,}\)

\( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\)

\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\)

\( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

\( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vectorC}[1]{\textbf{#1}} \)

\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

  Learning Objectives

• Describe the difference between hypothesis and theory as scientific terms.
• Describe the difference between a theory and scientific law.

Although many have taken science classes throughout the course of their studies, people often have incorrect or misleading ideas about some of the most important and basic principles in science. Most students have heard of hypotheses, theories, and laws, but what do these terms really mean? Prior to reading this section, consider what you have learned about these terms before. What do these terms mean to you? What do you read that contradicts or supports what you thought?

What is a Fact?

A fact is a basic statement established by experiment or observation. All facts are true under the specific conditions of the observation.

What is a Hypothesis?

One of the most common terms used in science classes is a "hypothesis". The word can have many different definitions, depending on the context in which it is being used:

• An educated guess: a scientific hypothesis provides a suggested solution based on evidence.
• Prediction: if you have ever carried out a science experiment, you probably made this type of hypothesis when you predicted the outcome of your experiment.
• Tentative or proposed explanation: hypotheses can be suggestions about why something is observed. In order for it to be scientific, however, a scientist must be able to test the explanation to see if it works and if it is able to correctly predict what will happen in a situation. For example, "if my hypothesis is correct, we should see ___ result when we perform ___ test."

A hypothesis is very tentative; it can be easily changed.

What is a Theory?

The United States National Academy of Sciences describes what a theory is as follows:

"Some scientific explanations are so well established that no new evidence is likely to alter them. The explanation becomes a scientific theory. In everyday language a theory means a hunch or speculation. Not so in science. In science, the word theory refers to a comprehensive explanation of an important feature of nature supported by facts gathered over time. Theories also allow scientists to make predictions about as yet unobserved phenomena."

"A scientific theory is a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experimentation. Such fact-supported theories are not "guesses" but reliable accounts of the real world. The theory of biological evolution is more than "just a theory." It is as factual an explanation of the universe as the atomic theory of matter (stating that everything is made of atoms) or the germ theory of disease (which states that many diseases are caused by germs). Our understanding of gravity is still a work in progress. But the phenomenon of gravity, like evolution, is an accepted fact.

Note some key features of theories that are important to understand from this description:

• Theories are explanations of natural phenomena. They aren't predictions (although we may use theories to make predictions). They are explanations as to why we observe something.
• Theories aren't likely to change. They have a large amount of support and are able to satisfactorily explain numerous observations. Theories can, indeed, be facts. Theories can change, but it is a long and difficult process. In order for a theory to change, there must be many observations or pieces of evidence that the theory cannot explain.
• Theories are not guesses. The phrase "just a theory" has no room in science. To be a scientific theory carries a lot of weight; it is not just one person's idea about something

Theories aren't likely to change.

What is a Law?

Scientific laws are similar to scientific theories in that they are principles that can be used to predict the behavior of the natural world. Both scientific laws and scientific theories are typically well-supported by observations and/or experimental evidence. Usually scientific laws refer to rules for how nature will behave under certain conditions, frequently written as an equation. Scientific theories are more overarching explanations of how nature works and why it exhibits certain characteristics. As a comparison, theories explain why we observe what we do and laws describe what happens.

For example, around the year 1800, Jacques Charles and other scientists were working with gases to, among other reasons, improve the design of the hot air balloon. These scientists found, after many, many tests, that certain patterns existed in the observations on gas behavior. If the temperature of the gas is increased, the volume of the gas increased. This is known as a natural law. A law is a relationship that exists between variables in a group of data. Laws describe the patterns we see in large amounts of data, but do not describe why the patterns exist.

What is a Belief?

A belief is a statement that is not scientifically provable. Beliefs may or may not be incorrect; they just are outside the realm of science to explore.

Laws vs. Theories

A common misconception is that scientific theories are rudimentary ideas that will eventually graduate into scientific laws when enough data and evidence has accumulated. A theory does not change into a scientific law with the accumulation of new or better evidence. Remember, theories are explanations and laws are patterns we see in large amounts of data, frequently written as an equation. A theory will always remain a theory; a law will always remain a law.

Video \(\PageIndex{1}\): What’s the difference between a scientific law and theory?

• A hypothesis is a tentative explanation that can be tested by further investigation.
• A theory is a well-supported explanation of observations.
• A scientific law is a statement that summarizes the relationship between variables.
• An experiment is a controlled method of testing a hypothesis.

Contributions & Attributions

Marisa Alviar-Agnew  ( Sacramento City College )

Henry Agnew (UC Davis)

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Biology library

Course: biology library   >   unit 1, the scientific method.

• Controlled experiments
• The scientific method and experimental design

Introduction

• Make an observation.
• Ask a question.
• Form a hypothesis , or testable explanation.
• Make a prediction based on the hypothesis.
• Test the prediction.
• Iterate: use the results to make new hypotheses or predictions.

Scientific method example: Failure to toast

1. make an observation..

• Observation: the toaster won't toast.

2. Ask a question.

• Question: Why won't my toaster toast?

3. Propose a hypothesis.

• Hypothesis: Maybe the outlet is broken.

4. Make predictions.

• Prediction: If I plug the toaster into a different outlet, then it will toast the bread.

5. Test the predictions.

• Test of prediction: Plug the toaster into a different outlet and try again.
• If the toaster does toast, then the hypothesis is supported—likely correct.
• If the toaster doesn't toast, then the hypothesis is not supported—likely wrong.

Logical possibility

Practical possibility, building a body of evidence, 6. iterate..

• Iteration time!
• If the hypothesis was supported, we might do additional tests to confirm it, or revise it to be more specific. For instance, we might investigate why the outlet is broken.
• If the hypothesis was not supported, we would come up with a new hypothesis. For instance, the next hypothesis might be that there's a broken wire in the toaster.

Want to join the conversation?

• Upvote Button navigates to signup page
• Downvote Button navigates to signup page
• Flag Button navigates to signup page

Incorporate STEM journalism in your classroom

• Exercise type: Discussion
• Topic: Earth
• Category: Research & Design

How a scientific theory is born

• Download Student Worksheet

Directions for teachers:

Use the online Science News article “ How the Earth-shaking theory of plate tectonics was born ,” and the prompts below to have students explore scientific theories and determine the process behind creating theories. A version of the story, “Shaking up Earth,” appears in the January 16, 2021 issue of Science News . As a final exercise, have students discuss the definition of a scientific theory and compare it with hypotheses and scientific laws.

This story is the first installment in a series that celebrates Science News ’ upcoming 100th anniversary by highlighting some of the biggest advancements in science over the last century. For more on the story of plate tectonics, and to see the rest of series as it appears, visit Science News ’ Century of Science site at www.sciencenews.org/century .

Want to make it a virtual lesson? Post the online Science News article“ How the Earth-shaking theory of plate tectonics was born ,” to your learning management system. Pair up students and allow them to connect via virtual breakout rooms in a video conference, over the phone, in a shared document or using another chat system. Have each pair submit its answers to the second set of questions to you.

Thinking about theories

Discuss the following questions with a partner before reading the Science News article.

1. What does it mean to say that you have a theory about something? Think of a theory you’ve had about something outside of science.

Typically, when people say that they have theory, it means that they have an idea or philosophy. Student examples of theories will vary.

2. What is one scientific theory you have learned about this year in science? Explain what you remember about it.

Student answers will vary, but may include the general theory of relativity, evolution, etc.

3. How does the general use of the term theory differ from its use in a scientific context?    

Theories in science are explanations rooted in data. Having a theory outside of the scientific context may be based on observations or data, or the term may be used to state a logical idea.

The theory of plate tectonics

Read the online Science News article “How plate tectonics upended our understanding of Earth,” and answer the following questions individually before discussing them as a class.

1. What is the theory of plate tectonics? Over how many years was it developed?

The theory of plate tectonics states that the Earth’s surface is broken up into various pieces (plates) and describes how and why they are constantly in motion and how that motion is linked to features seen on Earth. The theory was developed over about 50 years.

2. Who helped develop the theory and what did they contribute to it? What types of scientists were they and where were they from?

Meteorologist Alfred Wegner proposed the idea of continental drift in 1912, and geologist Arthur Holmes added to that proposal years later with an explanation for how the continents might drift. These ideas were the precursors to the development of the theory of plate tectonics. From there, seismologists, geophysicists, mathematicians and physicists established the ideas, such as seafloor spreading, and found the data necessary to develop the theory. Notable scientists include Lynn Sykes, Harry Hess, Robert S. Dietz, Robert Parker, W. Jason Morgan and Dan McKenzie.  The researchers were from England and the United States.

3. Before the theory’s development, what were the conflicting lines of thought?

Wegner’s proposal sparked debates between mobilists, who supported the idea that the Earth’s surface was in motion, and fixists, who thought the Earth’s surface was static.

4. What did scientists need to resolve the conflict? Why did the conflict take so long to resolve?

In order to resolve the debate, scientists needed evidence. Wegner made his proposal in the early 1900s, but scientific evidence for why the continents move and how didn’t become available until after World War II, when technological advancements allowed scientists to study Earth’s surface and interior, and particularly the bottom of the oceans, in unprecedented detail.

5. How was evidence communicated to other members of the scientific community? Why was the communication important?

Evidence was communicated at conferences attended by scientists including geologists and geophysicists. By building on each other’s ideas and using each other’s data, the scientists were able to go beyond the idea of continental drift and come up with the unified theory of plate tectonics.

Defining a scientific theory

Discuss the following questions with a classmate.

1. Based on your answers to the questions above, how would you define a scientific theory?

A scientific theory is an explanation for how and why a natural phenomenon occurs based on evidence.

2. Think about a scientific hypothesis that you have written or look up an example of a hypothesis. How would you define a hypothesis? How is it different than a theory?

A hypothesis is a proposed explanation for a scientific question that hasn’t been validated with evidence. A theory relies on evidence to explain phenomena, whereas a hypothesis is proposed before the gathering of evidence. A hypothesis can become a theory once it is proven or disproven with supporting evidence.

Possible Extension

What is a scientific law that you have learned about in school? Explain how a scientific law is different than a scientific theory. For more information, watch this Ted-Ed video called “ What’s the difference between a scientific law and a theory? ” by educator Matt Anticole.

Student answers will vary, but could include Newton’s three laws of motion, Bernoulli’s principle, etc. A scientific law is different than a scientific theory in that it describes and predicts the relationships among variables, whereas a scientific theory describes how or why something happens.

• Bipolar Disorder
• Therapy Center
• When To See a Therapist
• Types of Therapy
• Best Online Therapy
• Best Couples Therapy
• Best Family Therapy
• Managing Stress
• Sleep and Dreaming
• Understanding Emotions
• Self-Improvement
• Healthy Relationships
• Student Resources
• Personality Types
• Guided Meditations
• Verywell Mind Insights
• 2024 Verywell Mind 25
• Mental Health in the Classroom
• Editorial Process
• Meet Our Review Board
• Crisis Support

How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk,  "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

• Operationalization

Hypothesis Types

Hypotheses examples.

• Collecting Data

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.

Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

At a Glance

A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

• Forming a question
• Performing background research
• Creating a hypothesis
• Designing an experiment
• Collecting data
• Analyzing the results
• Drawing conclusions
• Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.

Unless you are creating an exploratory study, your hypothesis should always explain what you  expect  to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore numerous factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment  do not  support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk adage that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

• Is your hypothesis based on your research on a topic?
• Can your hypothesis be tested?
• Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the  journal articles you read . Many authors will suggest questions that still need to be explored.

How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

• Collect as many observations about a topic or problem as you can.
• Evaluate these observations and look for possible causes of the problem.
• Create a list of possible explanations that you might want to explore.
• After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method ,  falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that  if  something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

The Importance of Operational Definitions

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.

Replicability

One of the basic principles of any type of scientific research is that the results must be replicable.

Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. For example, how would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.

Hypothesis Checklist

• Does your hypothesis focus on something that you can actually test?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate the variables?
• Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

• Simple hypothesis : This type of hypothesis suggests there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type suggests a relationship between three or more variables, such as two independent and dependent variables.
• Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
• Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
• Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative population sample and then generalizes the findings to the larger group.
• Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the  dependent variable  if you change the  independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

• "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
• "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."​
• "Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."
• "Children who receive a new reading intervention will have higher reading scores than students who do not receive the intervention."

Examples of a complex hypothesis include:

• "People with high-sugar diets and sedentary activity levels are more likely to develop depression."
• "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

• "There is no difference in anxiety levels between people who take St. John's wort supplements and those who do not."
• "There is no difference in scores on a memory recall task between children and adults."
• "There is no difference in aggression levels between children who play first-person shooter games and those who do not."

Examples of an alternative hypothesis:

• "People who take St. John's wort supplements will have less anxiety than those who do not."
• "Adults will perform better on a memory task than children."
• "Children who play first-person shooter games will show higher levels of aggression than children who do not." 

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as  case studies ,  naturalistic observations , and surveys are often used when  conducting an experiment is difficult or impossible. These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a  correlational study  can examine how the variables are related. This research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods  are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually  cause  another to change.

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Thompson WH, Skau S. On the scope of scientific hypotheses .  R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607

Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:].  Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z

Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004

Nosek BA, Errington TM. What is replication ?  PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691

Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies .  Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Hypothesis, Model, Theory, and Law

Dorling Kindersley / Getty Images

• Physics Laws, Concepts, and Principles
• Quantum Physics
• Important Physicists
• Thermodynamics
• Cosmology & Astrophysics
• Weather & Climate

• M.S., Mathematics Education, Indiana University
• B.A., Physics, Wabash College

In common usage, the words hypothesis, model, theory, and law have different interpretations and are at times used without precision, but in science they have very exact meanings.

Perhaps the most difficult and intriguing step is the development of a specific, testable hypothesis. A useful hypothesis enables predictions by applying deductive reasoning, often in the form of mathematical analysis. It is a limited statement regarding the cause and effect in a specific situation, which can be tested by experimentation and observation or by statistical analysis of the probabilities from the data obtained. The outcome of the test hypothesis should be currently unknown, so that the results can provide useful data regarding the validity of the hypothesis.

Sometimes a hypothesis is developed that must wait for new knowledge or technology to be testable. The concept of atoms was proposed by the ancient Greeks , who had no means of testing it. Centuries later, when more knowledge became available, the hypothesis gained support and was eventually accepted by the scientific community, though it has had to be amended many times over the year. Atoms are not indivisible, as the Greeks supposed.

A model is used for situations when it is known that the hypothesis has a limitation on its validity. The Bohr model of the atom , for example, depicts electrons circling the atomic nucleus in a fashion similar to planets in the solar system. This model is useful in determining the energies of the quantum states of the electron in the simple hydrogen atom, but it is by no means represents the true nature of the atom. Scientists (and science students) often use such idealized models  to get an initial grasp on analyzing complex situations.

Theory and Law

A scientific theory or law represents a hypothesis (or group of related hypotheses) which has been confirmed through repeated testing, almost always conducted over a span of many years. Generally, a theory is an explanation for a set of related phenomena, like the theory of evolution or the big bang theory . 

The word "law" is often invoked in reference to a specific mathematical equation that relates the different elements within a theory. Pascal's Law refers an equation that describes differences in pressure based on height. In the overall theory of universal gravitation developed by Sir Isaac Newton , the key equation that describes the gravitational attraction between two objects is called the law of gravity .

These days, physicists rarely apply the word "law" to their ideas. In part, this is because so many of the previous "laws of nature" were found to be not so much laws as guidelines, that work well within certain parameters but not within others.

Scientific Paradigms

Once a scientific theory is established, it is very hard to get the scientific community to discard it. In physics, the concept of ether as a medium for light wave transmission ran into serious opposition in the late 1800s, but it was not disregarded until the early 1900s, when Albert Einstein proposed alternate explanations for the wave nature of light that did not rely upon a medium for transmission.

The science philosopher Thomas Kuhn developed the term scientific paradigm to explain the working set of theories under which science operates. He did extensive work on the scientific revolutions that take place when one paradigm is overturned in favor of a new set of theories. His work suggests that the very nature of science changes when these paradigms are significantly different. The nature of physics prior to relativity and quantum mechanics is fundamentally different from that after their discovery, just as biology prior to Darwin’s Theory of Evolution is fundamentally different from the biology that followed it. The very nature of the inquiry changes.

One consequence of the scientific method is to try to maintain consistency in the inquiry when these revolutions occur and to avoid attempts to overthrow existing paradigms on ideological grounds.

Occam’s Razor

One principle of note in regards to the scientific method is Occam’s Razor (alternately spelled Ockham's Razor), which is named after the 14th century English logician and Franciscan friar William of Ockham. Occam did not create the concept—the work of Thomas Aquinas and even Aristotle referred to some form of it. The name was first attributed to him (to our knowledge) in the 1800s, indicating that he must have espoused the philosophy enough that his name became associated with it.

The Razor is often stated in Latin as:

entia non sunt multiplicanda praeter necessitatem

or, translated to English:

entities should not be multiplied beyond necessity

Occam's Razor indicates that the most simple explanation that fits the available data is the one which is preferable. Assuming that two hypotheses presented have equal predictive power, the one which makes the fewest assumptions and hypothetical entities takes precedence. This appeal to simplicity has been adopted by most of science, and is invoked in this popular quote by Albert Einstein:

Everything should be made as simple as possible, but not simpler.

It is significant to note that Occam's Razor does not prove that the simpler hypothesis is, indeed, the true explanation of how nature behaves. Scientific principles should be as simple as possible, but that's no proof that nature itself is simple.

However, it is generally the case that when a more complex system is at work there is some element of the evidence which doesn't fit the simpler hypothesis, so Occam's Razor is rarely wrong as it deals only with hypotheses of purely equal predictive power. The predictive power is more important than the simplicity.

Edited by Anne Marie Helmenstine, Ph.D.

• Scientific Hypothesis, Model, Theory, and Law
• Theory Definition in Science
• The Basics of Physics in Scientific Study
• A Brief History of Atomic Theory
• Einstein's Theory of Relativity
• What Is a Paradigm Shift?
• Wave Particle Duality and How It Works
• Oversimplification and Exaggeration Fallacies
• Kinetic Molecular Theory of Gases
• Understanding Cosmology and Its Impact
• The Copenhagen Interpretation of Quantum Mechanics
• De Broglie Hypothesis
• Scientific Method
• The History of Gravity
• Tips on Winning the Debate on Evolution

Research Hypothesis In Psychology: Types, & Examples

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

A research hypothesis, in its plural form “hypotheses,” is a specific, testable prediction about the anticipated results of a study, established at its outset. It is a key component of the scientific method .

Hypotheses connect theory to data and guide the research process towards expanding scientific understanding

Some key points about hypotheses:

• A hypothesis expresses an expected pattern or relationship. It connects the variables under investigation.
• It is stated in clear, precise terms before any data collection or analysis occurs. This makes the hypothesis testable.
• A hypothesis must be falsifiable. It should be possible, even if unlikely in practice, to collect data that disconfirms rather than supports the hypothesis.
• Hypotheses guide research. Scientists design studies to explicitly evaluate hypotheses about how nature works.
• For a hypothesis to be valid, it must be testable against empirical evidence. The evidence can then confirm or disprove the testable predictions.
• Hypotheses are informed by background knowledge and observation, but go beyond what is already known to propose an explanation of how or why something occurs.

Predictions typically arise from a thorough knowledge of the research literature, curiosity about real-world problems or implications, and integrating this to advance theory. They build on existing literature while providing new insight.

Types of Research Hypotheses

Alternative hypothesis.

The research hypothesis is often called the alternative or experimental hypothesis in experimental research.

It typically suggests a potential relationship between two key variables: the independent variable, which the researcher manipulates, and the dependent variable, which is measured based on those changes.

The alternative hypothesis states a relationship exists between the two variables being studied (one variable affects the other).

A hypothesis is a testable statement or prediction about the relationship between two or more variables. It is a key component of the scientific method. Some key points about hypotheses:

• Important hypotheses lead to predictions that can be tested empirically. The evidence can then confirm or disprove the testable predictions.

In summary, a hypothesis is a precise, testable statement of what researchers expect to happen in a study and why. Hypotheses connect theory to data and guide the research process towards expanding scientific understanding.

An experimental hypothesis predicts what change(s) will occur in the dependent variable when the independent variable is manipulated.

It states that the results are not due to chance and are significant in supporting the theory being investigated.

The alternative hypothesis can be directional, indicating a specific direction of the effect, or non-directional, suggesting a difference without specifying its nature. It’s what researchers aim to support or demonstrate through their study.

Null Hypothesis

The null hypothesis states no relationship exists between the two variables being studied (one variable does not affect the other). There will be no changes in the dependent variable due to manipulating the independent variable.

It states results are due to chance and are not significant in supporting the idea being investigated.

The null hypothesis, positing no effect or relationship, is a foundational contrast to the research hypothesis in scientific inquiry. It establishes a baseline for statistical testing, promoting objectivity by initiating research from a neutral stance.

Many statistical methods are tailored to test the null hypothesis, determining the likelihood of observed results if no true effect exists.

This dual-hypothesis approach provides clarity, ensuring that research intentions are explicit, and fosters consistency across scientific studies, enhancing the standardization and interpretability of research outcomes.

Nondirectional Hypothesis

A non-directional hypothesis, also known as a two-tailed hypothesis, predicts that there is a difference or relationship between two variables but does not specify the direction of this relationship.

It merely indicates that a change or effect will occur without predicting which group will have higher or lower values.

For example, “There is a difference in performance between Group A and Group B” is a non-directional hypothesis.

Directional Hypothesis

A directional (one-tailed) hypothesis predicts the nature of the effect of the independent variable on the dependent variable. It predicts in which direction the change will take place. (i.e., greater, smaller, less, more)

It specifies whether one variable is greater, lesser, or different from another, rather than just indicating that there’s a difference without specifying its nature.

For example, “Exercise increases weight loss” is a directional hypothesis.

Falsifiability

The Falsification Principle, proposed by Karl Popper , is a way of demarcating science from non-science. It suggests that for a theory or hypothesis to be considered scientific, it must be testable and irrefutable.

Falsifiability emphasizes that scientific claims shouldn’t just be confirmable but should also have the potential to be proven wrong.

It means that there should exist some potential evidence or experiment that could prove the proposition false.

However many confirming instances exist for a theory, it only takes one counter observation to falsify it. For example, the hypothesis that “all swans are white,” can be falsified by observing a black swan.

For Popper, science should attempt to disprove a theory rather than attempt to continually provide evidence to support a research hypothesis.

Can a Hypothesis be Proven?

Hypotheses make probabilistic predictions. They state the expected outcome if a particular relationship exists. However, a study result supporting a hypothesis does not definitively prove it is true.

All studies have limitations. There may be unknown confounding factors or issues that limit the certainty of conclusions. Additional studies may yield different results.

In science, hypotheses can realistically only be supported with some degree of confidence, not proven. The process of science is to incrementally accumulate evidence for and against hypothesized relationships in an ongoing pursuit of better models and explanations that best fit the empirical data. But hypotheses remain open to revision and rejection if that is where the evidence leads.

• Disproving a hypothesis is definitive. Solid disconfirmatory evidence will falsify a hypothesis and require altering or discarding it based on the evidence.
• However, confirming evidence is always open to revision. Other explanations may account for the same results, and additional or contradictory evidence may emerge over time.

We can never 100% prove the alternative hypothesis. Instead, we see if we can disprove, or reject the null hypothesis.

If we reject the null hypothesis, this doesn’t mean that our alternative hypothesis is correct but does support the alternative/experimental hypothesis.

Upon analysis of the results, an alternative hypothesis can be rejected or supported, but it can never be proven to be correct. We must avoid any reference to results proving a theory as this implies 100% certainty, and there is always a chance that evidence may exist which could refute a theory.

How to Write a Hypothesis

• Identify variables . The researcher manipulates the independent variable and the dependent variable is the measured outcome.
• Operationalized the variables being investigated . Operationalization of a hypothesis refers to the process of making the variables physically measurable or testable, e.g. if you are about to study aggression, you might count the number of punches given by participants.
• Decide on a direction for your prediction . If there is evidence in the literature to support a specific effect of the independent variable on the dependent variable, write a directional (one-tailed) hypothesis. If there are limited or ambiguous findings in the literature regarding the effect of the independent variable on the dependent variable, write a non-directional (two-tailed) hypothesis.
• Make it Testable : Ensure your hypothesis can be tested through experimentation or observation. It should be possible to prove it false (principle of falsifiability).
• Clear & concise language . A strong hypothesis is concise (typically one to two sentences long), and formulated using clear and straightforward language, ensuring it’s easily understood and testable.

Consider a hypothesis many teachers might subscribe to: students work better on Monday morning than on Friday afternoon (IV=Day, DV= Standard of work).

Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and a Friday afternoon and then measuring their immediate recall of the material covered in each session, we would end up with the following:

• The alternative hypothesis states that students will recall significantly more information on a Monday morning than on a Friday afternoon.
• The null hypothesis states that there will be no significant difference in the amount recalled on a Monday morning compared to a Friday afternoon. Any difference will be due to chance or confounding factors.

More Examples

• Memory : Participants exposed to classical music during study sessions will recall more items from a list than those who studied in silence.
• Social Psychology : Individuals who frequently engage in social media use will report higher levels of perceived social isolation compared to those who use it infrequently.
• Developmental Psychology : Children who engage in regular imaginative play have better problem-solving skills than those who don’t.
• Clinical Psychology : Cognitive-behavioral therapy will be more effective in reducing symptoms of anxiety over a 6-month period compared to traditional talk therapy.
• Cognitive Psychology : Individuals who multitask between various electronic devices will have shorter attention spans on focused tasks than those who single-task.
• Health Psychology : Patients who practice mindfulness meditation will experience lower levels of chronic pain compared to those who don’t meditate.
• Organizational Psychology : Employees in open-plan offices will report higher levels of stress than those in private offices.
• Behavioral Psychology : Rats rewarded with food after pressing a lever will press it more frequently than rats who receive no reward.

Related Articles

Research Methodology

Qualitative Data Coding

What Is a Focus Group?

Cross-Cultural Research Methodology In Psychology

What Is Internal Validity In Research?

Research Methodology , Statistics

What Is Face Validity In Research? Importance & How To Measure

Criterion Validity: Definition & Examples

• Privacy Policy

Home » What is a Hypothesis – Types, Examples and Writing Guide

What is a Hypothesis – Types, Examples and Writing Guide

Table of Contents

Definition:

Hypothesis is an educated guess or proposed explanation for a phenomenon, based on some initial observations or data. It is a tentative statement that can be tested and potentially proven or disproven through further investigation and experimentation.

Hypothesis is often used in scientific research to guide the design of experiments and the collection and analysis of data. It is an essential element of the scientific method, as it allows researchers to make predictions about the outcome of their experiments and to test those predictions to determine their accuracy.

Types of Hypothesis

Types of Hypothesis are as follows:

Research Hypothesis

A research hypothesis is a statement that predicts a relationship between variables. It is usually formulated as a specific statement that can be tested through research, and it is often used in scientific research to guide the design of experiments.

Null Hypothesis

The null hypothesis is a statement that assumes there is no significant difference or relationship between variables. It is often used as a starting point for testing the research hypothesis, and if the results of the study reject the null hypothesis, it suggests that there is a significant difference or relationship between variables.

Alternative Hypothesis

An alternative hypothesis is a statement that assumes there is a significant difference or relationship between variables. It is often used as an alternative to the null hypothesis and is tested against the null hypothesis to determine which statement is more accurate.

Directional Hypothesis

A directional hypothesis is a statement that predicts the direction of the relationship between variables. For example, a researcher might predict that increasing the amount of exercise will result in a decrease in body weight.

Non-directional Hypothesis

A non-directional hypothesis is a statement that predicts the relationship between variables but does not specify the direction. For example, a researcher might predict that there is a relationship between the amount of exercise and body weight, but they do not specify whether increasing or decreasing exercise will affect body weight.

Statistical Hypothesis

A statistical hypothesis is a statement that assumes a particular statistical model or distribution for the data. It is often used in statistical analysis to test the significance of a particular result.

Composite Hypothesis

A composite hypothesis is a statement that assumes more than one condition or outcome. It can be divided into several sub-hypotheses, each of which represents a different possible outcome.

Empirical Hypothesis

An empirical hypothesis is a statement that is based on observed phenomena or data. It is often used in scientific research to develop theories or models that explain the observed phenomena.

Simple Hypothesis

A simple hypothesis is a statement that assumes only one outcome or condition. It is often used in scientific research to test a single variable or factor.

Complex Hypothesis

A complex hypothesis is a statement that assumes multiple outcomes or conditions. It is often used in scientific research to test the effects of multiple variables or factors on a particular outcome.

Applications of Hypothesis

Hypotheses are used in various fields to guide research and make predictions about the outcomes of experiments or observations. Here are some examples of how hypotheses are applied in different fields:

• Science : In scientific research, hypotheses are used to test the validity of theories and models that explain natural phenomena. For example, a hypothesis might be formulated to test the effects of a particular variable on a natural system, such as the effects of climate change on an ecosystem.
• Medicine : In medical research, hypotheses are used to test the effectiveness of treatments and therapies for specific conditions. For example, a hypothesis might be formulated to test the effects of a new drug on a particular disease.
• Psychology : In psychology, hypotheses are used to test theories and models of human behavior and cognition. For example, a hypothesis might be formulated to test the effects of a particular stimulus on the brain or behavior.
• Sociology : In sociology, hypotheses are used to test theories and models of social phenomena, such as the effects of social structures or institutions on human behavior. For example, a hypothesis might be formulated to test the effects of income inequality on crime rates.
• Business : In business research, hypotheses are used to test the validity of theories and models that explain business phenomena, such as consumer behavior or market trends. For example, a hypothesis might be formulated to test the effects of a new marketing campaign on consumer buying behavior.
• Engineering : In engineering, hypotheses are used to test the effectiveness of new technologies or designs. For example, a hypothesis might be formulated to test the efficiency of a new solar panel design.

How to write a Hypothesis

Here are the steps to follow when writing a hypothesis:

Identify the Research Question

The first step is to identify the research question that you want to answer through your study. This question should be clear, specific, and focused. It should be something that can be investigated empirically and that has some relevance or significance in the field.

Conduct a Literature Review

Before writing your hypothesis, it’s essential to conduct a thorough literature review to understand what is already known about the topic. This will help you to identify the research gap and formulate a hypothesis that builds on existing knowledge.

Determine the Variables

The next step is to identify the variables involved in the research question. A variable is any characteristic or factor that can vary or change. There are two types of variables: independent and dependent. The independent variable is the one that is manipulated or changed by the researcher, while the dependent variable is the one that is measured or observed as a result of the independent variable.

Formulate the Hypothesis

Based on the research question and the variables involved, you can now formulate your hypothesis. A hypothesis should be a clear and concise statement that predicts the relationship between the variables. It should be testable through empirical research and based on existing theory or evidence.

Write the Null Hypothesis

The null hypothesis is the opposite of the alternative hypothesis, which is the hypothesis that you are testing. The null hypothesis states that there is no significant difference or relationship between the variables. It is important to write the null hypothesis because it allows you to compare your results with what would be expected by chance.

Refine the Hypothesis

After formulating the hypothesis, it’s important to refine it and make it more precise. This may involve clarifying the variables, specifying the direction of the relationship, or making the hypothesis more testable.

Examples of Hypothesis

Here are a few examples of hypotheses in different fields:

• Psychology : “Increased exposure to violent video games leads to increased aggressive behavior in adolescents.”
• Biology : “Higher levels of carbon dioxide in the atmosphere will lead to increased plant growth.”
• Sociology : “Individuals who grow up in households with higher socioeconomic status will have higher levels of education and income as adults.”
• Education : “Implementing a new teaching method will result in higher student achievement scores.”
• Marketing : “Customers who receive a personalized email will be more likely to make a purchase than those who receive a generic email.”
• Physics : “An increase in temperature will cause an increase in the volume of a gas, assuming all other variables remain constant.”
• Medicine : “Consuming a diet high in saturated fats will increase the risk of developing heart disease.”

Purpose of Hypothesis

The purpose of a hypothesis is to provide a testable explanation for an observed phenomenon or a prediction of a future outcome based on existing knowledge or theories. A hypothesis is an essential part of the scientific method and helps to guide the research process by providing a clear focus for investigation. It enables scientists to design experiments or studies to gather evidence and data that can support or refute the proposed explanation or prediction.

The formulation of a hypothesis is based on existing knowledge, observations, and theories, and it should be specific, testable, and falsifiable. A specific hypothesis helps to define the research question, which is important in the research process as it guides the selection of an appropriate research design and methodology. Testability of the hypothesis means that it can be proven or disproven through empirical data collection and analysis. Falsifiability means that the hypothesis should be formulated in such a way that it can be proven wrong if it is incorrect.

In addition to guiding the research process, the testing of hypotheses can lead to new discoveries and advancements in scientific knowledge. When a hypothesis is supported by the data, it can be used to develop new theories or models to explain the observed phenomenon. When a hypothesis is not supported by the data, it can help to refine existing theories or prompt the development of new hypotheses to explain the phenomenon.

When to use Hypothesis

Here are some common situations in which hypotheses are used:

• In scientific research , hypotheses are used to guide the design of experiments and to help researchers make predictions about the outcomes of those experiments.
• In social science research , hypotheses are used to test theories about human behavior, social relationships, and other phenomena.
• I n business , hypotheses can be used to guide decisions about marketing, product development, and other areas. For example, a hypothesis might be that a new product will sell well in a particular market, and this hypothesis can be tested through market research.

Characteristics of Hypothesis

Here are some common characteristics of a hypothesis:

• Testable : A hypothesis must be able to be tested through observation or experimentation. This means that it must be possible to collect data that will either support or refute the hypothesis.
• Falsifiable : A hypothesis must be able to be proven false if it is not supported by the data. If a hypothesis cannot be falsified, then it is not a scientific hypothesis.
• Clear and concise : A hypothesis should be stated in a clear and concise manner so that it can be easily understood and tested.
• Based on existing knowledge : A hypothesis should be based on existing knowledge and research in the field. It should not be based on personal beliefs or opinions.
• Specific : A hypothesis should be specific in terms of the variables being tested and the predicted outcome. This will help to ensure that the research is focused and well-designed.
• Tentative: A hypothesis is a tentative statement or assumption that requires further testing and evidence to be confirmed or refuted. It is not a final conclusion or assertion.
• Relevant : A hypothesis should be relevant to the research question or problem being studied. It should address a gap in knowledge or provide a new perspective on the issue.

Advantages of Hypothesis

Hypotheses have several advantages in scientific research and experimentation:

• Guides research: A hypothesis provides a clear and specific direction for research. It helps to focus the research question, select appropriate methods and variables, and interpret the results.
• Predictive powe r: A hypothesis makes predictions about the outcome of research, which can be tested through experimentation. This allows researchers to evaluate the validity of the hypothesis and make new discoveries.
• Facilitates communication: A hypothesis provides a common language and framework for scientists to communicate with one another about their research. This helps to facilitate the exchange of ideas and promotes collaboration.
• Efficient use of resources: A hypothesis helps researchers to use their time, resources, and funding efficiently by directing them towards specific research questions and methods that are most likely to yield results.
• Provides a basis for further research: A hypothesis that is supported by data provides a basis for further research and exploration. It can lead to new hypotheses, theories, and discoveries.
• Increases objectivity: A hypothesis can help to increase objectivity in research by providing a clear and specific framework for testing and interpreting results. This can reduce bias and increase the reliability of research findings.

Limitations of Hypothesis

Some Limitations of the Hypothesis are as follows:

• Limited to observable phenomena: Hypotheses are limited to observable phenomena and cannot account for unobservable or intangible factors. This means that some research questions may not be amenable to hypothesis testing.
• May be inaccurate or incomplete: Hypotheses are based on existing knowledge and research, which may be incomplete or inaccurate. This can lead to flawed hypotheses and erroneous conclusions.
• May be biased: Hypotheses may be biased by the researcher’s own beliefs, values, or assumptions. This can lead to selective interpretation of data and a lack of objectivity in research.
• Cannot prove causation: A hypothesis can only show a correlation between variables, but it cannot prove causation. This requires further experimentation and analysis.
• Limited to specific contexts: Hypotheses are limited to specific contexts and may not be generalizable to other situations or populations. This means that results may not be applicable in other contexts or may require further testing.
• May be affected by chance : Hypotheses may be affected by chance or random variation, which can obscure or distort the true relationship between variables.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

You may also like

Data Collection – Methods Types and Examples

Delimitations in Research – Types, Examples and...

Research Process – Steps, Examples and Tips

Research Design – Types, Methods and Examples

Institutional Review Board – Application Sample...

Evaluating Research – Process, Examples and...

This is the Difference Between a Hypothesis and a Theory

What to Know A hypothesis is an assumption made before any research has been done. It is formed so that it can be tested to see if it might be true. A theory is a principle formed to explain the things already shown in data. Because of the rigors of experiment and control, it is much more likely that a theory will be true than a hypothesis.

As anyone who has worked in a laboratory or out in the field can tell you, science is about process: that of observing, making inferences about those observations, and then performing tests to see if the truth value of those inferences holds up. The scientific method is designed to be a rigorous procedure for acquiring knowledge about the world around us.

In scientific reasoning, a hypothesis is constructed before any applicable research has been done. A theory, on the other hand, is supported by evidence: it's a principle formed as an attempt to explain things that have already been substantiated by data.

Toward that end, science employs a particular vocabulary for describing how ideas are proposed, tested, and supported or disproven. And that's where we see the difference between a hypothesis and a theory .

A hypothesis is an assumption, something proposed for the sake of argument so that it can be tested to see if it might be true.

In the scientific method, the hypothesis is constructed before any applicable research has been done, apart from a basic background review. You ask a question, read up on what has been studied before, and then form a hypothesis.

What is a Hypothesis?

A hypothesis is usually tentative, an assumption or suggestion made strictly for the objective of being tested.

When a character which has been lost in a breed, reappears after a great number of generations, the most probable hypothesis is, not that the offspring suddenly takes after an ancestor some hundred generations distant, but that in each successive generation there has been a tendency to reproduce the character in question, which at last, under unknown favourable conditions, gains an ascendancy. Charles Darwin, On the Origin of Species , 1859 According to one widely reported hypothesis , cell-phone transmissions were disrupting the bees' navigational abilities. (Few experts took the cell-phone conjecture seriously; as one scientist said to me, "If that were the case, Dave Hackenberg's hives would have been dead a long time ago.") Elizabeth Kolbert, The New Yorker , 6 Aug. 2007

What is a Theory?

A theory , in contrast, is a principle that has been formed as an attempt to explain things that have already been substantiated by data. It is used in the names of a number of principles accepted in the scientific community, such as the Big Bang Theory . Because of the rigors of experimentation and control, its likelihood as truth is much higher than that of a hypothesis.

It is evident, on our theory , that coasts merely fringed by reefs cannot have subsided to any perceptible amount; and therefore they must, since the growth of their corals, either have remained stationary or have been upheaved. Now, it is remarkable how generally it can be shown, by the presence of upraised organic remains, that the fringed islands have been elevated: and so far, this is indirect evidence in favour of our theory . Charles Darwin, The Voyage of the Beagle , 1839 An example of a fundamental principle in physics, first proposed by Galileo in 1632 and extended by Einstein in 1905, is the following: All observers traveling at constant velocity relative to one another, should witness identical laws of nature. From this principle, Einstein derived his theory of special relativity. Alan Lightman, Harper's , December 2011

Non-Scientific Use

In non-scientific use, however, hypothesis and theory are often used interchangeably to mean simply an idea, speculation, or hunch (though theory is more common in this regard):

The theory of the teacher with all these immigrant kids was that if you spoke English loudly enough they would eventually understand. E. L. Doctorow, Loon Lake , 1979 Chicago is famous for asking questions for which there can be no boilerplate answers. Example: given the probability that the federal tax code, nondairy creamer, Dennis Rodman and the art of mime all came from outer space, name something else that has extraterrestrial origins and defend your hypothesis . John McCormick, Newsweek , 5 Apr. 1999 In his mind's eye, Miller saw his case suddenly taking form: Richard Bailey had Helen Brach killed because she was threatening to sue him over the horses she had purchased. It was, he realized, only a theory , but it was one he felt certain he could, in time, prove. Full of urgency, a man with a mission now that he had a hypothesis to guide him, he issued new orders to his troops: Find out everything you can about Richard Bailey and his crowd. Howard Blum, Vanity Fair , January 1995

And sometimes one term is used as a genus, or a means for defining the other:

Laplace's popular version of his astronomy, the Système du monde , was famous for introducing what came to be known as the nebular hypothesis , the theory that the solar system was formed by the condensation, through gradual cooling, of the gaseous atmosphere (the nebulae) surrounding the sun. Louis Menand, The Metaphysical Club , 2001 Researchers use this information to support the gateway drug theory — the hypothesis that using one intoxicating substance leads to future use of another. Jordy Byrd, The Pacific Northwest Inlander , 6 May 2015 Fox, the business and economics columnist for Time magazine, tells the story of the professors who enabled those abuses under the banner of the financial theory known as the efficient market hypothesis . Paul Krugman, The New York Times Book Review , 9 Aug. 2009

Incorrect Interpretations of "Theory"

Since this casual use does away with the distinctions upheld by the scientific community, hypothesis and theory are prone to being wrongly interpreted even when they are encountered in scientific contexts—or at least, contexts that allude to scientific study without making the critical distinction that scientists employ when weighing hypotheses and theories.

The most common occurrence is when theory is interpreted—and sometimes even gleefully seized upon—to mean something having less truth value than other scientific principles. (The word law applies to principles so firmly established that they are almost never questioned, such as the law of gravity.)

This mistake is one of projection: since we use theory in general use to mean something lightly speculated, then it's implied that scientists must be talking about the same level of uncertainty when they use theory to refer to their well-tested and reasoned principles.

The distinction has come to the forefront particularly on occasions when the content of science curricula in schools has been challenged—notably, when a school board in Georgia put stickers on textbooks stating that evolution was "a theory, not a fact, regarding the origin of living things." As Kenneth R. Miller, a cell biologist at Brown University, has said , a theory "doesn’t mean a hunch or a guess. A theory is a system of explanations that ties together a whole bunch of facts. It not only explains those facts, but predicts what you ought to find from other observations and experiments.”

While theories are never completely infallible, they form the basis of scientific reasoning because, as Miller said "to the best of our ability, we’ve tested them, and they’ve held up."

More Differences Explained

• Epidemic vs. Pandemic
• Diagnosis vs. Prognosis
• Treatment vs. Cure

Word of the Day

See Definitions and Examples »

Get Word of the Day daily email!

Games & Quizzes

Commonly Confused

'canceled' or 'cancelled', 'virus' vs. 'bacteria', your vs. you're: how to use them correctly, is it 'jail' or 'prison', 'deduction' vs. 'induction' vs. 'abduction', grammar & usage, more words you always have to look up, 'fewer' and 'less', 7 pairs of commonly confused words, more commonly misspelled words, every letter is silent, sometimes: a-z list of examples, great big list of beautiful and useless words, vol. 4, 9 other words for beautiful, why jaywalking is called jaywalking, the words of the week - may 17, birds say the darndest things.

• school Campus Bookshelves
• menu_book Bookshelves
• perm_media Learning Objects
• login Login
• how_to_reg Request Instructor Account
• hub Instructor Commons

Margin Size

• Download Page (PDF)
• Download Full Book (PDF)
• Periodic Table
• Physics Constants
• Scientific Calculator
• Reference & Cite
• Tools expand_more
• Readability

selected template will load here

This action is not available.

1.2: Theories, Hypotheses and Models

• Last updated
• Save as PDF
• Page ID 19359

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

\( \newcommand{\Span}{\mathrm{span}}\)

\( \newcommand{\id}{\mathrm{id}}\)

\( \newcommand{\kernel}{\mathrm{null}\,}\)

\( \newcommand{\range}{\mathrm{range}\,}\)

\( \newcommand{\RealPart}{\mathrm{Re}}\)

\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

\( \newcommand{\Argument}{\mathrm{Arg}}\)

\( \newcommand{\norm}[1]{\| #1 \|}\)

\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

\( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vectorC}[1]{\textbf{#1}} \)

\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

For the purpose of this textbook (and science in general), we introduce a distinction in what we mean by “theory”, “hypothesis”, and by “model”. We will consider a “theory” to be a set of statements (or an equation) that gives us a broad description, applicable to several phenomena and that allows us to make verifiable predictions. For example, Chloë’s Theory ( \(t \propto \sqrt{h}\) ) can be considered a theory. Specifically, we do not use the word theory in the context of “I have a theory about this...”

A “hypothesis” is a consequence of the theory that one can test. From Chloë’s Theory, we have the hypothesis that an object will take \(\sqrt{2}\) times longer to fall from \(1\:\text{m}\) than from \(2\:\text{m}\) . We can formulate the hypothesis based on the theory and then test that hypothesis. If the hypothesis is found to be invalidated by experiment, then either the theory is incorrect, or the hypothesis is not consistent with the theory.

A “model” is a situation-specific description of a phenomenon based on a theory , that allows us to make a specific prediction. Using the example from the previous section, our theory would be that the fall time of an object is proportional to the square root of the drop height, and a model would be applying that theory to describe a tennis ball falling by \(4.2\) m. From the model, we can form a testable hypothesis of how long it will take the tennis ball to fall that distance. It is important to note that a model will almost always be an approximation of the theory applied to describe a particular phenomenon. For example, if Chloë’s Theory is only valid in vacuum, and we use it to model the time that it take for an object to fall at the surface of the Earth, we may find that our model disagrees with experiment. We would not necessarily conclude that the theory is invalidated, if our model did not adequately apply the theory to describe the phenomenon (e.g. by forgetting to include the effect of air drag).

This textbook will introduce the theories from Classical Physics, which were mostly established and tested between the seventeenth and nineteenth centuries. We will take it as given that readers of this textbook are not likely to perform experiments that challenge those well-established theories. The main challenge will be, given a theory, to define a model that describes a particular situation, and then to test that model. This introductory physics course is thus focused on thinking of “doing physics” as the task of correctly modeling a situation.

Emma's Thoughts

What’s the difference between a model and a theory?

“Model” and “Theory” are sometimes used interchangeably among scientists. In physics, it is particularly important to distinguish between these two terms. A model provides an immediate understanding of something based on a theory.

For example, if you would like to model the launch of your toy rocket into space, you might run a computer simulation of the launch based on various theories of propulsion that you have learned. In this case, the model is the computer simulation, which describes what will happen to the rocket. This model depends on various theories that have been extensively tested such as Newton’s Laws of motion, Fluid dynamics, etc.

• “Model”: Your homemade rocket computer simulation
• “Theory”: Newton’s Laws of motion, Fluid dynamics

With this analogy, we can quickly see that the “model” and “theory” are not interchangeable. If they were, we would be saying that all of Newton’s Laws of Motion depend on the success of your piddly toy rocket computer simulation!

Exercise \(\PageIndex{2}\)

Models cannot be scientifically tested, only theories can be tested.

• Scientific Methods

What is Hypothesis?

We have heard of many hypotheses which have led to great inventions in science. Assumptions that are made on the basis of some evidence are known as hypotheses. In this article, let us learn in detail about the hypothesis and the type of hypothesis with examples.

A hypothesis is an assumption that is made based on some evidence. This is the initial point of any investigation that translates the research questions into predictions. It includes components like variables, population and the relation between the variables. A research hypothesis is a hypothesis that is used to test the relationship between two or more variables.

Characteristics of Hypothesis

Following are the characteristics of the hypothesis:

• The hypothesis should be clear and precise to consider it to be reliable.
• If the hypothesis is a relational hypothesis, then it should be stating the relationship between variables.
• The hypothesis must be specific and should have scope for conducting more tests.
• The way of explanation of the hypothesis must be very simple and it should also be understood that the simplicity of the hypothesis is not related to its significance.

Sources of Hypothesis

Following are the sources of hypothesis:

• The resemblance between the phenomenon.
• Observations from past studies, present-day experiences and from the competitors.
• Scientific theories.
• General patterns that influence the thinking process of people.

Types of Hypothesis

There are six forms of hypothesis and they are:

• Simple hypothesis
• Complex hypothesis
• Directional hypothesis
• Non-directional hypothesis
• Null hypothesis
• Associative and casual hypothesis

Simple Hypothesis

It shows a relationship between one dependent variable and a single independent variable. For example – If you eat more vegetables, you will lose weight faster. Here, eating more vegetables is an independent variable, while losing weight is the dependent variable.

Complex Hypothesis

It shows the relationship between two or more dependent variables and two or more independent variables. Eating more vegetables and fruits leads to weight loss, glowing skin, and reduces the risk of many diseases such as heart disease.

Directional Hypothesis

It shows how a researcher is intellectual and committed to a particular outcome. The relationship between the variables can also predict its nature. For example- children aged four years eating proper food over a five-year period are having higher IQ levels than children not having a proper meal. This shows the effect and direction of the effect.

Non-directional Hypothesis

It is used when there is no theory involved. It is a statement that a relationship exists between two variables, without predicting the exact nature (direction) of the relationship.

Null Hypothesis

It provides a statement which is contrary to the hypothesis. It’s a negative statement, and there is no relationship between independent and dependent variables. The symbol is denoted by “H O ”.

Associative and Causal Hypothesis

Associative hypothesis occurs when there is a change in one variable resulting in a change in the other variable. Whereas, the causal hypothesis proposes a cause and effect interaction between two or more variables.

Examples of Hypothesis

Following are the examples of hypotheses based on their types:

• Consumption of sugary drinks every day leads to obesity is an example of a simple hypothesis.
• All lilies have the same number of petals is an example of a null hypothesis.
• If a person gets 7 hours of sleep, then he will feel less fatigue than if he sleeps less. It is an example of a directional hypothesis.

Functions of Hypothesis

Following are the functions performed by the hypothesis:

• Hypothesis helps in making an observation and experiments possible.
• It becomes the start point for the investigation.
• Hypothesis helps in verifying the observations.
• It helps in directing the inquiries in the right direction.

How will Hypothesis help in the Scientific Method?

Researchers use hypotheses to put down their thoughts directing how the experiment would take place. Following are the steps that are involved in the scientific method:

• Formation of question
• Doing background research
• Creation of hypothesis
• Designing an experiment
• Collection of data
• Result analysis
• Summarizing the experiment
• Communicating the results

Frequently Asked Questions – FAQs

What is hypothesis.

A hypothesis is an assumption made based on some evidence.

Give an example of simple hypothesis?

What are the types of hypothesis.

Types of hypothesis are:

• Associative and Casual hypothesis

State true or false: Hypothesis is the initial point of any investigation that translates the research questions into a prediction.

Define complex hypothesis..

A complex hypothesis shows the relationship between two or more dependent variables and two or more independent variables.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

Visit BYJU’S for all Physics related queries and study materials

Your result is as below

Request OTP on Voice Call

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Post My Comment

• Share Share

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

Watch CBS News

'Young Sheldon' series finale airing May 16, Jim Parson and Mayim Bialik reprising 'Big Bang Theory' roles

May 15, 2024 / 2:31 PM EDT / CBS Pittsburgh

"Funeral" – YOUNG SHELDON ends its seven-year run with a must-see two-episode series finale. Jim Parsons and Mayim Bialik reprise their roles as Sheldon Cooper and Amy Farrah Fowler in an unforgettable hour of television, on the series finale of YOUNG SHELDON, Thursday, May 16 (8:00-8:30 PM, ET/PT) on the CBS Television Network, and streaming on Paramount+ ( live and on-demand for Paramount+ with SHOWTIME subscribers, or on-demand for Paramount+ Essential subscribers the day after the episode airs )*.  

Featured Local Savings

More from cbs news.

Sacramento County caregiver received oral sex from developmentally disabled patient, officials say

Jim Otto, "Mr. Raider" and Pro Football Hall of Famer, dies at 86

7 displaced after fire breaks out in Modesto alley

JetBlue to suspend SMF to JFK, BOS routes later in 2024

• Action/Adventure
• Children's/Family
• Documentary/Reality
• Amazon Prime Video

More From Decider

New Shows & Movies To Watch This Weekend: 'Bridgerton' Season 3 on...

Jax Taylor Admits His "Delivery Is Awful" In 'The Valley': "That's One Of...

What Happened to Regé-Jean Page? Did the Duke Bomb His Movie Star Career...

'9-1-1's Malcolm-Jamal Warner On Amir And Bobby, Working With Peter...

'Unfrosted' Has Everyone Wondering "What's The Deal With Jerry Seinfeld?"

Chrissy Teigen Stuns John Legend On 'The Drew Barrymore Show' With Reveal...

Brooke Shields Flashed Her ‘Mother of the Bride’ Co-Star Benjamin...

Andy Cohen Reveals Sarah Jessica Parker's Reaction When He Suggested Rosie...

Share this:.

• Click to share on Facebook (Opens in new window)
• Click to share on Twitter (Opens in new window)
• Click to share on WhatsApp (Opens in new window)
• Click to email a link to a friend (Opens in new window)
• Click to copy URL

When Will ‘Young Sheldon’ Season 7 Be on Netflix? What We Know

Where to stream:.

• Young Sheldon
• iain armitage

‘Young Sheldon’s Annie Potts Blasts CBS For Ending The Series Amid Strong Ratings: “A Stupid Business Move”

‘the big bang theory’ star jim parsons agrees that michael keaton would make a great older sheldon, jim parsons and mayim bialik return as beloved ‘big bang theory’ couple in ‘young sheldon’ finale, stream it or skip it: ‘young sheldon’ season 7 on cbs, where a tornado and a trip overseas shakes up the cooper family in the final season.

Young Sheldon has grown up.

The Big Bang Theory prequel spin-off starring Iain Armitage in the title role of young Sheldon Cooper came to a close with two back-to-back finale episodes that aired in May of 2024.

Jim Parsons , who originated the role of Sheldon Cooper on the CBS flagship series, even reprised his beloved role alongside his former co-star Mayim Bialik (who played his on-screen love interest, Amy Farrah Fowler) in the show’s final episode, titled “Memoir” — see a picture below!

The network announced their decision to conclude Young Sheldon after Season 7 in November 2023, prompting an emotional post from Armitage on Instagram shortly after.

Annie Potts , who portrayed Sheldon’s grandmother Meemaw, told Variety that bidding farewell to the series “was especially hard because she [was] completely unprepared.”

“I was shocked,” she continued. “I mean, the No. 1 show on network TV, No. 1 on Netflix . We’re, I think, all that people watch on TikTok besides a couple of recipes for pasta. It just seemed like such a stupid business move. Forgive me, but I don’t know.”

During an appearance on The Tonight Show in April, Parsons recently weighed in on the fan theory that Michael Keaton should take on the role of an older Sheldon , should another spin-off be created. While Parsons said he “doubt[s] that’s going to happen,” he noted that he “would be so excited  to have Michael Keaton added to the lineage of Sheldon portrayers.”

So, will Season 7 of Young Sheldon be on Netflix? If so, when will Young Sheldon Season 7 be on Netflix?

When will Season 7 of Young Sheldon be on Netflix?

Unfortunately, we don’t know exactly when just yet. However, Seasons 1-6 of Young Sheldon are currently streaming on Netflix, with Season 6 arriving on the streamer on Feb. 1, 2024 — about eight and a half months following the Season 6 broadcast finale on May 18, 2023. If we can anticipate a similar timeline with the Netflix release of Season 7, then the most recent, final installment should be available on Netflix around early 2025, as noted by The Direct .

Meanwhile, What’s on Netflix estimated that Season 7 will hit Netflix “sometime between September 2024 and February 2025.”

Is Season 7 of Young Sheldon streaming?

Yes! Young Sheldon Seasons 1-7 are streaming on Paramount+ .

Additionally, like Netflix, Seasons 1-6 of Young Sheldon are streaming on Max .

Ted Danson Tells Drew Barrymore That Woody Harrelson Was Once A No-Show To 'Cheers' Set Because He Was Watching The Berlin Wall Come Down

'The Resident's Malcolm-Jamal Warner Says Cast Would Be Open To Returning For A Season 7: "I Think We Would All Jump At The Opportunity"

Jenna Bush Hager Boldly Puts Jake Gyllenhaal’s 'SNL' Performance Down On 'Today': "I Don’t Know He’s That Good"

Stream It Or Skip It: ‘Monster’ on Netflix, a Dialogue-Free Indonesian Horror-Thriller

‘Bridgerton’ Season 3 Part 1 Climaxes With Penelope and Colin’s Steamy Carriage Ride

Does 'Yellowstone' Return Tonight? 'Yellowstone's Season 5, Part 2 Premiere Date, Streaming Info, And Kevin Costner Updates

• Category: Games

How Ninja Theory Strives to Make Senua the Most Human Character in Gaming

2017’s Hellblade: Senua’s Sacrifice was an exceedingly special game. A bold, brash direction for Ninja Theory, the decision to craft a short, narrative experience revolving around mental health was a brave leap, but one that ultimately paid off. Now, seven years later, the studio is gearing up to reveal a sequel to Senua’s story, built with the same love and care, but expanding on the debut in every conceivable way. 

In the run up to launch, we’ll be bringing you the story of Senua’s Saga: Hellblade II from inside the studio itself, as well as stories and lessons from Hellblade’s creative leads. This is Ninja Theory’s ultimate form, filled with industry-leading talent, groundbreaking technology, and one of the most unique approaches to game development you’ve ever seen to fulfil the ultimate goal – the pursuit of true immersion. 

If you need a catch-up on the story so far, Ninja Theory has put together a recap video (below) to refresh you on the events of Hellblade, Senua’s journey up to this point, and where she is as we prepare to experience the next step in Hellblade II.

During one particularly tense cutscene in Senua’s Saga: Hellblade II , I’m rooted in place as I watch Senua make a critical decision. After triumphing in a bloody battle against Viking slavers, she’s presented with the choice to save a new character from a terrible fate. Ninja Theory’s incredible performance capture and Unreal Engine 5 visuals allow me to scan every emotion soaring across Senua’s face – concern, worry, distrust – as she considers the consequences of rescuing someone in need.

In the first game, she might not have experienced the same internal conflict, but in the sequel, she’s making choices and processing emotions in new ways. Senua has not arrived here overnight. She’s gone through and will continue to go through an incredible narrative evolution in Hellblade II . In gaming, “growth” is so often mechanical, statistical – but the Hellblade series makes it a truly characterful experience, and it’s one of many things that makes Ninja Theory’s work stand out.

At the end of Hellblade: Senua’s Sacrifice , we see Senua come to terms with the loss of her love, Dillion, and soak in the physical and emotional journey she’s undertaken. Her sequel begins with the sum of that evolution; she’s hardened by her experiences, familiar and accepting of her condition, and tasked with a wider, more selfless goal. This emergence of Senua’s personality and extraversion of herself as she meets new people is an extraordinary step in making her feel real.

“Her purpose in the first game was very interior, the guilt that she felt over Dillion was a very personal mission to her,” says Lara Derham, Stage Director and Writer on Hellblade II . “While that drive is still present in this game, she’s pushing her goal a little more out of herself and into the world. It’s not about her personal love or her circumstances, it’s about preventing harm from coming to other people now.”

This evolution in Senua’s character is also outlined by a deeper understanding of herself, and how her experiences are no fault of her own. Professor Paul Fletcher, who has served as the mental health consultant on the Hellblade series, outlines the tonal shift between the two games: “The hallmark of [ Senua’s Sacrifice ] was it was totally enveloped by a darkness, and I think she’s emerging from that and finding a different meaning.”

“It’s not about [Senua’s] personal love or her circumstances, it’s about preventing harm from coming to other people now.” Lara Derham

She’s still faced with the ever-present mental load of the Furies – the name given to the competing voices in her head – but they’ve evolved with her, and have more external factors to react to as Senua meets new characters. They don’t really have a consistent tone of voice, they’re reactive to Senua’s state of mind; if she’s anxious or frightened, they tend to be a little more chaotic and overbearing, when things are calm, they’re quieter. This dynamic ruleset allows for brief moments of respite for the player, but it also showcases growth in how Senua manages her condition. 

According to Fletcher, this is in keeping with the clinical experiences of those living with psychosis – the voices do shift in what they mean to an individual.

“What I find interesting is that the voices now comment on what other people are doing, which was never really a part of the first game,” Fletcher says. “So they may encourage her to distrust what another person is saying, which really captures the dual reality that people might face in the midst of psychosis.”

Derham notes that most people have some sort of internal monologue active when we’re being spoken to, but it’s mostly not at the foreground, and it’s also not audible: “Imagine if every time someone was talking to you, you had that constant commentary on what they’re saying, maybe even arguing about the meaning. Every time Senua meets a new character, the voices are going to react to that.”

Fletcher accentuates this by describing a big step in the understanding of psychosis from a research perspective, which revolves around the meaningfulness of experiences for those living with psychosis. They’re not just neural noise – the experiences are constructed in the same way we all construct our reality.

“What’s exciting to me about Hellblade II is the growing interest that people can entertain two levels of reality,” Fletcher says. “Senua may have the darkness and the voices, but at the same time, she can recognise and be part of other people’s constructions too.”

“Senua may have the darkness and the voices, but at the same time, she can recognise and be part of other people’s constructions too.” Professor Paul Fletcher

Senua’s willingness to be part of other people’s stories – as we briefly mentioned earlier regarding her choice to save someone who is a stranger to her – also showcases another aspect of how she’s moving past certain experiences that made her so insular.

“Her psychosis had influenced her relationships with other people to a point where she was weary and withdrawn from the world, Derham says. “What we’re showing now is her starting to overcome that, depending on who she meets, and we’re showing that her perspective is just as valuable as anyone else’s.”

“Some people will react to her with harshness or horror, but some will see her differently, and she’ll find common ground and share positive experiences with them. It’s really exciting to watch Senua explore these interpersonal dynamics and relationships with other characters, and how she can help them.”

Senua’s Sacrifice is considered one of, if not the most authentic representation of psychosis in modern media, but Derham and Fletcher both agree that there may never be a truly complete depiction of the condition, as it “doesn’t remain static, and people’s relationship to it changes over time,” according to Derham.

One line in particular struck me during my time with Senua Saga: Hellblade II , which sees Senua calmly and assertively say “it’s not a prison, it’s a promise.” In this moment, we see Senua make peace with her past, and prepare to pursue her new goal confidently, not just for herself, but for the people around her. It’s in this line where I really feel her growth as a character, as a survivor, and more widely, as a woman living in a harsh world with a chronic, invisible condition.

“It was important for us to show that Senua is still on a journey,” Derham adds. “The courage and persistence that she showed in the first game is still evident, but it’s more self-directed now. She will still hear voices that’ll try to influence her, but she can choose whether to respond to that or not. She has agency in a way she didn’t have in the first game, and that evolution really is key.”

Senua is just one element of Hellblade II that has evolved significantly. The next piece in our takeover, right here, focuses on the game’s next level combat systems, and the performance capture that brought it to life .

Senua’s Saga: Hellblade II will be released on May 21, 2024 for Xbox Series X|S, Windows PC, Steam and Cloud – and will be available with Xbox Game Pass and PC Game Pass day one.