what is vagueness in critical thinking

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Chapter 9: Vagueness, Ambiguity, and Philosophy

If you prefer a video version of this chapter, click below:

Vague and Ambiguous Video

Some disagreements are merely verbal, which means clearly defining terms can resolve such disagreements. Vague and ambiguous words lead to the most common types of verbal disagreement.

Vagueness refers to a lack of clarity in meaning. For example, Go down the road a ways and then turn right  is vague because “a ways” does not precisely explain how far one should go down the road.

Ambiguity is when there is more than one clear meaning, and it is difficult to choose which meaning was intended. For example, Paul went to the bank is ambiguous because bank could mean a river bank or a financial institution. He was cut could mean he was cut from the team or he was cut by a sharp object.

Another example: The stool is in the garden is ambiguous because stool could mean poop or chair.

Exercise 1 : Explain why these statements are vague. 1. I’ll be back later. 2. We should raise taxes on the wealthy.

Exercise 2 : Explain why these statements are ambiguous. 1. The new pitcher is great. 2. I am renting the new apartment.

Exercise 3 : Are the following statements ambiguous? Discuss/Explain. 1. Mother of eight makes a hole in one. 2. Kids make nutritious snacks. 3. God makes sense.

Answers: Later (2 hours or 2 days?), wealthy (50,000 or 100,000 or 1,000,000?), pitcher (container or baseball player?), renting (landlord or tenant?), Mother of eight (playing golf or put a hole in one of her children?), kids/snacks (kids make snacks or kids are the snacks?), God (God is logically consistent or God creates logic?). 

Application and Value Precisely define your terms. This will reduce vagueness and ambiguity so that you are not talking past each other. It will also help you avoid the equivocation fallacy.

Logicians have taken this topic much further by identifying several fallacies of ambiguity (i.e. composition, division, equivocation, amphiboly, and accent), distinguishing ambiguity from indexicality, polsymey, and sense generality, comparing syntactic and semantic ambiguity, and exploring deeper issues related to this distinction.

*Thank you to Lawrence Pasternack at Oklahoma State University for some of the examples in this chapter.

Return to Logic Home                        Next (Chapter 10: Deductive & Inductive Arguments)

If you cannot be nice then at least be vague.

What goes "ha ha ha, plop?" Someone laughing his head off.

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Critical Thinking: Definitions: Vagueness, Ambiguity, Euphemisms, Emotional Language, and the Fallacy of Equivocation

Introduction Many a philosopher has argued that “happiness” is  the  or one of the most important elements of human life.  Some even go so far as to say that an action is moral to the degree that it brings about happiness.  Whether we accept such assertions will have much to do with what is meant by “happiness.”

If all that is meant by “happiness” is that momentary good feeling you can get from eating cake or doing crack, then we will probably be less inclined to accept happiness as a measuring stick for morality.  If we mean by “happiness” something closer to Aristotle’s “eudaimonia” (i.e., human flourishing), then we might be more persuaded to accept the assertion.

So, how does this all fit in with critical thinking?  As you may have guessed  how  terms are used has much to do with whether we find a premise or conclusion acceptable.  So, in this next segment we are going to look at how to evaluate the way in which a term is being used and how that evaluation fits with how much we accept a premise.

Interpretation 1:  Context By now, you should be alert to the role of context in interpretation.  Regarding a word’s definition, context can impact our interpretation in several ways.

The first is  time .  A word’s meanings change over time.  For example, if we are reading an 19th Century book and a character describes all the guests as being “very gay,” it probably doesn’t mean the same thing it would mean today.  It does not make sense to impose our current meanings of words that had different meanings in the past.  We must be sensitive to temporal context.

The next is  audience .  For example, “theory” means something very different in daily conversation than what it means in a scientific context.  The colloquial meaning is something closer to “hypothesis,” while the scientific meaning is an account of nature that has been verified and supported through (often) multiple lines of independent evidence, and from which we can make accurate predictions.  So,  I should interpret “theory” differently depending on the context identifiable through the audience for which the argument is written.

Euphemisms and Emotional Language A  euphemism  is the substitution of an offensive or disturbing word with a more polite or socially/politically acceptable word.   We might say of a child that he has behavioural challenges instead of telling his parents that their kid is a little sh*t.   The 80s marked the beginning of what some people thought was politically correct overkill.  People would joke that now we have to call anyone who is short, “vertically challenged.”

Yesterday, I took my dogs to the vet and “had their anal glands expelled.”  This sounds much nicer than what actually occurred.   Long story short, people use euphemisms to express ideas in less jarring and/or offensive ways.

Like most things, there are  legitimate and illegitimate uses of euphemisms    In a legitimate use, the primary idea contained in the word remains intact.   In an illegitimate use, important content is obscured.  Consider the US military’s term “collateral damage” to indicate accidental killing of innocent civilians.  The important content of what actually occurred is lost/obscured by the sanitized term.

An example from the corporate world might be “downsizing.”  It sounds pretty harmless but when we look at the essential features of downsizing (many people losing their jobs) we can reasonably claim that the term is misleading.

The most fertile ground for illegitimate euphemisms is in politics.  As one of my political science professors once said, if a country has “People’s Republic of…” or “Democratic Republic of …”, you can pretty much guarantee that they are anything but what their titles profess.

Determining whether a euphemism is legitimate or illegitimate will not always be obvious, but with a little critical thinking you should be able to identify instances.

Emotional language  uses words that are intentionally chosen to evoke or present an emotional bias.  Taking their cue from Nazi propaganda, politicians often use emotional language.  For example we commonly hear phrases like “militant homosexual agenda” (but I thought gays weren’t allowed in the military until recently…); “bleeding-heart liberal”; “religious fanatics”; “hysterical” or “bigoted” opponents, etc…

In the context of critical thinking, the use of emotional language should be a red flag.  Essentially, anyone who uses strong emotional language is  assuming  that their position is right and accurate.  But as we know by know, there is a tremendous difference between assuming something to be true and arguing for its truth.  If something is so obviously true, then we would reasonably suppose there’s an argument for it too!

Let’s take the example “militant homosexual agenda.”  Both “militant” and “agenda” are emotionally evocative.  But we need to ask: if they’re so militant, then surely there must be evidence to support this assertion…and we should demand it before accepting the assertion.

“Agenda” also has a negative connotation.  Does every group who wants equal right have an “agenda”?  It really depends on what side of the political spectrum you sit on.  “Bleeding-heart liberals” will argue that the NRA has an “agenda” too.  Instead, we should ask for clarification on what is meant by “agenda” before we evaluate whether it’s desirable or not.

Another of my favorite emotional words is “activist judge.”  This is another one where it really depends on what side of the political aisle you’re sitting on.  If a judge interprets the law in a way that rules against your “team,” then they’re activists.

Euphemisms, Emotional Language, and Argument Construction Returning back to our theme of being good critical thinkers, we can also take this information into account when we construct our own arguments.  That is, if we think that something is obviously good or bad or true, then we should provide an argument for it, rather than use euphemisms and emotional language.  A good argument gets the point across without relying on either of these.

Vagueness and Ambiguity Vagueness When a definition is  vague  it has no specific meaning for the intended audience.  Here are a few examples of vague definitions from the goldmine of pseudo-wisdom that is Depak Chopra:

Happiness is a continuation of happenings which are not resisted. To think is to practice brain chemistry. A person is a pattern of behavior, of a larger awareness.

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One thought on “ critical thinking: definitions: vagueness, ambiguity, euphemisms, emotional language, and the fallacy of equivocation ”.

Thank you so much for the very useful information.

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Definition and Examples of Vagueness in Language

Joanna Cepuchowicz / EyeEm / Getty Images

• An Introduction to Punctuation
• Ph.D., Rhetoric and English, University of Georgia
• M.A., Modern English and American Literature, University of Leicester
• B.A., English, State University of New York

In speech or writing, vagueness is the imprecise or unclear use of language. Contrast this term with clarity and specificity . As an adjective, the word becomes vague .

Although vagueness often occurs unintentionally, it may also be employed as a deliberate rhetorical strategy to avoid dealing with an issue or responding directly to a question. Macagno and Walton note that vagueness "can also be introduced for the purpose of allowing the speaker to redefine the concept he wishes to use" ( Emotive Language in Argumentation , 2014).

In  Vagueness as a Political Strategy (2013), Giuseppina Scotto di Carlo observes that vagueness is "a pervasive phenomenon in natural language , as it seems to be expressed through nearly all linguistic categories." In short, as philosopher Ludwig Wittgenstein said, "Vagueness is an essential feature of the language." 

From the Latin, "wandering"

Examples and Observations

"Use details . Don't be vague ." -Adrienne Dowhan et al., Essays That Will Get You into College , 3rd ed. Barron's, 2009

Vague Words and Phrases

" Vagueness arises from the use of terms that are inherently vague. The cabinet minister who says,

My officials are monitoring this situation very closely, and I can promise that we shall take all appropriate measures to ensure that the situation is resolved in a way that is fair to all the parties involved.

should be challenged on grounds of vagueness. Despite the appearance of having promised to do something specific, the minster has not really promised to do anything at all. What are appropriate measures ? They could be anything or nothing.

What does fair to all the parties mean? We have no clear idea. Such phrases are inherently vague and can mean almost anything. People who use them should be challenged to say more precisely what they mean."

-Willam Hughes and Jonathan Lavery, Critical Thinking: An Introduction to the Basic Skills , 5th ed. Broadview Press, 2008

Vagueness Versus Specificity

" Vague or abstract words can create wrong or confusing meanings in your receiver's mind. They state a general idea but leave the precise meaning to the receiver's interpretation...The following examples show vague or abstract words and ways to make them specific and precise:

• many - 1,000 or 500 to 1,000
• early - 5 a.m.
• hot - 100 degrees Fahrenheit
• most - 89.9 percent
• others - business administration students
• poor student - has a 1.6 grade point average (4.0 = A)
• very rich - a millionaire
• soon - 7 p.m., Tuesday
• furniture - an oak desk

Notice in the preceding examples how adding a few words makes the meaning precise."

Varieties of Vagueness

"One characteristic of vagueness ...is that it is related to the degree of formality, or rather informality, of the situation; the less formal the situation the more vagueness there will be..."

Vagueness in Oratory

"[T]he need in oratory of the specific example , either in place of or immediately following the general statement, cannot be too strongly urged. Generalizations alone have no persuasive value. And yet this truth is constantly overlooked by public speakers . How often do we hear the common criticism of the typically weak, impressionless address: 'Platitudes and glittering generalities.' In one of George Ade's Forty Modern Fables a man has certain stock phrases which he uniformly uses in all discussions pertaining to art, literature, and music; and the moral is, 'For parlor use, the vague generality is a life-saver.' But for the public speaker, generalizations are useless for either imparting or impressing his thought; a single concrete example has far more convincing and persuasive force."

Vagueness in Survey Questions

"Vague words are very common on surveys. A word is vague when it is not obvious to a respondent what referents (e.g., instances, cases, examples) fall under the umbrella of the word's intended meaning...For example, consider the question, 'How many members of your household work?' This question has several vague words, most of which would be missed by the vast majority of respondents. It could be argued that members, household , and work are all vague words. Who counts as being a member of the household?...What falls under the category of household?... What counts as someone working?... Vagueness is ubiquitous in most survey questions."

Ambiguity Versus Vagueness

"The difference between ambiguity and vagueness is a matter of whether two or more meanings associated with a given phonological form are distinct (ambiguous), or united as non-distinguished subcases of a single, more general meaning (vague). A standard example of ambiguity is bank 'financial institution' vs. bank 'land at river's edge,' where the meanings are intuitively quite separate; in aunt 'father's sister' vs. aunt 'mother's sister,' however, the meanings are intuitively united into one, 'parent's sister.' Thus ambiguity corresponds to separation, and vagueness to unity, of different meanings."

Vagueness in Sentences and Words

"The primary application of 'vague' is to sentences, not to words. But the vagueness of a sentence does not imply that vagueness of every constituent word. One vague word is enough. It may be essentially doubtful whether this is a red shape because it is essentially doubtful whether this is red, although beyond doubt that it is a shape. The vagueness of 'This is a red shape' does not imply the vagueness of 'This is a shape.'"

• A. C. Krizan, Patricia Merrier, Joyce Logan, and Karen Williams,  Business Communication , 8th ed. South-Western, Cengage Learning, 2011
• (Anna-Brita Stenström, Gisle Andersen, and Ingrid Kristine Hasund,  Trends in Teenage Talk: Corpus Compilation, Analysis, and Findings . John Benjamins, 2002)
• Edwin Du Bois Shurter,  The Rhetoric of Oratory . Macmillan, 1911
• Arthur C. Graesser, "Question Interpretation."  Polling America: An Encyclopedia of Public Opinion , ed. by Samuel J. Best and Benjamin Radcliff. Greenwood Press, 2005
• David Tuggy, "Ambiguity, Polysemy, and Vagueness."  Cognitive Linguistics: Basic Readings , ed. by Dirk Geeraerts. Mouton de Gruyter, 2006
• Timothy Williamson,  Vagueness . Routledge, 1994
• Specificity in Writing
• What Is a Natural Language?
• Indeterminacy (Language)
• Glittering Generality: A Virtue Word
• Diction - Word Choice and Enunciation
• Equivocation (Fallacy)
• Definition and Examples of Anti-Rhetoric
• Definition and Examples of Language Contact
• AP English Exam: 101 Key Terms
• Definition and Examples of Speakers in Language Studies
• English Language Sentence Structure
• What Is Entailment in Semantics?
• Pejoration in Language
• Information Content (Language)
• Examples of Indexicality (Language)
• What is Lexicology?

Middle Way Society

An ethical approach to a better life, by integrating desires and avoiding dogmatic extremes, critical thinking 5: ambiguity.

Arguments are, of course, made out of language, and language is always ambiguous to some extent. If you apply the embodied meaning understanding of the meaning of language, there can never be any precise equivalence between the meaning of a word, sentence or other symbol for any two people. Each understands that meaning in relation to their own body. We do manage to communicate, but only on a more-or-less  basis. If your language means something similar enough to you and to your audience, you will communicate to an extent. The same problem applies between you and your past or future self. The words you wrote in your diary ten years ago may not mean the same now.

However, issues of ambiguity are more striking in some cases than others, and where they arise more strongly in argument they are more likely to create misunderstandings and conflicts. There are two types of problematic ambiguity: ambiguity proper, which is multiple meanings for the same word or term, and vagueness, which is the lack of clear boundaries on the application of a term.

Very often, but not always, ambiguities and vagueness are just resolved by contextual judgement. For example, if I say “I’m going to the bank” and I’m carrying a chequebook, you don’t think I’m going to sit by the side of a river; and if I’m carrying a picnic basket, you don’t tend to think I’m going to have a relaxed picnic inside my local branch of HBOS. Vagueness also often does not matter: if I tell you I’m going for “a short walk”, you don’t need to know exactly how many metres I will be walking – and indeed, nor do I.

Ambiguity that affects the justification of an argument is known as equivocation . If you use the same term in a reason and a conclusion, but don’t realise that they have an importantly different meaning in each case, the justification of your conclusion is likely to be seriously undermined. Abstract words are most prone to this: for example, life, civilised, natural, beautiful, meaning, good, art , and (oddly enough) logical . Equivocal arguments often have a baggy abstract term in the middle of them that is in need of a bit of clarification, and if it’s not clarified needless disputes can ensue. Here’s an example of a dispute between Ken and Thelma:

Ken: Wind turbines are a natural way of generating energy without burning fossil fuel, so the government should be investing in them much faster.

Thelma: Natural! You’ve got to be joking! They’re the most artificial monstrosities you ever saw! A blot on the landscape!

Here Ken is using the idea of the “naturalness” of wind turbines as the basis of his argument for them, but “natural” obviously means something quite different to Thelma. They will not be able to make progress in resolving their disagreement until they have resolved what they mean by this deeply ambiguous word. They can do this by defining what each means by the term. Let’s imagine that the conversation continues in a helpful direction.

Ken:  So what do you mean by “natural”, there, Josh? Is it to do with what wind turbines look like?

Thelma: Of course! It can’t be natural if it’s a big noisy metal contraption sticking up on a green hill, can it?

Ken: So “natural” means not noisy and metal? What does it mean more positively?

Thelma: In harmony with the landscape. Trees and pastures are natural, but wind turbines aren’t.

Ken: What about buildings? Are they natural?

Thelma: Most of them aren’t, but the more traditional buildings like stone barns are more natural-looking than modern buildings.

Ken: So, by “natural” you mean that it has an appearance that you feel blends harmoniously with the landscape?

Thelma: That’s right.

Ken: Well, that’s not what I meant when I said that wind turbines are a natural way of generating energy. I meant that they are sustainable and don’t cause pollution. They cause much less disruption to the eco-system as a whole when you compare them to a coal-fired power station, for example.

Whether or not Ken and Thelma can now resolve their disagreement about wind turbines, at least now they have clarified what they are arguing about.

1. Jake (looking at object pictured on right in an art gallery): How can that be art? This guy has just bought a urinal and stuck it in an art gallery!

Sandip: That’s precisely it. He’s stuck it in an art gallery. That makes it art.

2. Mother : I thought you were going to go to bed early tonight! It’s 11.30 already!

Teenaged son: But I went to bed at 12.30 last night.

3. Unionist: The management’s pay offer is only a 0.8% increase on last year’s pay, when the inflation rate is 2.3%. Some other workers in the same group are getting 2.7% rises. That makes the offer both unfair and unreasonable.

Manager: The pay offer is in line with the going market rate in the industry. That makes it perfectly fair. It is all that the company can afford without threatening its competitiveness. It would not be reasonable to expect the company to go out of business to meet an excessive pay settlement. 

4. Camilla: The Quakers are not really Christians. They don’t believe in the Trinity, or that the Bible is the Word of God.

Billy: But they have an idea of God, and they come from the Christian tradition. They rely on personal experience of God rather than on the Bible or doctrines, that’s all. 

5. Rosie : Your directions were rubbish! You said to go straight ahead by the Dog and Duck Inn, but there isn’t any road straight ahead at the Dog and Duck Inn, just left and right. I didn’t know which way to go! I was wandering around for ages!

Lee: The directions were perfectly clear. You just have to interpret them with common sense, that’s all! There’s a staggered junction by the Dog and Duck Inn, which means you go left and then right, but that’s practically the same as straight ahead. It should have been obvious!

3 thoughts on “ Critical Thinking 5: Ambiguity ”

1. The question what is ‘art’ – the word art used here is with a lack of clear boundaries so there is vagueness? ‘Urinal,’ is its use only functional or has it become an art object – more than one meaning -ambiguity proper? 2. What is early, referring to ‘time’ – vague or maybe ambiguous proper? 3. ‘Pay offer’ an equivical argument? Fear of going out of business – equivocation? 4. ‘Christians’ – differing beliefs – ambiguity proper? ‘experience of God’ equivocal argument? 5. ‘Go straight ahead’ -vagueness, lack of boundaries? Interpret ‘with common sense ‘ equivocal argument?

1. Art is the ambiguous term. Jake appears to view art as something that is the product of skill and application and is possibly ethically pleasing to look at. Sandip seems to take the view that an object is or becomes a work of art if it is displayed in an art gallery. 2. Early is the ambiguous term, with mother and son believing early to be before and after 11.30 respectively. 3. Fair and reasonable and pay offer are the ambiguous terms. The unionist believes a fair and reasonable pay offer is one that is in line with inflation and with the pay rises of other workers in the same group. The manager believes such a pay offer is one that is in line with the going rate of the industry and is set at a level that doesn’t compromise the company’s competitiveness. 4. The main ambiguity here is arguably what it means to be a Christian. For Camilla, a Christian needs to believe in the Trinity or that the Bible is the word of God. For Billy, the Quakers conform to being Christians by coming from the Christian tradition and relying on personal experience of God rather than the Bible or doctrines. 5. In this example the ambiguous term is directions. Rosie believes they should be written in such a way so they can be interpreted literally. Lee believes directions need to be interpreted with a degree of common sense.

Here are my answers: 1. I’d agree with Barry’s account of the two meanings of ‘art’ here. I didn’t think of ‘urinal’ being ambiguous, but I guess it is, as you say, Norma. 2. The ambiguous term is ‘early’. The mother seems to have a fixed scale determining what is ‘early’, by which 11.30 would not be so. The son think of ‘early’ relative to other occasions. 3. ‘Fair’ and ‘reasonable’ are the key ambiguous terms here. I agree with Barry’s explanation of them 4. Here the definition of ‘Christian’ is ambiguous, one using belief as the criterion and the other using relationship to a tradition. 5. The ambiguous term here, as Norma spotted, is ‘straight ahead’. This is a vague term when applied to a crossroads, because we don’t know how far a junction can be staggered but still count as ‘straight ahead’. I’m not sure that ‘directions’ is especially ambiguous – the two people agree about what directions are but just differ on what constitutes a good example of them.

The last example is based on a real misunderstanding I had with my wife Viryanaya. She has a poor sense of direction, and I find it easy to constantly underestimate the explicitness of the directions she needs – they have to be extremely explicit and unambiguous. It also seems to be a widespread problem that written or oral directions are inadequate for the more geographically challenged. If people are unable to follow directions, this can then create a feedback loop whereby a lack of confidence about directions is reinforced by the gap between different people’s ability to interpret the language used to describe them.

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Pursuing Truth: A Guide to Critical Thinking

Chapter 9 informal fallacies.

A fallacy is a mistake in reasoning. A formal fallacy is a fallacy that can be identified merely by examining the argument’s form or using a tool like a truth table. An informal fallacy cannot be detected from the argument’s form. There are no foolproof tools for detecting informal fallacies. Unlike validity, these fallacies can occur in degrees. Sometimes, it is clear that a fallacy has been committed, at other times, there can be legitimate questions about whether a fallacy has been committed.

9.1 Emotions and Critical Thinking

There are two important uses of language that play an important role in critical thinking. The first is to convey information, or what is sometimes called cognitive content. The premises and the conclusion of an argument all have cognitive content. It is on the basis of the information they convey that we can evaluate them as true or false. Another use of language, however, is to express emotion, which often tends to evoke similar feelings in the audience. The emotions that are expressed by the language is its emotive content.

Good critical thinkers are persuaded by relevant cognitive content, and are not unduly persuaded by irrelevant emotive content.

9.2 Slanters

Slanters are words or phrases that are used to manipulate by using emotive language. Slanters can have both positive and negative connotations. Slanters are types of non-argumentative persuasion. Sometimes, people will use them innocently, maybe because they have passionate feelings about the subject being discussed. Other time, though, they are used because the speaker knows that he does not have a good argument for his position. They are ways for people to affect the beliefs of others without offering reasons for their positions.

9.2.1 Euphemisms and Dysphemisms

Different words and phrases passages can have the same cognitive content but differ in their emotive content. A euphemism is a positive synonym for some neutral term. A dysphemism is a negative synonym. For example, think of the words that we use to talk about the death of a pet:

• Neutral: euthanize
• Euphemism: put to sleep
• Dysphemism: ?

Euphemisms are common in the military and in advertising. Here are some examples:

• Enhanced interrogation methods
• Collateral damage
• Depopulated area
• Pre-owned, Pre-loved
• Genuine imitation leather

In other cases, a person may use a euphemism when they have been caught doing something wrong, but want to minimize the wrongness of the action. I heard a politician once, who was caught telling a falsehood, admit to having “committed terminological inexactitude.”

Dysphemisms convey a negative attitude towards something. Examples of dysphemisms include:

• Cancer stick
• Dead tree edition

9.2.2 Innuendoes

Innuendoes imply something by what is not said. A common scene in crime films has a gangster go into a store and say something like “Nice store you got. It would be a shame if anything happened to it.” Notice that he didn’t actually say he would damage the store, although he certainly implied it.

Another use of an innuendo is to condemn with faint praise. Imagine receiving a reference letter for a student applying to graduate school. The letter only says that the student was never late to class. The implication is that her punctuality is the best that can be said of her.

Finally, there is the apophasis, which is mentioning something by saying that it won’t be mentioned. For example, “I’m not going to talk about your failure to turn assignments in on time.”

9.2.3 Weaselers

A weaseler is a way of qualifying a claim in order to avoid criticism. Weaselers include words and phrases like “perhaps,” “there’s a good chance that,” and “it’s possible that.” A weaseler that is common in advertising is “up to” — “By using our diet plan, you can lose up to ten pounds in a month.” Notice that “up to ten pounds” means “no more than ten pounds.” So, if a customer loses no weight at all, then there is no grounds for a lawsuit.

9.2.4 Downplayers

A downplayer is a way of making something seem less important than it is. The most common downplayers are “mere, merely, and so-called.” A person might say, “That’s merely your opinion” to avoid having to respond with facts. A politician might talk about his opponent’s “so-called” plan to cut spending, implying that it isn’t much of a plan at all. Improper use of quotation marks can also serve as a downplayer.

9.2.5 Proof surrogate

A proof surrogate offers no real support, but just claims that support exists. Examples are using “studies show” without saying what those studies are and where they can be found. Another proof surrogate is just to say that “It’s obvious that….” Doing so implies that proof is simply not needed.

9.2.6 Hyperbole

Hyperbole is an inappropriate or extreme exaggeration. “Taking critical thinking is the most exciting thing you’ll do in your whole life!” Since it is an extreme exaggeration, no one will be fooled into believing it, so what’s the danger? The danger of hyperbole is that once the exaggeration is made, the listener is then prepared to accept a weaker version of the statement. The weaker version, compared to the extreme exaggeration, sounds more believable.

9.3 Fallacies of Ambiguity and Vagueness

An ambiguous word or phrase is one that has more than one meaning. “Bank” is an ambiguous term, it can refer to a financial institution, a riverbank, a kind of basketball or pool shot, etc. A vague term is one that does not have a precise meaning. That is, there will be cases where a vague term clearly applies, cases in which it clearly does not apply, and cases in the middle where it’s just not clear whether it applies. Terms like “rich” and “heap” are vague terms.

9.3.1 Equivocation

The fallacy of equivocation is committed by using the same term in two different senses in the same argument. Here is my favorite example:

• God is love.
• Love is blind
• Ray Charles is blind.
• Ray Charles is God.

There are several things wrong with this argument, one of them is equivocating on “blind.” To say that love is blind, is to say that people overlooks the faults of those they love. To say that Ray Charles is blind is to say that he cannot physically see anything, not that he just overlooks things.

9.3.2 Amphiboly

Amphibolies rely on syntactic ambiguities. Those are ambiguities that result from the arrangement of the words. Church bulletin bloopers are good places to find amphibolies: “The Rev. Adams spoke briefly, much to the delight of his audience.”

9.3.3 Accent

The fallacy of accent is an equivocation resulting from accenting different words in a sentence. Think about the different meanings that are implied from accenting different words in this sentence: “I didn’t take the exam yesterday.”

9.3.4 Division and Composition

The last two fallacies of ambiguity are division and composition. The fallacy of division improperly attributes a property of the whole to its parts. The fallacy of division improperly attributes a property of the parts to the whole. Here is an example of division: “That wall weighs more than 500 pounds, so each brick in it weighs more than 500 pounds.” A similar example of composition is “Each brick in that wall weighs less than a pound, so the entire wall weighs less than a pound.”

Some properties, however, can be attributed from the parts to the whole or the whole to the parts. For example, “Each link in that chain is solid gold, so the whole chain is solid gold.”

9.3.5 Line-Drawing Fallacy

The line-drawing fallacy is a fallacy of vagueness, having the form “Since there is no precise line that can be drawnd between A and not-A, there is no real difference between A and not-A.” Example: “Since no one can say where the line should be drawn between legitimate uses of force and excessive uses of force, then no one can honestly claim that any use of force is excessive.”

9.4 Fallacies of Relevance

A good critical thinker will offer arguments that have premises that are logically relevant to their conclusions. A fallacy of relevance is committed when the premises of the argument are not logically relevant to the truth of the conclusion. They may be, however, psychologically relevant, so that we can be deceived in thinking that the argument is valid, when in fact it is not.

9.4.1 Ad Hominem

The Ad Hominem fallacy is committed by attacking the person giving the argument, rather than responding to the argument itself. There are four common types:

9.4.1.1 Personal Attack

This is also known as an ad hominem abusive. This is committed when one verbally attacks the person giving the argument instead of responding to the argument itself. For example:

Jack: “There are so many unexplored planets out there. Surely, there must be life somewhere out there”

Jill: “You can’t be right, you’re just a loser who watches too much television.”

9.4.1.2 Circumstantial Ad Hominem

A person commits the circumstantial ad hominem by referring to circumstances that discredit the arguer. This is often a charge of bias or vested interest. A person has a vested interest when they stand to gain, financially or otherwise, by something. For example, a doctor has a vested interest in a pharmaceutical study when she owns stock in the company that produces the drug. Bias or vested interest is a good reason to examine an argument carefully, but not a good reason to simply dismiss it.

Jill: John has made an excellent case for increasing the budget of the church’s youth program.

Jack: Of course he would say that — he’s the youth minister! You can just forget everything he said.

9.4.1.3 Tu Quoque

This is also known as a pseudorefutation. It accuses the arguer of hypocrisy. Example: “Don’t tell me I shouldn’t start smoking. I know how many packs a day you inhale!”

A person’s behavior may very well be inconsistent with their argument, but that doesn’t mean that the argument is bad.

9.4.1.4 Poisoning the Well

Poisoning the well is an ad hominem committed before the arguer has spoken. The goal is to provide harmful information about the speaker to preemptively discredit anything that the speaker might say. Any of the previous examples can be turned into examples of poisoning the well. For example: “John is about make his case for increasing the church’s youth budget. Don’t pay any attention to him — he’s the youth minister, what else would he say?”

9.4.2 Appeal to Force

The appeal to force, also called scare tactics, is a threat, either explicit or implicit. For example, imagine a student saying to a professor, “I deserve an A because my father is a major donor to this university and a very good friend of the dean.” The appeal to force tries to instill fear in the listener, and to be fallacious, the fear must be irrelevant to the truth of the claim. These are common in both advertising and politics. An example of an appeal to force in advertising would be an ad for a Medicare supplement policy with an elderly woman weeping in front of a pile of unpaid bills. The advertisement works by making the viewer afraid of ending up like the person in the commercial.

9.4.3 Appeal to Pity

The appeal to pity is like the appeal to force, except that the goal is to evoke pity, not fear. For example: “I deserve an A because my mother is very ill, and I had to spend most of my time caring for her this semester.”

9.4.4 Popular Appeal

This is also called appeal to the people. Here, the goal is to use the desire to be loved, admired, accepted, etc. to get others to accept the conclusion. Two important types are the bandwagon fallacy and the appeal to vanity.

9.4.4.1 Bandwagon

The bandwagon fallacy tells the listener that since everyone does, or believes, something, then they should too.

Example: “Everyone supports Smith for president. You need to get with the program and support him too!”

9.4.4.2 Appeal to Vanity

This is a claim that you will be admired if you do this. Unlike bandwagon, which claims that everyone does this, the appeal to vanity is usually about something that not everyone can do or have.

Example: “Wear a Rolex — that way everyone will know that you’re not just somebody.”

9.4.5 Appeal to Ignorance

9.4.5.1 burden of proof.

On most issues, one side will have the burden of proof. That means that if that side fails to make its case, then the other side wins by default. There are two standard rules for determining burden of proof:

• Especially for existence claims, the side making the positive case has the burden of proof.
• The side making the more implausible claim has the burden of proof.

Sometimes, these conditions can conflict. Here is an example:

Jill: Surely, there are species of insects that we have not yet discovered.

Jack: I don’t think that’s true.

Who has the burden of proof? Jill is making a positive existence claim, but it is one that very plausible. That makes Jack’s claim very implausible. In this case, I’d say that Jack has the burden of proof.

9.4.5.2 The Law

One area where these rules do not apply is the American legal system. There, the prosecution always has the burden of proof. That is, if the prosecution fails to make its case against the defendant, then the defense wins.

Burden of proof should not be confused with standard of proof. Burden of proof is concerned with who needs to make their case. Standard of proof is concerned with how strong a case needs to be made. There are four different levels of standard of proof in the law:

• Beyond a reasonable doubt
• Clear and convincing evidence
• Preponderance of evidence
• Probable cause

Criminal cases use the highest standard of proof, which is “beyond a reasonable doubt.” This is a high degree of probability. It does not mean that no doubt at all is possible, but that any doubt, given the evidence, would be unreasonable. The next two level are used in civil cases. Most civil cases are tried at the “preponderance of evidence” level. This means that, given the evidence, it is more likely that the defendant is liable than not. Clear and convincing evidence is a standard of proof between preponderance of evidence and beyond a reasonable doubt. It is used in civil cases that involve the potential loss of important rights or interests, such as the termination of potential rights. The lowest standard of proof is probable cause. This is used to determine if a search or arrest is warranted, and also used by grand juries to issue indictments.

9.4.6 Straw Man

The straw man fallacy Distorts a position so that it can be easily attacked. It does not address the actual view held by the opponent, but responds to a weaker version. It is often committed by making the conclusion of an argument more extreme than it actually is, since extreme views are often easy to attack.

Example: “Senator Snodgrass has argued that there be a mandatory waiting period before any handgun purchase. Obviously, the senator wants to make all firearm ownership illegal.”

Here some subtle ways of committing the fallacy:

• Taking words out of context.
• Treating extreme views as representative.
• Criticizing early versions of a position.
• Criticizing deliberately simplified versions of a position.

9.4.7 Red Herring

The goal of the red herring fallacy is to lead the opponent off the track, by subtly changing the issue being discussed. The arguer changes the subject to a different but related one. To determine if something is a red herring, ask yourself if the issue at the beginning of the argument is the same as the issue at the end. Here is an example:

The American Cancer Society has argued that smoking is bad for your health. Many people in the Southeastern United States are dependent upon the tobacco industry for their jobs. Making smoking illegal would have a devastating economic effect on many states. Therefore, the ACS is simply wrong.

Notice the original isse is whether smoking has bad health consequences. By the end of the paragraph, the issue has been changed to the economic impact of making smoking illegal.

9.4.8 Horse Laugh

This occurs when someone simply ridicules the position held, and offers no real response to the argument at all. For example: “Mr. Jones has argued that watching television is emotionally unhealthy. If you believe that, then I’ve got a great deal on some swampland for you.”

9.5 Fallacies of Unwarranted Assumptions

9.5.1 begging the question.

An argument begs the question if it is impossible to believe at least one of the premises unless one already believes the conclusion. Note that if this is the case, then the premises cannot serve as reasons to believe the conclusion, since believing the premises requires already believing the conclusion. There are three common types of arguments that beg the question.

The first is a circular argument. That occurs when one explicitly uses the conclusion as support for one of the premises. Here is an example:

• The Bible says that God exists.
• The Bible is the inspired word of God.
• God exists.

The Bible can’t be the inspired word of God unless God exists, so the argument begs the question.

Another type of argument that begs the question is one that simply rephrases the conclusion and uses it as a premise. Example: “If such actions were not illegal, then they would not be prohibited by the law.” In this case, the conclusion is synonymous with one of the premises.

The last type is one that generalizes the conclusion and uses the generalized rule as a premise. Example: “Spanking children is wrong because corporal punishment is wrong.”

9.5.2 Appeal to Authority

The fallacy of appeal to authority is committed by using an pseudo-authority to support a claim. Note that it is not committed by merely appealing to an authority, but by appealing to an unqualified authority. Always ask, “Should this person know more about this subject than the average person?”

9.5.3 Loaded Question

A loaded question suggests something with the question. “Whem will you stop cheating on exams?” is a loaded question, the question implies that the person is cheating. Notice that there is no way to directly answer the question without admitting to cheating on exams.

9.5.4 False Dilemma

This is sometimes called the either-or fallacy. This happens when a person asserts a disjunction, a sentence of the form "either A or B , when there is at least one more option that is true. Disjunctions are true whenever at least one of the disjuncts, the sentences joined by the ‘or,’ are true. A False dilemma asserts that one of the two sentences must be true when there is really a third alternative. Here are some examples:

“Either buy our personal financial guide or never have control of your finances.”

Child to parent: “Either let me go to the party or I’ll just die.”

False dilemmas are often expressed in pithy slogans on bumper stickers: “It’s my way or the highway” or “America, love it or leave it.”

Consider this example: “My opponent voted against the public schools spending bill. He must think educating our children is not important.” The claim is that either one votes for the bill or one believes that education is not important. This is a false dilemma since there may be many other reasons to vote against a particular bill.

It’s important to remember that a disjunction can be expressed as a conditional: “Either let me go to that party or I’ll die” is equivalent to “If you don’t let me go to that party, then I’ll die.” In general, P or Q is equivalent to if not-P then Q.

9.5.5 Slippery Slope

Slippery slopes rest a conclusion on a chain reaction that is not likely to occur. They generally have this form:

In order for this to be a fallacy, at least one of the conditional statements in the premises must not be likely to be true. Here’s an example: “If I fail this test, then I will fail the course. If I fail the course, then I’ll be expelled from school. If I’m expelled from school, then I’ll never be able to have a good job. If I can’t get a good job, then I can’t support a family…”

To test for a slippery slope, just ask, are there any weak links in this chain of conditionals? Is it really the case that one failed exam will result in an F for a course grade?

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There is wide agreement that a term is vague to the extent that it has borderline cases. This makes the notion of a borderline case crucial in accounts of vagueness. I shall concentrate on an historical characterization of borderline cases that most commentators would accept. Vagueness will then be contrasted with ambiguity and generality. This will clarify the nature of the philosophical challenge posed by vagueness. I will then discuss some rival theories of vagueness with an emphasis on many-valued logic, supervaluationism and contextualism. I will conclude with the issue of whether all vagueness is linguistic.

1. Inquiry Resistance

2. comparison with ambiguity and generality, 3. the philosophical challenge posed by vagueness, 4. many-valued logic, 5. supervaluationism, 6. subvaluationism, 7. contextualism, 8. is all vagueness linguistic, other internet resources, related entries.

If you cut one head off of a two headed man, have you decapitated him? What is the maximum height of a short man? When does a fertilized egg develop into a person?

These questions are impossible to answer because they involve absolute borderline cases. In the vast majority of cases, the unknowability of a borderline statement is only relative to a given means of settling the issue (Sorensen 2001, chapter 1). For instance, a boy may count as a borderline case of ‘obese’ because people cannot tell whether he is obese just by looking at him. A curious mother could try to settle the matter by calculating her son’s body mass index. The formula is to divide his weight (in kilograms) by the square of his height (in meters). If the value exceeds 30, this test counts him as obese. The calculation will itself leave some borderline cases. The mother could then use a weight-for-height chart. These charts are not entirely decisive because they do not reflect the ratio of fat to muscle, whether the child has large bones, and so on. The boy will only count as an absolute borderline case of ‘obese’ if no possible method of inquiry could settle whether he is obese. When we reach this stage, we start to suspect that our uncertainty is due to the concept of obesity rather than to our limited means of testing for obesity.

Absolute borderline cases are targeted by Charles Sander Peirce’s entry for ‘vague’ in the 1902 Dictionary of Philosophy and Psychology :

A proposition is vague when there are possible states of things concerning which it is intrinsically uncertain whether, had they been contemplated by the speaker, he would have regarded them as excluded or allowed by the proposition. By intrinsically uncertain we mean not uncertain in consequence of any ignorance of the interpreter, but because the speaker’s habits of language were indeterminate. (Peirce 1902, 748)

In the case of relative borderline cases, the question is clear but our means for answering it are incomplete. In the case of absolute borderline cases, there is incompleteness in the question itself.

When a term is applied to one of its absolute borderline cases the result is a statement that resists all attempts to settle whether it is true or false. No amount of conceptual analysis or empirical inquiry can settle whether removing one head from a two headed man counts as decapitating him. We could give the appearance of settling the matter by stipulating that ‘decapitate’ means ‘remove a head’ (as opposed to ‘make headless’ or ‘remove the head’ or ‘remove the most important head’). But that would amount to changing the topic to an issue that merely sounds the same as decapitation.

Vagueness is standardly defined as the possession of borderline cases. For example, ‘tall’ is vague because a man who is 1.8 meters in height is neither clearly tall nor clearly non-tall. No amount of conceptual analysis or empirical investigation can settle whether a 1.8 meter man is tall. Borderline cases are inquiry resistant.

Where does the tail of a snake begin? When posed as a rhetorical question, the speaker is hinting that there is no definite answer. But the tail can be located by tracing down from the snake’s rib cage. A false attribution of indeterminacy will lead to the premature abandonment of inquiry. The risk of futile inquiry into questions that cannot be answered must be balanced against the risk of abandoning questions that are actually answerable.

Inquiry resistance typically recurses. For in addition to the unclarity of the borderline case, there is normally unclarity as to where the unclarity begins. Twilight governs times that are borderline between day and night. But our uncertainty as to when twilight begins, shows there must be borderline cases of borderline cases of ‘day’. Consequently, ‘borderline case’ has borderline cases. This higher order vagueness seems to show that ‘vague’ is vague (Hu 2017).

The vagueness of ‘vague’ would have two important consequences. First, Gottlob Frege could no longer coherently characterize vague predicates as incoherent. For his accusation uses ‘vague’. Frege’s ideal of precision is itself vague because ‘precise’ is the complement of ‘vague’.

Second, the vagueness of ‘vague’ dooms efforts to avoid a sharp line between true and false with a buffer zone that is neither true nor false. If the line is not drawn between the true and the false, then it will be between the true and the intermediate state. Introducing further intermediates just delays the inevitable.

This motivates second thoughts about second order vagueness. Instead of continuing to treat higher order vagueness as an insight, several philosophers repudiate higher order vagueness as an illusion (Wright 2010). They deny that there is an open-ended iteration of borderline status. They find it telling that speakers do not go around talking about borderline borderline cases and borderline borderline borderline cases and so forth (Raffman 2005, 23).

Defenders of higher order vagueness say that ordinary speakers avoid iterating ‘borderline’ for the same reason they avoid iterating ‘million’ or ‘know’. The iterations are confusing but perfectly meaningful. ‘Borderline’ behaves just like a vague predicate. For instance, ‘borderline’ can be embedded in a sorites argument. Defenders of higher order vagueness have also tried to clinch the case with particular specimens such as borderline hermaphrodites (reasoning that these individuals are borderline borderline males) (Sorensen 2010).

‘Tall’ is relative. A 1.8 meter pygmy is tall for a pygmy but a 1.8 meter Masai is not tall for a Masai. Although relativization disambiguates, it does not eliminate borderline cases. There are shorter pygmies who are borderline tall for a pygmy and taller Masai who are borderline tall for a Masai. The direct bearers of vagueness are a word’s full disambiguations such as ‘tall for an eighteenth century French man’. Words are only vague indirectly, by virtue of having a sense that is vague. In contrast, an ambiguous word bears its ambiguity directly—simply in virtue of having multiple meanings.

This contrast between vagueness and ambiguity is obscured by the fact that most words are both vague and ambiguous. ‘Child’ is ambiguous between ‘offspring’ and ‘immature offspring’. The latter reading of ‘child’ is vague because there are borderline cases of immature offspring. The contrast is further complicated by the fact that most words are also general. For instance, ‘child’ covers both boys and girls.

Ambiguity and vagueness also contrast with respect to the speaker’s discretion. If a word is ambiguous, the speaker can resolve the ambiguity without departing from literal usage. For instance, he can declare that he meant ‘child’ to express the concept of an immature offspring. If a word is vague, the speaker cannot resolve the borderline case. For instance, the speaker cannot make ‘child’ literally mean anyone under eighteen just by intending it. That concept is not, as it were, on the menu corresponding to ‘child’. He would be understood as taking a special liberty with the term to suit a special purpose. Acknowledging departure from ordinary usage would relieve him of the obligation to defend the sharp cut-off.

When the movie director Alfred Hitchcock mused ‘All actors are children’ he was taking liberties with clear negative cases of ‘child’ rather than its borderline cases. The aptness of his generalization is not judged by its literal truth-value (because it is obviously untrue). Likewise, we do not judge precisifications of borderline cases by their truth-values (because they are obviously not ascertainable as true or false). We instead judge precisifications by their simplicity, conservativeness, and fruitfulness. A precisification that draws the line across the borderline cases conserves more paradigm usage than one that draws the line across clear cases. But conservatism is just one desideratum among many. Sometimes the best balance is achieved at the cost of turning former positive cases into negative cases.

Once we shift from literal to figurative usage, we gain fictive control over our entire vocabulary—not just vague words. When a travel agent says ‘France is a hexagon’, we do not infer that she has committed the geometrical error of classifying France as a six sided polygon. We instead interpret the travel agent as speaking figuratively, as meaning that France is shaped like a hexagon. Similarly, when the travel agent says ‘Reno is the biggest little city’, we do not interpret her as overlooking the vagueness of ‘little city’. Just as she uses the obvious falsehood of ‘France is a hexagon’ to signal a metaphor, she uses the obvious indeterminacy of ‘Reno is the biggest little city’ to signal hyperbole.

Given that speakers lack any literal discretion over vague terms, we ought not to chide them for indecisiveness. Where there is no decision to be made, there is no scope for vice.

Speakers would have literal discretion if statements applying a predicate to its borderline cases were just permissible variations in linguistic usage. For instance, Crispin Wright and Stewart Shapiro say a competent speaker can faultlessly classify the borderline case as a positive instance while another competent speaker can faultlessly classify the case as a negative instance.

For the sake of comparison, consider discretion between alternative spellings. Professor Letterman uses ‘judgment’ instead of ‘judgement’ because he wants to promote the principle that a silent E signals a long vowel. He still has fond memories of Tom Lehrer’s 1971 children’s song “Silent E”:

Who can turn a can into a cane? Who can turn a pan into a pane? It’s not too hard to see, It’s Silent E. Who can turn a cub into a cube? Who can turn a tub into a tube? It’s elementary For Silent E.

Professor Letterman disapproves of those who add the misleading E but concedes that ‘judgement’ is a permissible spelling; he does not penalize his students for misspelling when they make their hard-hearted choice of ‘judgement’. Indeed, like other professors, he scolds students if they fail to stick with the same spelling throughout the composition. Choose but stick to your choice!

Professor Letterman’s assertion ‘The word for my favorite mental act is spelled j-u-d-g-m-e-n-t’ is robust with respect to the news that it is also spelled j-u-d-g-e-m-e-n-t. He would continue to assert it. He can conjoin the original assertion with information about the alternative: ‘The word for my favorite mental act is spelled j-u-d-g-m-e-n-t and is also spelled j-u-d-g-e-m-e-n-t’. In contrast, Professor Letterman’s assertion that ‘Martha is a woman’ is not robust with respect to the news that Martha is a borderline case of ‘woman’ (say, Letterman learns Martha is younger than she looks). The new information would lead Letterman to retract his assertion in favor of a hedged remark such as ‘Martha might be a woman and Martha might not be a woman’. Professor Letterman’s loss of confidence is hard to explain if the information about her borderline status were simply news of a different but permissible way of describing her. Discoveries of notational variants do not warrant changes in former beliefs.

News of borderline status has an evidential character. Loss of clarity brings loss of warrant. If you do not lower your confidence, you are open to the charge of dogmatism. To concede that Martha is a borderline case of ‘woman’ is to concede that you do not know that she is a woman. That is why debates can be dissolved by showing that the dispute is over a borderline case. The debaters should be agnostic if they are dealing with a borderline case. They do not have a license to form beliefs beyond their evidence.

News of an alternative sense is like news of an alternative spelling; there is no evidential impact (except for meta-linguistic beliefs about the nature of words). Your assertion that ‘All bachelors are men’ is robust with respect to the news that ‘bachelor’ has an alternative sense in which it means a male seal. Assertions are not robust with respect to news of hidden generality. If a South African girl says ‘No elephant can be domesticated’ but is then taught that there is another species of elephant indigenous to Asia, then she will lose some confidence; maybe Asian elephants can be domesticated. News of hidden generality has evidential impact. When it comes to robustness, vagueness resembles generality more than vagueness resembles ambiguity.

Mathematical terms such as ‘prime number’ show that a term can be general without being vague. A term can also be vague without being general. Borderline cases of analytically empty predicates illustrate this possibility.

Generality is obviously useful. Often, lessons about a particular F can be projected to other F s in virtue of their common F -ness. When a girl learns that her cat has a nictating membrane that protects its eyes, she rightly expects her neighbor’s cat also has a nictating membrane. Generality saves labor. When the girl says that she wants a toy rather than clothes, she narrows the range of acceptable gifts without going through the trouble of specifying a particular gift. The girl also balances values: a gift should be intrinsically desired and yet also be a surprise. If uncertain about which channel is the weather channel, she can hedge by describing the channel as ‘forty-something’. There is an inverse relationship between the contentfulness of a proposition and its probability: the more specific a claim, the less likely it is to be true. By gauging generality, we can make sensible trade-offs between truth and detail.

‘Vague’ has a sense which is synonymous with abnormal generality. This precipitates many equivocal explanations of vagueness. For instance, many commentators say that vagueness exists because broad categories ease the task of classification. If I can describe your sweater as red, then I do not need to ascertain whether it is scarlet. This freedom to use wide intervals obviously helps us to learn, teach, communicate, and remember. But so what? The problem is to explain the existence of borderline cases. Are they present because vagueness serves a function? Or are borderline cases side-effects of ordinary conversation—like echoes?

Every natural language is both vague and ambiguous. However, both features seem eliminable. Indeed, both are eliminated in miniature languages such as checkers notation, computer programming languages, and mathematical descriptions. Moreover, it seems that both vagueness and ambiguity ought to be minimized. ‘Vague’ and ‘ambiguous’ are pejorative terms. And they deserve their bad reputations. Think of all the automotive misery that has been prefaced by

Driver: Do I turn left? Passenger: Right.

English can be lethal. Philosophers have long motivated appeals for an ideal language by pointing out how ambiguity creates the menace of equivocation:

No child should work. Every person is a child of someone. Therefore, no one should work.

Happily, we know how to criticize and correct all equivocations. Indeed, every natural language is self-disambiguating in the sense that each has all the resources needed to uniquely specify any reading one desires. Ambiguity is often the cause but rarely the object of philosophical rumination.

Vagueness, in contrast, precipitates a profound problem: the sorites paradox. For instance,

Base step: A one day old human being is a child. Induction step: If an n day old human being is a child, then that human being is also a child when it is n + 1 days old. Conclusion: Therefore, a 36,500 day old human being is a child.

The conclusion is false because a 100 year old man is clearly a non-child. Since the base step of the argument is also plainly true and the argument is valid by mathematical induction, we seem to have no choice but to reject the second premise.

George Boolos (1991) observes that we have an autonomous case against the induction step. In addition to implying plausible conditionals such as ‘If a 1 day old human being is a child, then that human being is also a child when it is 2 days old’, the induction step also implies ludicrous conditionals such as ‘If a 1 day old human being is a child, then that human being is also a child when it is 36,500 days old’.

Boolos is puzzled why we overlook these clear counterexamples. One explanation is that we tend to treat the induction step as a generic generalization such as ‘ People have ten toes’(Sorensen 2012). Whereas the formal generalization ‘All people have ten toes’ is refuted by people with eleven toes, the generic generalization tolerates exceptions.

This hypothesis is plausible for newcomers to the sorites paradox. But it is less plausible for those being tutored by Professor Boolos. He guides logic students to the correct interpretation of the induction step. When students drift to a generic reading, Boolos reminds them that induction step is a formal generalization.

Guided by Boolos’ firm hand, logic students drive a second stake into the heart of the sorites paradox. Yet the paradox seems far from dead. The negation of the second premise classically implies a sharp threshold for childhood. For it implies the existential generalization that there is a number n such that an n day old human being is a child but is no longer a child one day later.

Epistemicists accept this astonishing consequence. They think vagueness is a form of ignorance. Timothy Williamson (1994) traces the ignorance of the threshold for childhood to “margin for error” principles. If one knows that an n day old human being is a child, then that human being must also be a child when n + 1 days old. Otherwise, one is right by luck. Given that there is a threshold, we would be ignorant of its location.

Debate over the margin for error principle draws us deep into epistemology and modality (Yli-Vakkuri 2016). Some commentators switch focus to attitudes weaker than knowledge. According to Nicholas Smith (2008, 182) we cannot even guess that the threshold for baldness is the 400th hair. Hartry Field (2010, 203) denies that a rational man can fear that he has just passed the threshold into being old. Hope, speculation, and wonder do not require evidence but they do require understanding. So it is revealing that these attitudes have trouble getting a purchase on the threshold of oldness (or any other vague predicate). A simple explanation is that bare linguistic competence gives us knowledge that are no such thresholds. This accounts for the comical air of the epistemicist. Just as there is no conceptual room to worry that there is a natural number between sixty and sixty one, there is no conceptual room to worry that one has passed the threshold of oldness between one’s sixtieth and sixty first birthday.

An old epistemicist might reply: My piecemeal confidence that a given number is not the threshold for oldness does not agglomerate into collective confidence that there is no such number. If I bet against each number being the threshold, then I must have placed a losing bet somewhere. For if I won each bet then there was no opportunity for me to make the transition to oldness. My bookie could have made a “Dutch book” against me. He would have been entitled to payment without having to identify which bet I lost. Since probabilities may be extracted from hypothetical betting behavior, I must actually assign some small (normally negligible) probability to hypotheses identifying particular thresholds. So must you.

Stephen Schiffer (2003, 204) denies that classical probability calculations apply in vague contexts. Suppose Donald is borderline old and borderline bald. According to Schiffer we should be just as confident in the conjunction ‘Donald is old and bald’ as in either conjunct. Adding conjuncts does not reduce confidence because we have a “vague partial belief” rather than the standard belief assumed by mathematicians developing probability theory. Schiffer offers a calculus for this vagueness-related propositional attitude. He crafts the rules for vague partial belief to provide a psychological solution to the sorites paradox.

The project is complicated by the fact that vague partial beliefs interact with precise beliefs (MacFarlane 2010). Consider a statement that has a mixture of vague and precise conjuncts: ‘Donald is old and bald and has an even number of hairs’. Adding the extra precise conjunct should diminish confidence. Schiffer also needs to accommodate the fact that some speakers are undecided about whether the nature of the uncertainty involves vagueness. Even an idealized speaker may be unsure because there is vagueness about the borders between vagueness related uncertainty and other sorts of uncertainty.

Other commentators grant that it is logically possible that vague predicates have thresholds. They just think it would be a miracle: “It is logically possible that the words on this page will come to life and sort my socks. But I know enough about words to dismiss this as a serious possibility. So I am right to boggle at the possibility that our rough and ready terms such as ‘red’ could so sensitively classify objects.” Epistemicists counter that this bafflement rests on an over-estimate of the role of stipulation in meaning. Epistemicists say much meaning is acquired passively by default rather than actively by decision. If some boundaries are more eligible for reference than others, then the environment does the work.

Most philosophers doubt whether precise analytical tools fit vague arguments. H. G. Wells was amongst the first to suggest that we must moderate the application of logic:

Every species is vague, every term goes cloudy at its edges, and so in my way of thinking, relentless logic is only another name for stupidity—for a sort of intellectual pigheadedness. If you push a philosophical or metaphysical enquiry through a series of valid syllogisms—never committing any generally recognized fallacy—you nevertheless leave behind you at each step a certain rubbing and marginal loss of objective truth and you get deflections that are difficult to trace, at each phase in the process. Every species waggles about in its definition, every tool is a little loose in its handle, every scale has its individual.— First and Last Things (1908)

Many more believe that the problem is with logic itself rather than the manner in which it is applied. They favor solving the sorites paradox by replacing standard logic with an earthier deviant logic.

There is a desperately wide range of opinions as to how the revision of logic should be executed. Every form of deviant logic has been applied in the hope of resolving the sorites paradox.

An early favorite was many-valued logic. On this approach, borderline statements are assigned truth-values that lie between full truth and full falsehood. Some logicians favor three truth-values, others prefer four or five. The most popular approach is to use an infinite number of truth-values represented by the real numbers between 0 (for full falsehood) and 1 (for full truth). This infinite spectrum of truth-values might be of service for a continuous sorites argument involving ‘small real number’ (Weber and Colyvan 2010).

Critics object that this proliferation of truth-values exacerbates the over-precision of classical logic. Instead of having just one artificially sharp line between the true and the false, the many-valued logician has infinitely many sharp lines such as that between statements with a truth of .323483925 and those with a higher truth-value. In Mark Sainsbury’s words, “… you do not improve a bad idea by iterating it.” (1996, 255)

A proponent of an infinite valued logic might reply to Sainsbury with an analogy. It is a bad idea to model a circle with a straight line. Using two lines is not much better, nor is there is much improvement using a three sided polygon (a triangle). But as we add more straight lines to the polygon (square, pentagon, hexagon, and so on) we make progress—by iterating the bad idea of modeling a circle with straight lines.

Indeed, it would be tempting to triumphantly conclude ‘The circle has been modeled as an infinitely sided polygon’. This victory declaration would itself need clarification. Has the circle been revealed to be an infinitely sided polygon? Have curved lines been replaced by straight lines? Have curved lines (and hence circles) been proven to not exist? A model can succeed without it being clear what has been achieved.

But it is premature to dwell on the simile ‘Precision is to vagueness as straightness is to curvature’. The many-valued logician must first vindicate the analogy by providing details about how to calculate the truth-values of vague statements from the truth-values of their component statements.

Proponents of many-valued logic approach this obligation with great industry. Precise new rules are introduced to calculate the truth value of compound statements that contain statements with intermediate truth-values. For instance, the revised rule for conjunctions is to assign the conjunction the same truth-value as the conjunct with the lowest truth-value.

These rules are designed to yield all standard theorems when all the truth values are 1 and 0. In this sense, classical logic is a limiting case of many-valued logic. Classical logic is agreed to work fine in the area for which it was designed—mathematics.

Most theorems of standard logic break down when intermediate truth-values are involved. (An irregular minority, such as ‘If P , then P ’, survive.) Even the classical contradiction ‘Donald is bald and it is not the case that he is bald’ receives a truth-value of .5 when ‘Donald is bald’ has a truth-value of .5. Many-valued logicians note that the error they are imputing to classical logic is often so small that classical logic can still be fruitfully applied. But they insist that the sorites paradox illustrates how tiny errors accumulate into a big error.

Critics of the many-valued approach complain that it botches phenomena such as hedging. If I regard you as a borderline case of ‘tall man’, I cannot sincerely assert that you are tall and I cannot sincerely assert that you are of average height. But I can assert the hedged claim ‘Either you are tall or of average height’. The many-valued rule for disjunction is to assign the whole statement the truth-value of its highest disjunct. Normally, the added disjunct in a hedged claim is not more plausible than the other disjuncts. Thus it cannot increase the degree of truth. Disappointingly, the proponent of many-valued logic cannot trace the increase of assertibility to an increase in the degree of truth.

Epistemicists explain the rise in assertibility by the increasing probability of truth. Since the addition of disjuncts can raise probability indefinitely, the epistemicists correctly predict that we can hedge our way to full assertibility. However, epistemicists do not have a monopoly on this prediction.

According to supervaluationists, borderline statements lack a truth-value. This neatly explains why it is universally impossible to know the truth-value of a borderline statement. Supervaluationists offer details about the nature of absolute borderline cases. Simple sentences about borderline cases lack a truth-value. Compounds of these statements can have a truth-value if they come out true regardless of how the statement is precisified. For instance, ‘Either Mr. Stoop is tall or it is not the case that Mr. Stoop is tall’ is true because it comes out true under all ways of sharpening ‘tall’. Thus the method of supervaluations allows one to retain all the theorems of standard logic while admitting “truth-value gaps”.

One may wonder whether this striking result is a genuine convergence with standard logic. Is the supervaluationist characterizing vague statements as propositions? Or is he merely pointing out that certain non-propositions have a structure isomorphic to logical theorems? (Some electrical circuits are isomorphic to tautologies but this does not make the circuits tautologies.) Kit Fine (1975, 282), and especially David Lewis (1982), characterize vagueness as hyper-ambiguity. Instead of there being one vague concept, there are many precise concepts that closely resemble each other. ‘Child’ can mean a human being at most one day old or mean a human being at most two days old or mean a human being at most three days old …. Thus the logic of vagueness is a logic for equivocators. Lewis’ idea is that ambiguous statements are true when they come out true under all disambiguations. But logicians normally require that a statement be disambiguated before logic is applied. The mere fact that an ambiguous statement comes out true under all its disambiguations does not show that the statement itself is true. Sentences which are actually disambiguated may have truth-values. But the best that can be said of those that merely could be disambiguated is that they would have had a truth-value had they been disambiguated (Tye 1989).

Supervaluationism will converge with classical logic only if each word of the supervaluated sentence is uniformly interpreted. For instance, ‘Either a carbon copy of Teddy Roosevelt’s signature is an autograph or it is not the case that a carbon copy of Teddy Roosevelt’s signature is an autograph’ comes out true only if ‘autograph’ is interpreted the same way in both disjuncts. Vague sentences resist mixed interpretations. However, mixed interpretations are permissible for ambiguous sentences. As Lewis himself notes in a criticism of relevance logic, ‘Scrooge walked along the bank on his way to the bank’ can receive a mixed disambiguation. When exterminators offer ‘non-toxic ant poison’, we charitably switch relativizations within the noun phrase: the substance is safe for human beings but deadly for ants.

Even if one agrees that supervaluationism converges with classical logic about theoremhood, they clearly differ in other respects. Supervaluationism requires rejection of inference rules such as contraposition, conditional proof and reductio ad absurdum (Williamson 1994, 151–152). In the eyes of the supervaluationist, a demonstration that a statement is not true does not guarantee that the statement is false.

The supervaluationist is also under pressure to reject semantic principles which are intimately associated with the application of logical laws. According to Alfred Tarski’s Convention T, a statement ‘ S ’ is true if and only if S . In other words, truth is disquotational. Supervaluationists say that being supertrue (being true under all precisifications) suffices for being true. But given Convention T, supertruth would then be disquotational. Since the supervaluationists accept the principle of excluded middle, they would be forced to say ‘ P ’ is supertrue or ‘Not P ’ is supertrue (even if ‘ P ’ applies a predicate to a borderline case). This would imply that either ‘ P ’ is true or ‘Not P ’ is true. (Williamson 1994, 162–163) And that would be a fatal loss of truth-value gaps for supervaluationism.

There is a final concern about the “ontological honesty” of the supervaluationist’s existential quantifier. As part of his solution to the sorites paradox, the supervaluationist will assert ‘There is a human being who was a child when n days old but not when n + 1 days old’. For this statement comes out true under all admissible precisifications of ‘child’. However, when pressed the supervaluationist will add an unofficial clarification: “Oh, of course I do not mean that there really is a sharp threshold for childhood.”

After the clarification, some wonder how supervaluationism differs from drastic metaphysical skepticism. In his nihilist days, Peter Unger (1979) admitted that it is useful to talk as if there are children. But he insisted that strictly speaking, vague terms such as ‘child’ cannot apply to anything. Unger was free to use supervaluationism as a theory to explain our ordinary discourse about children. (Unger instead used other resources to explain how we fruitfully apply empty predicates.) But once the dust had cleared and the precise rubble came into focus, Unger had to conclude that there are no children.

Officially, the supervaluationist rejects the induction step of the sorites argument. Unofficially, he seems to instead reject the base step of the sorites argument.

Supervaluationism is also haunted by a logical analogy. Whereas the supervaluationist analyzes borderline cases in terms of truth-value gaps the dialetheist analyzes them in terms of truth-value gluts. A glut is a proposition that is both true and false. The rule for assigning gluts is the mirror image of the rule for assigning gaps: A statement is true exactly if it comes out true on at least one precisification. The statement is false just if it comes out false on at least one precisification. So if the statement comes out true under one precisification and false under another precisification, the statement is both true and false.

To avoid triviality, the dialetheist must adopt a logic that stops two contradictory statements from jointly implying everything. The resulting “subvaluationism” is a dual of supervaluationism.

The spiritual father of subvaluationism is Georg Hegel. For Hegel, the basic kind of vagueness is conflict vagueness. The man at the threshold of your doorway is both inside your room and outside your room. Degree vagueness is just a special case of the conflict inherit in becoming. Any process requires a gradual manifestation of a contradiction inherit in the original state. At some stage, a metamorphosizing caterpillar is not a butterfly (by virtue of what it was) and a butterfly (by virtue of what it will be). Hegelians believed this dialectical conception of vagueness solved the sorites and demonstrated the inadequacy of classical logic. The Russian Marxist Georgi Plekhanov (1908 [1937]) proposed a logic of contradiction to succeed classical logic (Hyde 2008, 93–5). One of his students, Henry Mehlberg (1958) went on to substitute gaps for gluts. The first version of supervaluationism is thus a synthesis, reconciling the thesis of classical logic with the anti-thesis posed by the logic of contradiction.

Viewed formally, there seems no more reason to prefer one departure from classical logic rather than the other. Since Western philosophers abominate contradiction, parity with dialetheism would diminish the great popularity of supervaluationism.

A Machiavellian epistemicist will welcome this battle between the gaps and the gluts. He roots for the weaker side. Although he does not want the subvaluationist to win, the Machiavellian epistemicist does want the subvaluationist to achieve mutual annihilation with his supervaluationist doppelgänger. His political calculation is: Gaps + Gluts = Bivalence.

Pablo Corberos (2011) has argued that subvaluationism provides a better treatment of higher order vagueness than supervaluationism. But for the most part, the subvaluationists (and their frenemies) have merely claimed subvaluationism to be at least as attractive as supervaluationism (Hyde and Colyvan 2008). This modest ambition seems prudent. After all, truth-value gaps have far more independent support from the history of philosophy (at least if confined to Western philosophy). Prior to the explosive growth of vagueness research after 1975, ordinary language philosophers amassed a panoramic battery of analyses suggesting that gaps are involved in presupposition, reference failure, fiction, future contingent propositions, performatives, and so on and so on. Supervaluationism rigorously consolidated these appeals to ordinary language.

Dialetheists characterize intolerance for contradiction as a shallow phenomenon, restricted to a twentieth Western academic milieu (maybe even now being eclipsed by the rise of China). Experimental philosophers have challenged the old appeals to ordinary language with empirical results suggesting that glutty talk is as readily stimulated by borderline cases as gappy talk (Alxatib and Pelletier 2011, Ripley 2011).

Just as contextualism in epistemology runs orthogonal to the familiar divisions amongst epistemologists (foundationalism, reliabilism, coherentism, etc.), there are contextualists of every persuasion amongst vagueness theorists. They develop an analogy between the sorites paradox and indexical sophistries such as:

1. Base step: The horizon is more than 1 meter away. 2. Induction step: If the horizon is more than n meters away, then it is more than n + 1 meters away. 3. Conclusion: The horizon is more than a billion meters away.

The horizon is where the earth meets the sky and is certainly less than a billion meters away. (The circumference of the earth is only forty million meters.) Yet when you travel toward the horizon to specify the n at which the induction step fails, your trip is as futile as the pursuit of the rainbow. You cannot reach the horizon because it shifts with your location.

All contextualists accuse the sorites monger of equivocating. In one sense, the meaning of ‘child’ is uniform; the context-invariant rule for using the term (its “character”) is constant. However, the set of things to which the term applies (its “content”) shifts with the context. In this respect, vague words resemble indexical terms such as: I, you, here, now, today, tomorrow. When a debtor tells his creditor on Monday ‘I will pay you back tomorrow’ and then repeats the sentence on Tuesday, there is a sense in which he has said the same thing (the character is the same) and a sense in which he has said something different (the content has shifted because ‘tomorrow’ now picks out Wednesday).

According to the contextualists, the rules governing the shifts prohibit us from interpreting any instance of the induction step as having a true antecedent and a false consequent. The very process of trying to refute the induction step changes the context so that the instance will not come out false. Indeed, contextualists typically emphasize that each instance is true. Assent is mandatory. Consequently, direct attacks on the induction step must fail. One is put in mind of Seneca’s admonition to his student Nero: “However many you put to death, you will never kill your successor.”

Hans Kamp, the founder of contextualism, maintained that the extension of vague words orbits the speaker’s store of conversational commitments. In a more psychological vein, Diana Raffman says changes in context trigger gestalt shifts between look-alike categories.

Stewart Shapiro integrates Kamp’s ideas with Friedrich Waismann’s concept of open texture. Shapiro thinks speakers have discretion over borderline cases because they are judgment dependent. They come out true in virtue of the speaker judging them to be true. Given that the audience does not resist, borderline cases of ‘child’ can be correctly described as children. The audience recognizes that other competent speakers could describe the borderline case differently. As Waismann lyricizes “Every description stretches, as it were, into a horizon of open possibilities: However far I go, I shall always carry this horizon with me.” (1968, 122)

American pragmaticism colors Delia Graff Fara’s contextualism. Consider dandelion farms. Why would someone grow weeds? The answer is that ‘weed’ is relative to interests. Dandelions are unwanted by lawn caretakers but are desired by farmers for food, wine, and medical uses. Fara thinks this interest relativity extends to all vague words. For instance, ‘child’ means a degree of immaturity that is significant to the speaker. Since the interests of the speaker shift, there is an opportunity for a shift in the extension of ‘child’. Fara is reluctant to describe herself as a contextualist because the context only has an indirect effect on the extension via the changes it makes to the speaker’s interest.

How strictly are we to take the comparison between vague words and indexical terms? Scott Soames (2002, 445) answers that all vague words literally are indexical.

This straightforward response is open to the objection that the sorites monger could stabilize reference. When the sorites monger relativizes ‘horizon’ to the northeast corner of the Empire State Building’s observation deck, he seems to generate a genuine sorites paradox that exploits the vagueness of ‘horizon’ (not its indexicality).

All natural languages have stabilizing pronouns, ellipsis, and other anaphoric devices. For instance, in ‘Jack is tired now and Jill is too’, the ‘too’ forces a uniform reading of ‘tired’. Jason Stanley suggests that the sorites monger employ the premise:

If that 1 is a child then that 2 is too, and if that 2 is too, then that 3 is too, and if that 3 is too, then that 4 is too, … and then that i is too.

Each ‘that n ’ refers to the n th element in a sequence of worsening examples of ‘child’. The meaning of ‘child’ is not shifting because the first occurrence of the term governs all the subsequent clauses (thanks to ‘too’). If vague terms were literally indexical, the sorites monger would have a strong reply. If vague terms only resemble indexicals, then the contextualist needs to develop the analogy in a way that circumvents Stanley’s counsel to the sorites monger.

The contextualist would also need to address a second technique for stabilizing the context. R. M. Sainsbury (2013) advises the sorites monger to present his premises in apparently random order. No pair of successive cases raises an alarm that similar cases are being treated differently. Unless the hearer has extraordinary memory, he will not feel pressured to adjust the context.

The contextualist must find enough shiftiness to block every sorites argument. Since vagueness seeps into every syntactic category, critics complain that contextualism exceeds the level of ambiguity countenanced by linguistics and psycholinguists.

Another concern is that some sorites arguments involve predicates that do not give us an opportunity to equivocate. Consider a sorites with a base step that starts from a number too large for us to think about. Or consider an inductive predicate that is too complex for us to reason with. One example is obtained by iterating ‘mother of’ a thousand times (Sorensen 2001, 33). This predicate could be embedded in a mind numbing sorites that would never generate context shifts.

Other unthinkable sorites arguments use predicates that can only be grasped by individuals in other possible worlds or by creatures with different types of minds than ours. More fancifully, there could be a vague predicate, such as Saul Kripke’s “killer yellow”, that instantly kills anyone who thinks about it. The basic problem is that contextualism is a psychologistic theory of the sorites. Arguments can exist without being propounded.

Supervaluationists encourage the view that all vagueness is a matter of linguistic indecision: the reason why there are borderline cases is that we have not bothered to make up our minds.

The method of supervaluation allows us to assign truth-values prior to any decisions. Expressivists think this is a mistake akin to assigning truth-values to normative claims (MacFarlane 2016). They model vagueness as practical uncertainty as to whether to treat a borderline F as an F. The deliberator may accept the tautologies of classical logic as constraints governing competing plans for drawing lines. I can accept ‘Either Donald is bald or not’ without accepting either disjunct. An existentially quantified sentence can be accepted even when no instance is. A shrug of the shoulders signals readiness to go either way, not ignorance as to which possible world one inhabits. The supervaluationist tries to express this insight by expanding the conditions under which truth-values can be assigned. This the wrong medium for the message.

The expressivist is poised to explain how supervaluationism developed into the most respected theory of vagueness. Frege portrayed vagueness as a side-effect of laziness. But supervaluationists countered that indecision is functional. Instead of committing ourselves prematurely, we can fill in meanings as we go along in light of new information and interests. This conjecture is promising for the highly stipulative enterprise of promulgating and enforcing laws (Endicott 2000). Judges frequently seem to exercise and control discretion by means of vague language. Uncertainties about the scope of discretion may arise from higher order vagueness (Schauer 2016).

Discretion through gap-filling pleases those who regard adjudication as a creative process. It alarms those who think we should be judged by laws rather than men. The doctrine of discretion through indeterminacy has also been questioned on grounds that the source of the discretion is the generality of the legal terms rather than their vagueness (Poscher 2012).

Supervaluationists emphasize the distinction between words and objects. Objects themselves do not seem to be the sort of thing that can be general, ambiguous, or vague (Eklund 2011). From this perspective, Georg Hegel appears to commit a category mistake when he characterizes clouds as vague. Although we sometimes speak of clouds being ambiguous or even being general to a region, this does not entitle us to infer that there is metaphysical ambiguity or metaphysical generality.

Supervaluationists are here incorporating an orthodoxy dating back to Bertrand Russell’s seminal article “Vagueness” (1923). This consensus was re-affirmed by Michael Dummett (1975) and ritualistically re-avowed by subsequent commentators.

In 1978 Gareth Evans focused opposition to vague objects with a short proof modeled after Saul Kripke’s attack on contingent identity. If there is a vague object, then some statement of the form ‘ a = b ’ must be vague (where each of the flanking singular terms precisely designates that object). For the vagueness is allegedly due to the object rather than its representation. But any statement of form ‘ a = a ’ is definitely true. Consequently, a has the property of being definitely identical to a . Since a = b , then b must also have the property of being definitely identical to a . Therefore ‘ a = b ’ must be definitely true!

Evans agrees that there are vague identity statements in which one of the flanking terms is vague (just as Kripke agrees that there are contingent identity statements when one of the flanking terms is a flaccid designator). But then the vagueness is due to language, not the world.

Despite Evans’ impressive assault, there was a renewal of interest in vague objects in the 1980s. As a precedent for this revival, Peter van Inwagen (1990, 283) recalls that in the 1960s, there was a consensus that all necessity is linguistic. Most philosophers now take the possibility of essential properties seriously.

Some of the reasons are technical. Problems with Kripke’s refutation of contingent identity have structural parallels that affect Evans’ proof. Evans also relies on inferences that deviant logicians challenge (Parsons 2000).

In the absence of a decisive reductio ad absurdum , many logicians feel their role to be the liberal one of articulating the logical space for vague objects. There should be “Vague objects for those who want them” (Cowles and White 1991). Logic should be ontologically neutral.

Since epistemicists try to solve the sorites with little more than a resolute application of classical logic, they are methodologically committed to a partisan role for logic. Instead of looking for loopholes, we should accept the consequence (Williamson 2015).

Some non-enemies of vague objects also have an ambition to consolidate various species of indeterminacy (Barnes and Williams 2011). Talk of indeterminacy is found in quantum mechanics, analyses of the open future, fictional incompleteness, and the continuum hypothesis. Perhaps vagueness is just one face of indeterminacy.

This panoramic vision contrasts with the continuing resolution of many to tether vagueness to the sorites paradox (Eklund 2011). They fear that the clarity achieved by semantic ascent will be muddied by metaphysics.

But maybe the mud is already on the mountain top. Trenton Merricks (2001) claims that standard characterizations of linguistic vagueness rely on metaphysical vagueness. If ‘Donald is bald’ lacks a truth-value because there is no fact to make the statement true, then the shortage appears to be ontological.

The view that vagueness is always linguistic has been attacked from other directions. Consider the vagueness of maps (Varzi 2001). The vagueness is pictorial rather than discursive. So one cannot conclude that vagueness is linguistic merely from the premise that vagueness is representational.

Or consider vague instrumental music such as Claude Debussy’s “The Clouds”. Music has syntax but too little semantics to qualify as language. There is a little diffuse reference through devices such as musical quotation, leitmotifs, and homages. These referential devices are not precise. Therefore, some music is vague (Sorensen 2010). The strength and significance of this argument depends on the relationship between music and language. Under the musilanguage hypothesis, language and music branched off from a common “musilanguage” with language specializing in semantics and music specializing in the expression of emotion. This scenario makes it plausible that purely instrumental music could have remnants of semantic meaning.

Mental imagery also seems vague. When rising suddenly after a prolonged crouch, I “see stars before my eyes”. I can tell there are more than ten of these hallucinated lights but I cannot tell how many. Is this indeterminacy in thought to be reduced to indeterminacy in language? Why not vice versa? Language is an outgrowth of human psychology. Thus it seems natural to view language as merely an accessible intermediate bearer of vagueness.

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Critical Thinking: A Simple Guide and Why It’s Important

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Critical Thinking: A Simple Guide and Why It’s Important was originally published on Ivy Exec .

Strong critical thinking skills are crucial for career success, regardless of educational background. It embodies the ability to engage in astute and effective decision-making, lending invaluable dimensions to professional growth.

At its essence, critical thinking is the ability to analyze, evaluate, and synthesize information in a logical and reasoned manner. It’s not merely about accumulating knowledge but harnessing it effectively to make informed decisions and solve complex problems. In the dynamic landscape of modern careers, honing this skill is paramount.

The Impact of Critical Thinking on Your Career

☑ problem-solving mastery.

Visualize critical thinking as the Sherlock Holmes of your career journey. It facilitates swift problem resolution akin to a detective unraveling a mystery. By methodically analyzing situations and deconstructing complexities, critical thinkers emerge as adept problem solvers, rendering them invaluable assets in the workplace.

☑ Refined Decision-Making

Navigating dilemmas in your career path resembles traversing uncertain terrain. Critical thinking acts as a dependable GPS, steering you toward informed decisions. It involves weighing options, evaluating potential outcomes, and confidently choosing the most favorable path forward.

☑ Enhanced Teamwork Dynamics

Within collaborative settings, critical thinkers stand out as proactive contributors. They engage in scrutinizing ideas, proposing enhancements, and fostering meaningful contributions. Consequently, the team evolves into a dynamic hub of ideas, with the critical thinker recognized as the architect behind its success.

☑ Communication Prowess

Effective communication is the cornerstone of professional interactions. Critical thinking enriches communication skills, enabling the clear and logical articulation of ideas. Whether in emails, presentations, or casual conversations, individuals adept in critical thinking exude clarity, earning appreciation for their ability to convey thoughts seamlessly.

☑ Adaptability and Resilience

Perceptive individuals adept in critical thinking display resilience in the face of unforeseen challenges. Instead of succumbing to panic, they assess situations, recalibrate their approaches, and persist in moving forward despite adversity.

☑ Fostering Innovation

Innovation is the lifeblood of progressive organizations, and critical thinking serves as its catalyst. Proficient critical thinkers possess the ability to identify overlooked opportunities, propose inventive solutions, and streamline processes, thereby positioning their organizations at the forefront of innovation.

☑ Confidence Amplification

Critical thinkers exude confidence derived from honing their analytical skills. This self-assurance radiates during job interviews, presentations, and daily interactions, catching the attention of superiors and propelling career advancement.

So, how can one cultivate and harness this invaluable skill?

✅ developing curiosity and inquisitiveness:.

Embrace a curious mindset by questioning the status quo and exploring topics beyond your immediate scope. Cultivate an inquisitive approach to everyday situations. Encourage a habit of asking “why” and “how” to deepen understanding. Curiosity fuels the desire to seek information and alternative perspectives.

✅ Practice Reflection and Self-Awareness:

Engage in reflective thinking by assessing your thoughts, actions, and decisions. Regularly introspect to understand your biases, assumptions, and cognitive processes. Cultivate self-awareness to recognize personal prejudices or cognitive biases that might influence your thinking. This allows for a more objective analysis of situations.

✅ Strengthening Analytical Skills:

Practice breaking down complex problems into manageable components. Analyze each part systematically to understand the whole picture. Develop skills in data analysis, statistics, and logical reasoning. This includes understanding correlation versus causation, interpreting graphs, and evaluating statistical significance.

✅ Engaging in Active Listening and Observation:

Actively listen to diverse viewpoints without immediately forming judgments. Allow others to express their ideas fully before responding. Observe situations attentively, noticing details that others might overlook. This habit enhances your ability to analyze problems more comprehensively.

✅ Encouraging Intellectual Humility and Open-Mindedness:

Foster intellectual humility by acknowledging that you don’t know everything. Be open to learning from others, regardless of their position or expertise. Cultivate open-mindedness by actively seeking out perspectives different from your own. Engage in discussions with people holding diverse opinions to broaden your understanding.

✅ Practicing Problem-Solving and Decision-Making:

Engage in regular problem-solving exercises that challenge you to think creatively and analytically. This can include puzzles, riddles, or real-world scenarios. When making decisions, consciously evaluate available information, consider various alternatives, and anticipate potential outcomes before reaching a conclusion.

✅ Continuous Learning and Exposure to Varied Content:

Read extensively across diverse subjects and formats, exposing yourself to different viewpoints, cultures, and ways of thinking. Engage in courses, workshops, or seminars that stimulate critical thinking skills. Seek out opportunities for learning that challenge your existing beliefs.

✅ Engage in Constructive Disagreement and Debate:

Encourage healthy debates and discussions where differing opinions are respectfully debated.

This practice fosters the ability to defend your viewpoints logically while also being open to changing your perspective based on valid arguments. Embrace disagreement as an opportunity to learn rather than a conflict to win. Engaging in constructive debate sharpens your ability to evaluate and counter-arguments effectively.

✅ Utilize Problem-Based Learning and Real-World Applications:

Engage in problem-based learning activities that simulate real-world challenges. Work on projects or scenarios that require critical thinking skills to develop practical problem-solving approaches. Apply critical thinking in real-life situations whenever possible.

This could involve analyzing news articles, evaluating product reviews, or dissecting marketing strategies to understand their underlying rationale.

In conclusion, critical thinking is the linchpin of a successful career journey. It empowers individuals to navigate complexities, make informed decisions, and innovate in their respective domains. Embracing and honing this skill isn’t just an advantage; it’s a necessity in a world where adaptability and sound judgment reign supreme.

So, as you traverse your career path, remember that the ability to think critically is not just an asset but the differentiator that propels you toward excellence.

Wrestling with Philosophy

In this blog I present, in an informal way, core ideas in philosophy and their application to current events and everyday life. For critical thinking lessons and resources, please check out my free online course reasoningforthedigitalage.com

Monday, April 1, 2013

Critical thinking: definitions: vagueness, ambiguity, euphemisms, emotional language, and the fallacy of equivocation, 2 comments:.

Thank you so much for the very useful information.

Brief but insightful. Good job

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Vagueness: an introduction (sort of)

Fred ablondi tells you everything you always wanted to know about vagueness. but not quite..

The ‘Problem of Vagueness’ is, fittingly, not one precise problem, but several related ones. A vague predicate can be defined in terms of boundarylessness (i.e., lacking sharp boundaries): F is vague if there are cases in which it is not determinate whether some particular x is F or not. (Vague predicates are also often defined as having borderline cases .) For example, when does the successive removal of grains of salt make a heap of salt a nonheap? How short can a person be for an increase of 1/1000 of an inch in height to make her no longer short? Over the last 25 years or so, several issues relating to vagueness have received considerable attention from philosophers in the analytic tradition. In this brief introduction to the topic, I wish to discuss a few of them.

One feature of vague predicates which has been the subject of philosophers’ attentions is the fact that they fall prey to the sorites paradox . Like so much in contemporary philosophy, the sorites paradox can be traced back to the ancient Greeks; Eubulides is usually credited with what has been called ‘the problem of the heap’. Consider the following argument involving the vague predicate ‘is rich’:

1. A person with £5,000,000,000 is rich. 2. Someone does not go from being rich to being not rich by losing £1. 3. Therefore, someone with £4,999,999,999 is rich. By repeated applications of 2, we get: (C) Therefore, someone with £6 is rich.

Of course, we can reverse the process and generate a similar paradox involving the predicate ‘is poor’. (Other predicates frequently used in sorites examples are ‘is bald’ and ‘is tall’.) On the face of it, the premises are true, and imply the conclusion (C), yet (C) is clearly false. There have been several attempts to solve, or at least explain, the paradox, but none have met with universal approval.

Another problem which vagueness generates has to do with its origins: what is the source of vagueness? Here too there are many views, and, corresponding to these, we encounter many ‘solutions’ to the problems to which vagueness gives rise. Some would say vagueness is nothing more than a result of imprecision in our language. On this view, a precisification of language would eliminate vagueness. Critics of this position point out that such a precisification, were it even possible, would eliminate many of the thing we value most in our world. For example, ‘goodness’, ‘justice’, and ‘beauty’ are all vague terms, as are terms denoting concrete objects, such as ‘pebble’ and ‘conscious being’. Still, some philosophers are comfortable taking this to ‘nihilistic’ conclusions, denying, for example, that there are even such things as ‘heaps’. 1 Others,while still maintaining that vagueness is a purely semantic phenomena, ‘solve’ the problem by appealing to the concept of supervenience, claiming that vague expressions supervene on elements of a precise language.

Other philosophers, known as epistemists, agree that there is no ‘real’ vagueness in the world, but rather than attributing vagueness to our language, they hold it to be a result of a limitation of our knowing powers. 2 Consequently, there is no ‘solution’ to the problem of vagueness – it’s just something we have to learn to live with (and why should we humans think we can know everything, anyway?). For example, according to the epistemist, there is a pound amount such that if x has £n, then x is rich, but if x has £(n-1), then x is not rich. The selling point of this view is that it retains for classical logic the principle of bivalence (i.e., it is either true that x is F, or it is false that x is F). But aside from being quite counter-intuitive, inasmuch as it declares there is, for example, a one hair difference between a bald and a non-bald person, this view has the curious feature of being unable to say just what it is we are unable to know. 3 Note too that neither the epistemic nor the semantic account deny the phenomena of vagueness; they are (rival) attempts to explain from where it comes.

Some philosophers, on the other hand, ‘bite the bullet’ and admit not only that vague sets and vague properties are real, but that there exist vague objects in the world. Frequently used examples of such objects include clouds, deserts, and Mt. Everest. For example, it is indeterminate exactly where a desert stops and starts. There are grains of sand which are definitely in the Sahara Desert, and grains of sand which are definitely not. But there are some grains of which it could neither be said of them that they are nor that they are not part of the Sahara Desert. Imagine a field on the edge of the Sahara Desert on which there are no grains of sand. If a strong wind blows several million grains onto the field, where now does the Desert begin? The difficulty answering this and similar questions with precision or exactness makes a strong case for the existence of vague objects. 4

The late philosopher Gareth Evans argued against the possibility of vague objects on logical grounds (though there is, it should be noted, some debate about exactly what Evans was seeking to demonstrate). Imagine an object a about which it is indefinite whether a = b not due to any lack of knowledge on our parts, but because (we're assuming as our premise) the identity of a and b really is vauge. It is surely not the case that it is indefinite whether a = a. In fact, it is both determinate and true that a = a. Now by Leibniz’s law, if a = b, there can be no property which a possesses which b does not. So if a has the property of definitely being identical with a, and b does not – in fact, it has the property of being indefinitely identical with a – then we know that it is definite that a ≠ b. Therefore, there can be no vague objects. Evans’ argument has been both attacked and defended, though most philosophers today do not accept it.

Another issue receiving attention involves higher-order vagueness, that is, the question of whether ‘vague’ is itself vague. Of the borderline cases between the class of definitely tall men and the class of definitely non-tall men, aren’t some more borderline than others? In other words, of all those men who are neither clearly tall men nor clearly non-tall men, aren’t there those who are less clearly neither tall nor non-tall than others? Aren’t some regions of the ‘gray area’ grayer than others? If, as it seems, ‘vague’ is indeed vague, what are the implications for an account of vagueness? It would surely seem that any acceptable theory of vagueness would have to accommodate the existence of higher-order vagueness. Yet what does the existence of higher-order vagueness say for the hopes of producing a theory of vagueness which is able to say anything precise?

There is also the matter of the possible implications vagueness has for classical logic. Work in the latter has included the development of fuzzy logics, in which truth values range in real numbers from 1 (determinately, or absolutely true) to 0 (determinately, or absolutely false). For instance, the statement “This is a heap” said of a collection of eleven grains of salt might be assigned a truth value of 0.2 – though note: even this assignment is vague! Another approach is supervaluation, according to which a statement involving a vague term is true if and only if it is true on every precisification of that term, false if and only if it is false on every precisification, and neither true nor false if it is true on some and false on others. For example, it would be truly said of a collection of 1,000,000,000 grains of salt that it is a heap no matter where we might reasonably draw the line separating heaps from non-heaps, and it would likewise be false if said of two grains of salt that it was a heap, no matter where we might reasonably draw the line. With regard to a collection of 20 grains of salt, however, it would be neither true nor false to say of it “This is a heap,” since on some precisifications it would be true (e.g., if the line separating heaps from non-heaps were set at 15 grains), and on some it would be false (e.g., if the line were set at 25).

Vagueness may seem at this point to be a problem only a philosopher could love. But I would, in closing, ask the reader to consider the implications for ethics if it is granted that ‘good’ is vague, for biology, religion and ethics (and legislation) if ‘child’ is vague, and for philosophy of mind and our view of the person if ‘consciousness’ is vague.

(I would like to thank Emily Austin, John Churchill, and Roy Sorensen for their helpful comments on earlier drafts of this article.)

© Fred Ablondi 1999

Fred Ablondi is an assistant professor at Hendrix College, Arkansas

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A Model of Ambiguity and Vagueness in Clinical Practice Guideline Recommendations

Ambiguity and vagueness in clinical practice guidelines reduce the likelihood of clinician adherence. They lead to inconsistent interpretation and, in turn, to inappropriate practice variation and medical errors.

Resolving ambiguity and vagueness is an essential step in the computerized implementation of clinical practice guidelines. Successful resolution of ambiguity and vagueness requires an understanding of their characteristics, yet ambiguity and vagueness have not been differentiated, classified and described in medical context.

In this paper, we propose a tri-axial model to describe ambiguity and vagueness in clinical practice guidelines: differentiation of true ambiguity from vagueness, classification of ambiguity and vagueness, intentionality and components involved. Our goals in introducing this model are: (a) to provide guidance to guideline authors to enable them to reduce inadvertent use of ambiguous or vague language, (b) to improve transparency when vague language is used deliberately and (c) to create a framework for the development of tools to apply the model during authoring and implementation of clinical practice guidelines.

INTRODUCTION

Ambiguity and vagueness have been the subject of considerable attention in linguistics and philosophy 1 – 4 , but despite the significant detrimental effect of ambiguity and vagueness on CPG adherence and implementation, these concepts have not been explored and differentiated in a medical context. The term “ambiguity” is often used indiscriminately in the medical literature to denote both vagueness and ambiguity and the term “disambiguation” has been used to describe the resolution of both vagueness and ambiguity.

Ambiguity exists when a term can reasonably be interpreted in more than one way, for example, the word “bank” can refer to a financial institution or a riverside. Vagueness occurs when the boundaries of a word’s meaning are not well defined, as in the word “tall” 5 . Vagueness also exists when a word or phrase reduces the level of information contained in a statement, as in stating that an action “may be appropriate”; this phrase reduces the clarity about whether or not the action should be performed.

CPGs are promoted as a means to decrease inappropriate practice variation and to reduce medical errors. For these goals to be achieved, clinicians must adhere to the CPG recommendations in a consistent manner. Use of ambiguous and vague terms hampers communication and leads to uncertainty and to variable interpretation. This uncertainty is an established cause of decreased adherence to clinical practice guidelines (CPGs) 6 – 8 .

The interpretation of vague terms by clinicians varies greatly 9 , 10 , leading to reduced adherence or to increased practice variation despite apparent CPG adherence.

In this paper, we propose a model for ambiguity and vagueness in CPG recommendations. Our goals in introducing this model are to provide guidance to CPG authors to enable them to reduce inadvertent use of ambiguous and vague language, to improve transparency when vague language is used deliberately, and to create a framework for the development of tools to diminish the various forms of ambiguity and vagueness during the CPGs authoring and implementation processes. We believe that achieving these goals will facilitate CPGs implementation and lead to a reduction in variable interpretation of CPGs, ultimately diminishing inappropriate practice variation by clinicians.

Previous approaches have focused largely on clinicians’ assignment of numerical values to vague terms. Kong et al. studied the “use of qualitative expressions of probability” among medical professionals, asking physicians to assign a numerical value to twelve vague terms which the authors called “probabilistic terms” 10 . Their results show great variability of interpretation of these terms among observers. Other researchers showed comparable results applying similar methodology to judgments by radiologists, pathologists, surgeons and non-physician scientists.

The major shortcoming of this research is that subjects were not provided with a context for interpreting the vague terms. The importance of context on the interpretation of vague terms was shown by Mapes who conducted a study in which physicians were asked to assign a numerical value to the phrase “side effects with [this drug] are rare” in two different contexts: beta adrenergic blocking agents and antihistaminic drugs 11 . The average numerical estimate was much lower for the beta-blocker agents than for the antihistaminic drug. Mapes suggests that these different interpretations reflect the perceived severity of side effects for the different drug classes. Further complicating matters is the effect of framing. Tversky and Kahneman demonstrated that formulating identical statements in terms of “lives lost” or “lives saved” yielded different preferences, despite identical overall outcomes 12 .

Previously suggested approaches to resolving vagueness have included: assigning numerical values to vague terms 10 , ranking vague terms in relation to one another 10 , maintaining a “black-list” of terms that have been found to be particularly prone to variable interpretation 13 or that have particular legal implications 14 , creating a controlled vocabulary of vague terms from which authors could choose, mapping vague terms to specific actions 15 and applying fuzzy logic methods 16 .

Creating a controlled vocabulary of vague terms has the potential to reduce variable interpretation. Researchers have found hundreds of vague terms used in the medical literature, and reducing these to a manageable set of terms is a viable solution. A closely related solution is to require users to apply a limited structured vocabulary. This approach has been implemented in radiology where a lexicon of terms was created for the purpose of reporting mammography results 15 . Although some of the six choices are worded in a highly vague manner (“Suspicious. Biopsy should be considered”), clinical uncertainty is diminished since there are only 6 categories.

Researchers have noticed that a rank order of vague terms relative to one other was maintained across studies, despite wide variability in the interpretation of specific terms in the individual studies. This finding indicates it might be possible to create an ordinal scale of ranked vague terms from which authors could select when deliberately using vague terms.

Certain terms yield a wider range of interpretation than others, and should be avoided when possible; examples of such terms are “probably”, “normally” and “possibly”. The Agency for Health Care Policy and Research suggested that words such as “should” be avoided in guideline recommendations because of concern over potential legal implications 14 .

Areas not addressed in previous research include the various forms of ambiguity and vagueness, the source (deliberate or inadvertent) and rationale for using them, and the component of the CPG recommendations affected by them, e.g. the condition, the action or the explanation.

We reviewed the literature on ambiguity and vagueness in medical communication with the goals of determining the scope of previous research in this field and identifying previously recognized forms of vagueness of ambiguity.

The term “vagueness” is not mapped by Medical Subject Headings (MeSH). “Ambiguity” is mapped to the keyword “fuzzy logic”, which does not sufficiently describe the scope of ambiguity as we define it in this work. We therefore performed a text search of the terms “vague*” and “ambigu*”. This search yielded over 3000 results for each term, with very few of the results pertaining to the linguistic concepts of ambiguity or vagueness.

We next identified relevant terms, by traversing pertinent branches of the 2005 MeSH. Potentially relevant terms appeared in several main headings in MeSH, such as Humanities (logic), Information science (linguistics, semantics, terminology and fuzzy logic), and Psychiatry and psychology (comprehension, decision making, judgment and uncertainty). MEDLINE was searched with each of the MeSH keywords alone, and in combination with either “vagueness” or “ambiguity” using (MeSH term)[mesh] AND (vague* OR ambigu*). We further expanded our literature search by searching for the MeSH terms identified above with each of the MeSH terms “guidelines” and “physicians”.

Bibliographic lists of articles identified were searched for additional relevant articles. In addition, we searched the Web of Science database for articles citing the relevant articles identified so far. This process was performed iteratively, until no additional relevant articles were found.

Articles retrieved by this process provided the background for our model. Lists of vague terms from these articles were compiled, as were forms of vagueness that were previously described. Classes of ambiguity and their definitions were derived from the linguistics literature.

PROPOSED MODEL

Our proposed model comprises three axes ( Figure ). The first axis explores semantics, differentiating ambiguity from vagueness and classifying each of them. The second axis describes authors’ intent: the source of ambiguity or vagueness, i.e. whether it is deliberate or inadvertent, and when deliberate, the specific rationale for its use. The third axis defines what recommendation component is affected.

Model of vagueness and ambiguity in CPG recommendations

First axis: differentiation and classification

Ambiguity is classified into syntactic, semantic and pragmatic ambiguity, paralleling the three aspects of information 17 . Syntactic ambiguity arises when ambiguity is caused by the structure or syntax of a statement. This can occur when punctuation (or lack thereof) or Boolean connectors in a statement leave its meaning unclear. An example is “A or B and C” without clarifying whether this means “(A or B) and C” or “A or (B and C)”. Semantic ambiguity is the “classic” form of ambiguity in which a term can be interpreted in more than one way, such as the word “bank” in the sentence “I will meet you at the bank”. A special case of semantic ambiguity lies in the use of abbreviations whose reference is unclear. Pragmatic ambiguity refers to usage; as in saying on Wednesday: “See you next Friday”. Does the speaker mean to meet you in two or in nine days?

Pragmatic ambiguity can be created when two or more recommendations within a CPG are inconsistent or conflict with one another. Guideline recommendations that do not include instructions for all clinical scenarios are not comprehensive and lead to pragmatic ambiguity because clinician users of the CPG can reasonably act in more than one way 18 .

Underspecification is a form of vagueness that occurs when terms are used with insufficient details for definitive interpretation. Examples of underspecification are terms such as “moderate”, “elderly” and “adequate”. Some groups of underspecified terms have shared characteristics and can be represented on an ordinal scale of terms. The temporal vagueness scale ranges from “never” to “always” and includes intermediate terms such as “rare” and “common”. Probabilistic terms, range from “impossible” to “certain”, with terms such as “unlikely” and “probable” in between. Quantitative terms range from “none” to “all” with intermediate terms such as “few” and “many”. The terms at the extremes of each scale are not vague; they represent the only non-vague terms in each scale. Other forms of underspecification, such as implicit statements and incomplete information, can not be classified using ordinal scales, and are classified as non-ordinal underspecification.

Phrases that qualify the strength of CPG recommendations make up another category of vague terms. Examples of such terms are “it is prudent to recommend” and “is recommended as probably effective”. Vague terms in this class overlap with the other forms of vagueness, which can also be used as strength qualifiers as in “[a certain action] may be beneficial” and “[a certain action] is often beneficial”. We found it impossible to rank these qualifiers relative to one another.

The use of the passive voice as in “should be performed” is a form of vagueness 19 . Such usage has long been considered the norm in scientific writing but it obscures who is expected to perform the action. The actor may be a critical factor in some CPG statements.

As with ambiguity, terms can be considered vague because of the context in which they are used. One guideline recommendation includes both of the following statements: “present data are insufficient to support the use of [drug A]” and “there are no data to support the use of [drug B]”. Either of these, on its own, would be considered clear. When found together, however, the reader cannot determine whether there is more evidence supporting the use of drug A or B, or that both are equally not recommended.

Second axis: source and rationale

Ambiguity or vagueness may be deliberately or inadvertently introduced in CPG recommendations. Inadvertent ambiguity or vagueness generally reflect insufficient editing by the authors, reviewers and publishers of CPGs, and should be addressed by careful attention to the issue of ambiguity and vagueness during CPG authoring.

Deliberate use of vagueness or ambiguity poses a significant problem to the CPG audience. Attempts to resolve the vagueness might contradict the authors’ intention. Successful resolution of deliberate vagueness requires an understanding of its rationale, and of the range of possible interpretations the authors consider appropriate. The process by which CPG authors use vague terms has not been studied.

Insufficient scientific evidence and failure to reach a consensus among CPG authors are probably a common cause of deliberate vagueness. Reporting the quality of evidence and strength of recommendations partially address this cause of deliberate vagueness, but fail to provide clinicians or implementers with the range of acceptable interpretations.

Liability concerns have been reported in connection with CPG authoring, and have included advice on the naming of policy statements by professional societies, as well as advice on the choice of vague terms 14 . Ethical and religious concerns have been reported regarding the deliberate use of vague terms such as the term “futility”. Economic considerations are also likely to play a role in the choice of vague terms when a CPG recommendation presents an unusual financial burden.

Third axis: recommendation component affected

Clinical practice guideline recommendations typically describe an action ( what should be done) and the conditions under which this action should take place ( when it should be done). It is rare for CPG recommendations to be formatted as a pure if-then structure; there is often additional text qualifying or explaining the condition or the action (e.g. why it should be done).

Ambiguous and vague terms can occur within any or all of these three components: the condition(s), the action(s), and the explanation(s) for the recommendation. When the conditions are affected, decidability of the recommendation is undermined. When the actions are unclear, executability is hampered. Vagueness affecting the explanation segment has the least impact on implementability. For example, in the statement “If a 20-foot visual acuity measurement is required, a projected standard Snellen chart should be used because acuities… may not correlate to…” the probabilistic vague term “may not” has minimal effect on implementability, because it is not part of the condition or the action.

Vagueness and ambiguity in CPG recommendations are a significant barrier to widespread adherence and impede computer-based representation and implementation. Computerized implementation of CPG recommendations requires the resolution of ambiguity and vagueness. The product of this resolution process is a revised recommendation statement that clearly states what action is to be taken and under what circumstances. The resolution process is successful when the intended audience of the CPG interprets the revised CPG recommendations in the manner intended by the authors, with minimal variation between readers. The best ways to ‘disambiguate’ ambiguity and ‘resolve’ vagueness are not known. We propose that the three axes in our model can serve as a basis for addressing the problem.

The ideal timing for remedying ambiguity and vagueness is during the authoring of CPGs. At this stage careful editing can remove inadvertent ambiguity and vagueness. When authors deliberately choose to use vague terms, they should take into consideration the average and range of values that have been assigned by clinicians in interpreting the terms (axis 1). Vague terms can be categorized according to the first axis of our model, ranked in relation to one another and made available to authors. Where deliberate vagueness is deemed necessary because of insufficient evidence or lack of consensus the reasoning is most appropriately placed in the explanation part of the recommendation, as this part least affects the implementability of the recommendation (axis 3).

Once the CPG has been published, resolving the remaining ambiguity and vagueness is left to clinicians and to informaticians attempting to represent or implement the CPG recommendations. Attempting to understand the source and rationale for vague terms is an essential step in resolving the vagueness as attempting to resolve vague terms which are deliberate runs the danger of significantly altering the authors’ intention (axis 2). Implementers should also be aware of the classification of vague terms, and can use numerical data and the order in which terms are ranked in the ordinal scales in deciding how to interpret vague terms (axis 1). Finally, for recommendations that can be parsed into the three components of axis 3, implementers can concentrate on interpreting terms in the condition and action components.

Our model can be used to develop software tools that would be of help during the authoring and implementation stages. Such software tools could identify and classify vague terms, inform authors (or implementers) of numerical values associated with the term, display an ordinal scale of similar terms, and suggest alternative terms.

Our next step will be to validate this model by examining a random selection of 100 CPG recommendations, classifying vague and ambiguous terms (axis 1), and determining the affected component (axis 3). To assess axis 2 will require polling guideline authors as to their reasons for introducing vague statements. The model will be iteratively refined and reevaluated with an additional set of random CPG recommendations.

We propose a novel model of ambiguity and vagueness in CPG recommendations. This model can be used during the development of CPGs to identify and eliminate unnecessary ambiguity and vagueness. When deemed necessary, the use of vagueness can be facilitated by our model aiming to reduce variable interpretation and inappropriate practice variation.

ACKNOWLEDGEMENTS

The National Library of Medicine supported this work through grants T15 LM 07065 and R01 LM 07199.

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1 The Problem of Vagueness

• Published: May 2020
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This chapter introduces the philosophical concept of vagueness and explains its significance for contemporary philosophy. The concept is seen to give rise to two main problems: the ‘soritic problem’ of finding a solution to the paradoxes of vagueness; and the ‘semantic problem’ of finding a satisfactory semantics and logic for vague language. It discusses three of the main attempts to deal with these problems – Supervaluationism, Degree theory, and Epistemicism. It indicates why none of these theories has been regarded as satisfactory and it concludes with a general impossibility result which seems to rule out any satisfactory account of the concept.

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Senators studied AI for a year. Critics call the result ‘pathetic.’

The 31-page “road map” calls for a $32 billion infusion for AI research and development and asks congressional committees to develop legislation.

For much of the last year, Senate Majority Leader Charles E. Schumer and a bipartisan group of his colleagues have been huddling with tech CEOs, civil rights leaders and top researchers to develop an “all hands on deck” plan to address the urgent threats posed by artificial intelligence.

On Wednesday, the Senate AI Gang, as the group is known, unveiled the fruits of that effort, celebrating a sprawling 31-page road map that calls for billions of new funding in AI research as the “deepest” AI legislative document to date. But consumer advocates are furious about the final product, saying that the document is far too vague about how it will protect people from AI’s harms and that the senators’ initiative is sucking up the oxygen from other efforts to aggressively regulate the technology.

“This road map leads to a dead end,” Evan Greer, the director of Fight for the Future, an advocacy group, said in a statement that called the plan “pathetic” — a criticism echoed by others.

The immediate divisions over the plan bring to the fore the challenges of regulating the swiftly evolving technology in a deeply polarized Congress during an election year. Rather than pursuing a single comprehensive bill, the AI Gang has decided to delegate the legislative work to Senate committees, which are at drastically different stages in their efforts to understand the promise and peril of AI.

Schumer (D-N.Y.) expects that some AI bills could pass the Senate and potentially the House by the end of the year, but he noted that much of this work will extend into the next Congress. But the plan faces an uncertain future next year, as key lawmakers working on tech issues are scheduled to retire and the 2024 elections could reshape the leadership of Congress and the White House. The Senate Rules Committee on Wednesday advanced a trio of bipartisan bills addressing the role of AI in elections, which Schumer noted was one of the most urgent issues facing Congress amid the 2024 elections.

“We’re not going to wait on legislation that addresses every aspect of AI in society,” Schumer said. “If some areas are ready earlier than others, they should go forward.”

Other congressional committees are just beginning their work on artificial intelligence, as major tech companies are plowing forward with ever more advanced systems intended to further entrench the technology in consumers’ lives. On Monday, OpenAI announced a handful of upgrades that will make it easier for people to talk to ChatGPT, drawing comparisons with the 2013 film “Her,” which depicts a human falling in love with a digital voice assistant. On Tuesday, Google announced that it would roll out this week AI-generated answers to the top of everyone’s search results in the United States, transforming the way people access information online.

Lawmakers have repeatedly promised that they will regulate AI with greater urgency than they did with social media. For the last half decade, lawmakers have held numerous hearings and introduced a flurry of bills to address the ways social media allegedly harms children, undermines elections and imperils users’ privacy. But to date, the main social media legislation that Congress has passed is a law that could force a sale or ban of TikTok. With the new roadmap, critics say lawmakers risk repeating the same mistakes.

Tech industry groups were largely supportive of the road map. TechNet, whose members include OpenAI, Google and Meta, said in a statement that the directive “will strengthen America’s global competitiveness in AI and emerging technologies” through providing $32 billion for AI research and development, which will be distributed to the Energy Department, Commerce Department, National Science Foundation, and National Institute of Standards and Technology.

Tony Samp, the head of AI policy at the DLA Piper law firm and former founding director of the Senate AI working group, said the Senate’s process helped raise awareness about AI among lawmakers and helped prompt ideas for how to legislate. DLA Piper, including Samp, has lobbied on behalf of clients including OpenAI, according to federal disclosures.

“There are some who think you can wave a magic wand and Congress could pass comprehensive AI legislation, but that thinking ignores the political realities in the United States, as well as the real objectives of the AI Insight Forums and the road map,” Samp told The Washington Post.

Reggie Babin, a senior counsel at the law firm Akin and a former chief counsel to Schumer, told The Post that the working group succeeded in its goals. Babin has lobbied on behalf of Akin clients, including Adobe, according to federal disclosures.

“The goal of the process was to figure out how to make sure that 80 percent of stakeholders in the middle of this conversation are satisfied while preserving space for continued engagement on all fronts,” he said. “I think the working group hit that mark.”

The lawmakers gathered input for the road map in private sessions dubbed Insight Forums. Over the nine sessions, lawmakers met with executives including OpenAI CEO Sam Altman and Tesla CEO Elon Musk, as well as consumer advocates and civil rights leaders, such as Maya Wiley, the president and CEO of the Leadership Conference on Civil and Human Rights, a Washington-based group that represents a number of civil rights organizations. Liz Shuler, the president of the AFL-CIO who participated in the Insight Forums, called the road map an “important start” to passing AI legislation.

But civil society leaders were frustrated that the road map only made a cursory mention of AI bias, amid widespread concerns that the technology can replicate and exacerbate harmful stereotypes. Nik Marda, a technical lead on AI governance at Mozilla, noted on X that “bias” was mentioned in the road map as many times as “space debris.”

Rashad Robinson, the president of the civil rights group Color of Change, said the report shows Schumer “is not taking AI seriously.” Robinson called for lawmakers to move swiftly to respond to the bias that AI can pose.

Schumer told The Post in a statement that he shares the goals of the advocates.

“Leader Schumer agrees with their goals and we’re going to continue to work closely with them as legislation is written,” said Schumer spokeswoman Allison Biasotti.

Greer said the report reads like industry had outsize influence over the process, and it was written by Altman and other tech lobbyists.

“They heard from experts about the urgency of addressing AI harms and then paid lip service to that while giving industry most of what they want: money and ‘light touch’ regulatory proposals,” Greer told The Post.

The United States’ efforts to regulate AI lag far behind those of the European Union, which last year advanced a wide-ranging AI Act that sets limits on AI based on how risky regulators deem an application to be. The E.U. AI Act, for instance, bans social scoring systems similar to those used in China, and it places transparency requirements on high-risk applications of AI in medical devices or employment settings.

Many observers hoped that the road map would provide clarity on a path forward for Congress to address some of the thorniest issues in AI governance that have divided the tech industry — including the future of copyright law and the growing debate over the regulation of AI models that are open source, or freely available to the public, without the guardrails that OpenAI, Google and Microsoft place on their models. But Schumer’s report doesn’t mention open source, and it largely punts issues of intellectual property rights to government agencies, directing lawmakers to review existing and forthcoming reports from the U.S. Copyright Office and the U.S. Patent and Trademark Office on AI.

In a briefing with reporters Tuesday night, Sen. Todd Young (R-Ind.), a member of the AI Gang, said the report had “a high level of specificity” for a document of its size and scope. But senators acknowledged the report leaves key questions unanswered. The report calls for a $32 billion investment in nondefense AI research and development, but it does not specify how much funding should be directed to the military. The report also leaves key questions about how Congress should regulate consumer privacy in the age of AI to the committees.

“Where vagueness was required to come to an agreement, we embrace vagueness,” Young said.

But that strategy doesn’t work, said Suresh Venkatasubramanian, a Brown University professor who co-authored the White House’s AI Bill of Rights. He participated in the forums and felt as if lawmakers ignored the problems raised during the sessions.

“Embracing vagueness at this point is basically saying the status quo is just fine," he said.

The report “repackages” many issues around AI that have been debated on Capitol Hill for years, and its delivery may prompt some legislators to “yearn for more than just polished reiterations,” said Divyansh Kaushik, a vice president at Beacon Global Strategies, which advises companies on national security issues.

“After almost a year of hearings, briefings and forums, I think members are hungry for tangible, actionable steps and crisp legislative blueprints, something beyond the theoretical … a call for concrete, actionable strategies,” he said. “The real challenge begins now and it’s one for congressional committees: ensuring that this report does more than stir the pot, but rather sparks a sustained drive toward innovative and decisive policymaking to ensure American competitiveness on these critical technologies."