Language, Concepts, and Definitions

“Political language ... is designed to make lies sound truthful and murder respectable, and to give an appearance of solidity to pure wind.”

— George Orwell, “Politics and the English Language” (1946)

A large share of disagreements are partly or wholly about words. Two people argue for an hour about whether a policy is “socialist,” whether a virus is “alive,” or whether a painting is “art,” and they never notice that they are using the word differently. Other disputes look verbal but are substantive. Many fallacies (equivocation, persuasive definition, motte-and-bailey) work by exploiting the gap between a word and the concept behind it.

This chapter gives you the tools to handle language carefully: kinds of definition, ambiguity and vagueness, verbal disputes, loaded language, the fact–value distinction, and the use of thought experiments and intuitions as evidence.

Why language is an epistemic issueListen

Beliefs are expressed in language, arguments are built from sentences, and most of what we know we learned through words (see Testimony). If the words are unclear, the beliefs are unclear, and nobody can tell whether the argument is valid.

Recall Bacon’s Idols of the Marketplace (see Chapter 2): errors that arise because “words are imposed according to the apprehension of the vulgar,” so that “the ill and unfit choice of words wonderfully obstructs the understanding.” Locke devoted all of Book III of his Essay to the “imperfection” and “abuse” of words. Twentieth-century philosophy took a “linguistic turn” in which many philosophers thought that most philosophical problems were confusions about language. You need not go that far to see that clarity about language is a precondition of clear thinking.

A practical rule to start with: when a discussion stalls, ask each person to say what they mean by the key term, in other words. Often the disagreement changes shape or disappears.

Use and mentionListen

A word can be used to talk about something, or mentioned to talk about the word itself.

• Use: Boston is a large city.
• Mention: “Boston” has six letters.

Philosophers mark mention with quotation marks. The distinction sounds pedantic, but confusing the two creates real errors:

• “The word ‘natural’ appears on this package, so the product is natural.” A fact about the label (mention) is taken as a fact about the product (use).
• “Nobody can define ‘justice,’ so there is no such thing as justice.” The difficulty of defining a word does not show that the thing it refers to does not exist. Nobody can give a watertight definition of “game” either, and games clearly exist.
• “‘Freedom’ is just a word.” True of the word, and irrelevant to whether people should be free.

Sense and referenceListen

In “On Sense and Reference” (1892), Gottlob Frege posed a puzzle. Ancient astronomers called the bright star seen in the evening Hesperus and the bright star seen in the morning Phosphorus. Both are in fact the planet Venus. Now compare:

1. Hesperus is Hesperus.
2. Hesperus is Phosphorus.

Both sentences are true, and both terms refer to the same object. But (1) is trivial and knowable a priori, while (2) was an astronomical discovery. How can two sentences about the same object differ in informativeness?

Frege’s answer: a term has both a reference (Bedeutung), the object it picks out, and a sense (Sinn), the way it presents that object, its “mode of presentation.” “Hesperus” and “Phosphorus” have the same reference and different senses.

This matters because in some contexts, you cannot substitute co-referring terms without changing truth value. These are opaque (or intensional) contexts, especially contexts of belief and knowledge.

• Lois Lane believes Superman can fly. (True)
• Superman is Clark Kent. (True)
• So Lois Lane believes Clark Kent can fly. (False, in the story)

The masked man fallacy

The masked man fallacy (an intensional fallacy) substitutes co-referring terms inside a knowledge or belief context:

I know who my father is.
I don’t know who the masked man is.
Therefore, the masked man is not my father.

The conclusion does not follow. The masked man could be your father. Your knowledge is sensitive to how a person is presented, not just to who they are.

Some philosophers argue that one version of Descartes’ argument for mind–body dualism commits this fallacy: “I can doubt that my body exists; I cannot doubt that my mind exists; so my mind is not my body.” Being doubtable is not a property of a thing itself but of the thing as thought of in a certain way. So this argument cannot establish that mind and body are distinct. (Descartes’ main argument, from clear and distinct conceivability, is different and more sophisticated.)

Kinds of definitionListen

Definitions serve different purposes. Much confusion comes from treating one kind of definition as if it were another.

Lexical definition. Reports how a word is actually used in a language community, as in a dictionary. It can be accurate or inaccurate. “‘Bachelor’ means an unmarried adult man.”

Stipulative definition. Introduces a new term, or a new meaning for an old one, by fiat. It is neither true nor false, only more or less useful. “Let’s call these particles ‘quarks.’” Stipulations are legitimate if they are announced openly and used consistently.

Precising definition. Narrows the meaning of a vague term for a particular purpose. “For this study, a household is ‘in poverty’ if its income is below 60% of the national median.” This is common in law, science, and policy. It is legitimate, but conclusions drawn under one precising definition cannot automatically be carried over to the ordinary meaning of the word, and different definitions can give very different results.

Theoretical definition. Defines a term by embedding it in a theory. “Heat is the average kinetic energy of molecules.” “Water is H₂O.” Theoretical definitions can be revised when theories change.

Operational definition. Defines a term by the procedure used to measure it. “Intelligence is what IQ tests measure.” (The psychologist Edwin Boring wrote in 1923 that “intelligence is what the tests test.”) Operational definitions make concepts measurable. They also create a risk: the measurement can drift away from the thing we actually care about. This is the insight behind Goodhart’s law, in the form given by the anthropologist Marilyn Strathern: “When a measure becomes a target, it ceases to be a good measure.” If a hospital is judged by waiting times, it may shorten waiting times in ways that do not improve care (such as reclassifying patients). If schools are judged by test scores, they may teach to the test.

Persuasive definition. Charles Stevenson (“Persuasive Definitions,” Mind, 1938) identified definitions that keep a word’s emotional force while changing its descriptive meaning, in order to influence attitudes. “Real freedom means economic security.” “True democracy is rule by the virtuous.” “Taxation is theft.” The word’s positive or negative charge is transferred to the new content. Persuasive definitions are often disguised as lexical definitions, and that disguise is what makes them illegitimate. When you meet a phrase like “real X,” “true X,” or “X, properly understood,” check for one.

Ostensive definition. Defines by pointing at examples. “That is red.” All language learning begins with ostension, but ostension alone is ambiguous: pointing at a red ball could be teaching “red,” “ball,” “round,” or “toy.”

Extensional (enumerative) definition. Lists the members of a class. “The Nordic countries are Denmark, Finland, Iceland, Norway, and Sweden.”

Definition by genus and difference. Aristotle’s model: state the general kind (genus) and the feature that distinguishes this species within it (differentia). “A human is a rational (difference) animal (genus).” “A triangle is a polygon with three sides.”

Rules for good definitionsListen

Traditional logic textbooks give these rules, originally derived from Aristotle’s Topics:

1. Not too broad. “A bird is an animal with wings” includes bats and insects.
2. Not too narrow. “A bird is a feathered animal that flies” excludes penguins and ostriches.
3. Not circular. “A cause is something that causes an effect.” Circularity can be subtle and spread over several definitions.
4. Not obscure or figurative. “Architecture is frozen music” may be illuminating as a metaphor, but it is not a definition.
5. Not negative when it can be positive. “A cat is an animal that is not a dog” says almost nothing.
6. Capture the essential or important features, not incidental ones. “A human is a featherless biped” (see below) picks out the right creatures for the wrong reason.
7. Fit the purpose. A definition of “death” for a biology textbook, a hospital, and a life-insurance contract may properly differ.

The last rule matters most in practice. When someone disputes a definition, ask: definition for what purpose? A great deal of arguing about “what X really means” dissolves once the purposes are separated.

Necessary and sufficient conditions and their limitsListen

The classical ideal, from Socrates onward, is to define a concept by giving conditions that are individually necessary and jointly sufficient. (See Necessary and sufficient conditions.) A definition of that form lets you decide every case.

The method for testing such definitions is the counterexample. According to Diogenes Laertius, when Plato defined a human as “a featherless biped,” the Cynic philosopher Diogenes plucked a chicken, brought it into the Academy, and announced: “Here is Plato’s human!” Plato then added “with broad, flat nails” to the definition. The story is probably apocryphal, but it shows the method perfectly. A proposed definition is refuted by a single case that meets the conditions but is not an instance of the concept, or is an instance but fails the conditions.

The most famous modern example is the Gettier problem: a counterexample to the definition of knowledge as justified true belief that set off decades of attempts at repair.

Here is the worry. After 2,400 years, philosophers have produced very few uncontroversial definitions in terms of necessary and sufficient conditions of philosophically interesting concepts: knowledge, cause, justice, art, meaning, person. This suggests that many concepts may not have such definitions. Several alternatives have been proposed.

Family resemblance and prototypesListen

In the Philosophical Investigations (§§66–67), Wittgenstein asked what all games have in common:

“Consider for example the proceedings that we call ‘games’. I mean board-games, card-games, ball-games, Olympic games, and so on. What is common to them all? Don’t say: ‘There must be something common, or they would not be called “games”’—but look and see whether there is anything common to all. ... we see a complicated network of similarities overlapping and criss-crossing.”

Not all games involve winning and losing (a child throwing a ball against a wall). Not all involve skill (games of chance) or competition (solitaire) or fun (professional sport, for some). Instead, Wittgenstein said, games form a family: like members of a family who share various features (build, eyes, gait, temperament) in overlapping patterns, without one feature shared by all.

The psychologist Eleanor Rosch, in work from the 1970s, found empirical support for a related view, prototype theory. People judge a robin to be a “better” example of a bird than a penguin, respond faster when verifying “a robin is a bird,” and list it first. Categories seem to be organized around prototypes (typical examples), with membership graded by similarity to them, rather than defined by a strict list of conditions.

What follows for critical thinking:

• “That’s not really an X, because it lacks feature F” is a weak argument if X is a family-resemblance concept and F is only a typical feature. (Compare the No True Scotsman fallacy.)
• The lack of a precise definition does not mean a concept is useless or that there is no fact of the matter in clear cases. We can know that chess is a game without a definition of “game.”
• Disputes about borderline cases (is esports a sport? is a hot dog a sandwich?) often have no deep answer. They may be settled by stipulation for some purpose, or left open.

AmbiguityListen

A word or sentence is ambiguous when it has two or more distinct meanings. (This is different from being vague, which is having unclear boundaries.) Ambiguity is the raw material of the fallacy of equivocation.

Lexical ambiguity: a single word has several meanings.

• “bank” (riverbank, financial institution)
• “The judge found the argument sound.” (Logically valid with true premises, or merely reasonable?)

Syntactic ambiguity (amphiboly): the sentence structure allows several readings.

• “I saw the man with the telescope.” (Who has the telescope?)
• “Flying planes can be dangerous.”
• The newspaper headline “Squad Helps Dog Bite Victim.”

Scope ambiguity: the relative order of “all,” “some,” “not,” “only,” and modal words is unclear. See Predicate logic and quantifiers.

• “Everyone didn’t come.” (Nobody came, or not everyone came?)
• “You can’t be too careful.” (Is carefulness always good, or can it be excessive?)

Collective versus distributive readings:

• “The students lifted the piano.” (Together, or each one individually?)
• “Americans eat more hot dogs than anyone else.” (As a whole nation, or per person?) This ambiguity underlies the fallacies of composition and division.

Process versus product:

• “The observation was careful” (the act of observing) versus “the observation was surprising” (what was observed).

Type versus token:

• “We drove the same car.” (The same model, or the very same vehicle?)

A list of dangerous words

Some words cause so much confusion in public debate that it is worth memorizing their different senses.

Vagueness and the sorites paradoxListen

A term is vague if it has borderline cases: cases where it is unclear whether the term applies, and where no further information would settle the matter. “Bald,” “tall,” “heap,” “rich,” “adult,” “red,” “old,” and “alive” are vague. You can know exactly how many hairs someone has and still be unsure whether they are bald.

Vagueness gives rise to the sorites paradox (from Greek sōros, heap), attributed to Eubulides of Miletus in the 4th century BCE:

1. One grain of sand is not a heap.
2. If n grains are not a heap, then n + 1 grains are not a heap.
3. Therefore, 1,000,000 grains are not a heap.

Each premise seems true and the reasoning is valid (a million applications of modus ponens), yet the conclusion is false. Something has to give. The main theories are:

• Epistemicism (Timothy Williamson, Vagueness, 1994): there is a sharp boundary (some exact number of grains makes a heap), but we cannot know where it is. Premise 2 is false. Most people find this incredible at first; Williamson argues that the alternatives are worse.
• Supervaluationism (Kit Fine, 1975): a vague sentence is true if it comes out true on every acceptable way of making the term precise, false if false on every way, and neither in between. Premise 2 is false (every precisification has a cut-off), though there is no particular n at which it fails.
• Degrees of truth (fuzzy logic): “This is a heap” can be true to degree 0.7. Each step reduces the truth only slightly, and the conclusion ends up fully false.
• Contextualism: the boundary shifts with context, and it is never located where you are looking.

For critical thinkers, the most important point is not the theory of vagueness but a fallacy it tempts us into.

The continuum fallacy

The continuum fallacy (also called the fallacy of the beard, or the line-drawing fallacy) reasons: there is no sharp line between X and Y, so there is no real difference between X and Y.

• “There’s no precise moment when day becomes night, so day and night are the same.”
• “There’s no exact income at which someone becomes rich, so the distinction between rich and poor is meaningless.”
• “You can’t say exactly when a fetus becomes conscious, so there’s no difference between a zygote and a newborn.” (Whatever one’s view on abortion, this particular argument is fallacious.)

The fact that a boundary is vague does not mean there is no difference between clear cases on either side. Law handles vagueness with bright-line rules: you can vote at 18, not 17 years and 364 days. The line is arbitrary in its exact placement but not arbitrary in existing, and having some line is better than having none. The continuum fallacy is closely related to some forms of the slippery slope.

Verbal disputesListen

A dispute is merely verbal when the parties agree on all the relevant facts but use a key word differently, so that their apparent disagreement is only about which words to use.

William James opens Lecture II of Pragmatism (1907) with a story. On a camping trip, his friends were arguing: a squirrel clings to one side of a tree trunk, and a man walks quickly around the tree; the squirrel moves around the trunk just as fast, always keeping the tree between them. Does the man go round the squirrel? James said that it depends on what you mean by “going round.” If you mean passing from north of the squirrel to east, then south, then west, the man goes round. If you mean being first in front of it, then to its right, then behind it, then to its left, he does not, since the squirrel always faces him. “Make the distinction, and there is no occasion for any farther dispute.”

The classic example: If a tree falls in a forest and no one hears it, does it make a sound? If “sound” means pressure waves in air, yes. If “sound” means an auditory experience, no. Once this is noticed, there is nothing left to argue about. (Unless someone wants to argue about which meaning is better, which is a different debate.)

David Chalmers (“Verbal Disputes,” Philosophical Review, 2011) proposed a test, the method of elimination: ban the disputed word. Ask the parties to state their positions without using it. If the disagreement disappears, it was verbal. If it persists in new terms, it was substantive.

“Is Pluto a planet?”
Ban “planet.” Now: “Pluto orbits the sun, is massive enough to be round, and has not cleared its orbital neighborhood of other objects.” Both sides agree. The remaining question is which classification scheme is more useful for astronomy, which is a real question, but not a question about Pluto.

Verbal disputes are not always trivial. Legal definitions have consequences. In Nix v. Hedden (1893), the US Supreme Court had to decide whether tomatoes were “vegetables” for the purposes of a tariff on imported vegetables. Botanically, a tomato is a fruit. The Court ruled that in ordinary language, and therefore for the tariff, it is a vegetable. The verbal question had a financial answer. Similar disputes about whether an act is “torture,” whether an organization is “terrorist,” or whether a worker is an “employee” determine rights and penalties.

The practical lesson: when a dispute feels endless, check whether it is verbal. If it is, separate the factual question (on which you may agree) from the classificatory question (which may be about purposes and consequences). See Step 2: Identify the kind of disagreement.

Loaded language, euphemism, and framingListen

Words describe, but they also evaluate and emphasize. The same facts can be described in ways that push the listener toward different conclusions.

Euphemism softens: “collateral damage” (civilian deaths), “enhanced interrogation” (torture, on most definitions), “downsizing” or “rightsizing” (firing people), “passed away” (died), “revenue enhancement” (tax increase).

Dysphemism harshens: “death tax” (estate tax), “job-killing regulations,” “bureaucrats” (public servants).

Paired labels in political debates each encode one side’s framing: “pro-life” versus “pro-choice” (each side names itself by what it supports, and often names the other side by what it opposes), “illegal aliens” versus “undocumented immigrants,” “tax relief” versus “tax cuts for the rich,” “gun rights” versus “gun safety.”

The linguist George Lakoff (Don’t Think of an Elephant!, 2004) argued that words evoke frames, structures of background assumptions. “Tax relief” frames taxation as an affliction from which one needs relief, and whoever relieves it is a hero. Accepting the phrase means accepting the frame, even if you then argue against the policy.

Psychologists have shown that framing effects can reverse people’s choices even when the options are logically identical. In Amos Tversky and Daniel Kahneman’s “Asian disease” problem (1981), people prefer a sure option when outcomes are described as lives saved and a risky option when the same outcomes are described as lives lost. See Framing effects.

Practical defense: before evaluating a claim, translate it into neutral language. Ask how someone on the other side would describe the same facts. If the conclusion only seems compelling in one vocabulary, the vocabulary is doing the work, not the evidence.

Essentially contested conceptsListen

The philosopher W. B. Gallie (“Essentially Contested Concepts,” Proceedings of the Aristotelian Society, 1956) identified a class of concepts whose correct application is permanently disputed, not because people are confused, but because of the nature of the concepts. His examples included democracy, art, social justice, and a Christian life. Such concepts are:

• Appraisive: calling something “democratic” or “art” praises it.
• Internally complex: they have several components (for democracy: majority rule, rights protection, participation, equality).
• Variously describable: people weight the components differently.
• Open: they evolve in response to new circumstances.

Other examples: freedom, equality, fairness, harm, violence, terrorism, racism, person, merit, rule of law.

John Rawls, in A Theory of Justice (1971), drew a useful distinction between a concept and conceptions of it. People can share the concept of justice (roughly, no arbitrary distinctions between persons and a proper balance between competing claims) while holding different conceptions (utilitarian, libertarian, egalitarian). When a debate involves an essentially contested concept, it helps to name the rival conceptions explicitly: “On a libertarian conception of freedom, this law reduces freedom. On a conception of freedom as real capacity to act, it may increase it.” You may still disagree about which conception is best, but you are no longer talking past each other.

Thick and thin conceptsListen

Bernard Williams (Ethics and the Limits of Philosophy, 1985) distinguished:

• Thin evaluative concepts: good, bad, right, wrong, ought. These evaluate without describing much.
• Thick concepts: cruel, brave, generous, rude, honest, lazy, reckless. These both describe (cruelty involves causing suffering) and evaluate (cruelty is bad).

Thick concepts carry evaluation into what sounds like description. “The minister’s response was reckless” presents an evaluation as a description. In a debate, it helps to separate the two: “What did the minister do? And was that bad?” The descriptive part can be checked against the facts; the evaluative part needs a separate argument.

Pairs like “freedom fighter”/“terrorist,” “moderation”/“censorship,” “reform”/“cuts,” and “investment”/“spending” often describe the same actions with opposite evaluations built in.

Facts, values, and the is-ought gapListen

In a famous passage of A Treatise of Human Nature (1739–40, Book 3, Part 1, Section 1), David Hume noted that authors reasoning about morality proceed with statements about what is, and then suddenly switch to what ought to be, without explaining “how this new relation can be a deduction from others, which are entirely different from it.” This is the is–ought gap (or Hume’s law): no set of purely factual premises logically entails a normative conclusion.

Smoking causes cancer. (Is.)
Therefore, you ought not to smoke. (Ought.)

This argument is invalid as it stands. It needs a normative premise, such as “You ought not to do things that seriously damage your health.” Once that premise is supplied, the argument is valid, and the debate can focus on whether the normative premise is acceptable.

Related but distinct is G. E. Moore’s naturalistic fallacy (Principia Ethica, 1903): the attempt to define “good” in terms of a natural property such as pleasure or survival. Moore’s open question argument: for any natural property N, the question “This is N, but is it good?” remains open and meaningful, which it would not be if “good” just meant N. (Moore’s term is often misused to mean the appeal to nature, which is a different mistake.)

Some philosophers resist a sharp fact–value divide. John Searle (“How to Derive ‘Ought’ from ‘Is’,” 1964) argued that from the fact that someone uttered “I promise to pay you five dollars,” one can derive that he ought to pay, via institutional facts about promising. Hilary Putnam (The Collapse of the Fact/Value Dichotomy, 2002) argued that thick concepts and scientific judgments (such as “simple,” “coherent,” “reasonable”) entangle facts and values. These challenges are serious, but for analyzing everyday arguments the practical rule stands:

Every argument for a policy or action has at least one normative premise and at least one factual premise. Find them both.

This lets you locate the disagreement. Two people can agree on every fact and disagree on values (“Nuclear power produces little carbon, and we agree on the accident statistics, but I weigh the risk of catastrophe more heavily”). Or they can agree on values and disagree on facts (“We both want fewer deaths; we disagree about whether this policy will reduce them”). Most real disputes are a mixture. Arguing about values when the disagreement is factual, or about facts when it is about values, wastes everyone’s time. See Step 2: Identify the kind of disagreement.

Thought experiments and intuitionsListen

Philosophers often test theories with thought experiments: imagined scenarios designed to elicit a judgment (an intuition) about a case. If a theory implies something about the case that seems clearly wrong, that counts against the theory.

Famous thought experiments in epistemology and nearby fields:

• Gettier cases (does this person know?). Chapter 5
• Brain in a vat (could you tell?). Chapter 8
• Mary’s room (does she learn something?). Chapter 1
• Truetemp and Norman the clairvoyant (is reliability enough?). Chapter 6
• Fake barn country (does luck undermine knowledge?). Chapter 5
• The trolley problem in ethics (Philippa Foot, 1967; Judith Jarvis Thomson, 1976 and 1985).

Science uses thought experiments too. Galileo refuted Aristotle’s claim that heavier bodies fall faster with one: tie a heavy stone to a light one. The light stone should slow the heavy one (so the pair falls slower than the heavy stone alone), but the pair is heavier than the heavy stone (so it should fall faster). Contradiction. So weight cannot determine falling speed in the way Aristotle said. Einstein’s elevator, Maxwell’s demon, and Schrödinger’s cat are other examples.

Are intuitions good evidence? This is debated.

• Defenders point out that all reasoning must start somewhere, and that judgments about cases are often more reliable than judgments about abstract principles. Timothy Williamson (The Philosophy of Philosophy, 2007) argues that “intuitions” are just ordinary judgments, and they are as good or bad as the judgment behind them.
• Critics from experimental philosophy have shown that intuitions about some cases can be affected by irrelevant factors, such as the order in which cases are presented (Swain, Alexander, and Weinberg, 2008) or the wording of the scenario. Edouard Machery (Philosophy Within Its Proper Bounds, 2017) argues this should make us much more modest about the method of cases. Note that some early findings of cultural variation in epistemic intuitions failed to replicate in larger samples (see Contemporary directions).
• A radical critic, Robert Cummins (“Reflection on Reflective Equilibrium,” 1998), argued that we could only tell which intuitions are trustworthy if we had some independent, intuition-free access to the facts they concern, and if we had that, we wouldn’t need intuitions at all. So philosophy should stop relying on them.

A case study: knowledge intuitions. Jennifer Nagel (Knowledge: A Very Short Introduction, ch. 8) summarizes what experimental work has found about intuitions concerning knowledge. The 2001 study by Jonathan Weinberg, Shaun Nichols, and Stephen Stich reported that a Gettier-style story (Bob believes his friend Jill drives an American car because she has long driven a Buick; unknown to him, the Buick was stolen and replaced with a Pontiac, also American) was judged “only believes” by most Western participants but by less than half of small groups of East Asian and South Asian participants. Critics noted that the samples were small and the vignette easy to read in different ways. Later, much larger cross-cultural studies found that people in many cultures agree with philosophers that Gettier subjects lack knowledge, and developmental studies find that children in very different societies pass through the same stages in distinguishing knowledge from ignorance and false belief. But another pattern proved just as robust: merely mentioning a possibility of error reduces people’s willingness to attribute knowledge, even when the subject is in no danger of that error. In one study Nagel reports, most participants said that a shopper looking at a red table in a normally lit store knows it is red; when the story added that a white table under a red spotlight would look the same, and that he hadn’t checked the lighting, fewer than half said so. Whether the second, stingier intuition reveals the truth about knowledge (as the skeptic says), a shift in standards (as the contextualist says), or a cognitive illusion (as the moderate invariantist says) is exactly what is in dispute. See also Mindreading: how we attribute knowledge.

Nagel’s reply to Cummins is an analogy with vision. We did not have to wait for photometers before sorting accurate color perceptions from illusions; we compared impressions across conditions and angles, and our understanding of vision developed alongside our understanding of light. Likewise, our understanding of knowledge intuitions can improve alongside our theories of knowledge, each correcting the other. This is reflective equilibrium, informed by psychology.

Daniel Dennett coined the term intuition pump for a thought experiment designed to produce a particular intuition. His advice (Intuition Pumps and Other Tools for Thinking, 2013) is to “turn the knobs”: vary the details of the scenario and see whether the intuition changes. If a small, irrelevant change flips the intuition, the intuition was responding to the framing, not the philosophy.

How to use a thought experiment well:

1. State precisely what the case is supposed to show, and against which theory.
2. Check that the scenario is coherent and that all relevant details are specified.
3. Turn the knobs. Is the intuition robust across variations?
4. Ask whether the intuition might be driven by something irrelevant (unfamiliarity, vividness, emotional reaction).
5. Remember that an intuition is evidence, not proof. It can be outweighed by theoretical considerations. This is the balancing process described in the next section.

Reflective equilibriumListen

How do we justify general principles in logic, ethics, and epistemology, when we cannot derive them from anything more basic? Nelson Goodman (Fact, Fiction, and Forecast, 1955) proposed an answer for the rules of inference:

“A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend.”

John Rawls (A Theory of Justice, 1971) named this method reflective equilibrium. We start with considered judgments about particular cases and with candidate general principles. Where they conflict, we adjust whichever we are less confident of, going back and forth until judgments and principles cohere. Wide reflective equilibrium (Norman Daniels, 1979) also brings in background theories and the strongest alternative views.

Reflective equilibrium is arguably the method of most philosophy, including this guide. When a theory of knowledge implies that a Gettier victim knows, we revise the theory. When a theory implies that we know almost nothing, we might revise the theory (Moore) or accept the verdict (the skeptic). The method is a form of coherentism about justification.

Objection: reflective equilibrium can simply systematize prejudice. If your starting judgments are biased, a coherent system built from them is coherently biased. Defenders reply that nothing better is available, and that the method’s openness to revision, including revision prompted by other people’s judgments, gives it a way to correct itself over time.

Conceptual engineeringListen

Most of this chapter concerns understanding the concepts we have. Conceptual engineering asks which concepts we should have, and how to improve them.

Rudolf Carnap (Logical Foundations of Probability, 1950) proposed explication: replacing a vague everyday concept (the explicandum) with a precise one (the explicatum) that can do the same work better. A good explicatum should be similar to the original, exact, fruitful (usable in many laws or generalizations), and simple. Carnap’s example: replacing the everyday “warm” with the scientific “temperature.”

Real cases of conceptual engineering:

• Planet: the International Astronomical Union’s 2006 definition, which reclassified Pluto.
• Death: the 1968 Harvard Medical School committee’s proposal of “irreversible coma” (brain death) as a criterion of death, which enabled organ transplantation.
• Marriage, rape, and person have been redefined in many legal systems.

Sally Haslanger (“Gender and Race: (What) Are They? (What) Do We Want Them to Be?”, 2000) called this kind of project ameliorative analysis: asking what a concept should be, given the legitimate purposes it serves. Herman Cappelen (Fixing Language, 2018) has developed a general theory of conceptual engineering.

What distinguishes legitimate conceptual engineering from illegitimate persuasive definition? Transparency. An engineer says openly, “I propose that we use this word in this new way, for these reasons.” A persuasive definer passes off a new usage as the existing one.

Check your understandingListen

1Identify the use/mention confusion: “‘Infinity’ is a word with eight letters, so infinity is finite.”

Answer

The premise is about the word “infinity” (mention); the conclusion is about infinity itself (use). The word’s finite length says nothing about the concept’s content.

2“The police are looking for the person who robbed the bank. I know that my neighbor is the kind of person who would never rob a bank. So the police are not looking for my neighbor.” What fallacy is this, and what’s wrong with it?

Answer

It is a relative of the masked man fallacy and involves an intensional context (“looking for”). The police are looking for whoever robbed the bank, under that description. If the neighbor did in fact rob the bank, the police are looking for the neighbor, whatever the speaker believes about the neighbor’s character. There is also a hidden inductive leap from character to action.

3What kind of definition is “Obesity means a body mass index of 30 or more”? What are its advantages and risks?

Answer

It is a precising definition that is also operational (defined by a measurement procedure). Advantages: clear, measurable, comparable across studies. Risks: BMI does not distinguish muscle from fat and varies in predictive value across populations. Conclusions about “obesity” in the BMI sense may not carry over to obesity in the medical sense of excess body fat that harms health. Goodhart’s law applies if BMI becomes a target.

4Find a counterexample to: “A chair is a piece of furniture with four legs that you sit on.”

Answer

Too narrow: three-legged stools and chairs with a single pedestal or runners. Too broad: a four-legged bench or sofa, or a four-legged table that someone sits on. “Chair” is probably a family-resemblance or prototype concept.

5Is this a verbal dispute? A: “Viruses are alive; they evolve and reproduce.” B: “Viruses are not alive; they have no metabolism and cannot reproduce on their own.”

Answer

Largely verbal. The parties agree on the facts (viruses evolve, reproduce only inside host cells, and lack their own metabolism) and disagree on whether “alive” requires metabolism and independent reproduction. Banning the word “alive” dissolves the factual disagreement. A substantive question may remain: which concept of life is most useful for biology?

6Explain the continuum fallacy and give an example.

Answer

It is the inference from “there is no sharp boundary between X and Y” to “there is no real difference between X and Y.” Example: “There is no precise number of drinks at which someone becomes drunk, so there’s no real difference between a sober driver and a drunk one.” Clear cases on each side differ greatly even if the boundary between them is vague.

7Identify the missing normative premise: “This factory’s emissions raise local asthma rates by 15%, so it should be shut down.”

Answer

Something like “Any facility whose emissions raise asthma rates by this much should be shut down.” That premise is doubtful as stated, since alternatives such as filters or relocation might be better, and the benefits of the factory must be weighed. A more defensible premise, “Facilities that cause serious avoidable health harms should be required to reduce them,” supports a weaker conclusion.

8Distinguish conceptual engineering from persuasive definition.

Answer

Both change the meaning of a word. Conceptual engineering does so openly, with reasons tied to the purposes the concept serves, and invites evaluation. Persuasive definition does so covertly, presenting a new meaning as the ordinary one in order to transfer the word’s emotional force.

Further reading

• Gottlob Frege, “On Sense and Reference” (1892). Short, foundational.
• Ludwig Wittgenstein, Philosophical Investigations (1953), §§1–133. Challenging but rewarding; §§65–78 on family resemblance.
• William James, Pragmatism (1907), Lecture II, “What Pragmatism Means” (the squirrel).
• Charles L. Stevenson, “Persuasive Definitions,” Mind 47 (1938).
• W. B. Gallie, “Essentially Contested Concepts,” Proceedings of the Aristotelian Society 56 (1956).
• David Chalmers, “Verbal Disputes,” Philosophical Review 120 (2011).
• Timothy Williamson, Vagueness (Routledge, 1994).
• Daniel Dennett, Intuition Pumps and Other Tools for Thinking (W. W. Norton, 2013).
• George Orwell, “Politics and the English Language” (1946). Short, and permanently relevant.
• Herman Cappelen, Fixing Language: An Essay on Conceptual Engineering (Oxford University Press, 2018).
• Stanford Encyclopedia of Philosophy entries: “Vagueness,” “Reflective Equilibrium,” “Thought Experiments,” “Definitions.”