Concepts and Their Functions

3.1 Concepts, terms, practices

The account requires three notions, and I shall try to use each in a way that carries as little theoretical baggage as possible.

By a concept I shall mean what is expressed by a general term together with the competence to apply it and the inferential and practical role it plays for those who have that competence. I do not assume that concepts are mental representations, abstract objects, or Fregean senses, and nothing in what follows turns on the choice. Cappelen (2018) has argued that talk of "concepts" in this area is best replaced by talk of terms and their meanings, and readers who share his suspicion may make the substitution throughout. What matters is that there is something, expressed by "knows" or "cause" or "same person", that is shared across a community, learned from cases, and put to work.

By a practice I shall mean a pattern of coordinated activity, sustained by its participants, that serves ends they have reason to pursue. Practices in this sense include testimony and inquiry, the holding of one another responsible, the making and keeping of commitments across time, the assignment of liability, the explanation and control of events, and the punishment of wrongdoing. The notion is Rawls's (1955), and I shall use it as he did: as a way of talking about what a set of rules and roles is for without yet committing to any view about the rules.

By a function I shall mean what a concept contributes to a practice. This is the load-bearing notion, and the rest of this chapter is devoted to it.

3.2 Two notions of function

The philosophical literature on functions distinguishes two families of account.

On the etiological account (Wright 1973; Millikan 1984, 1989), the function of an item is the effect it has had in the past that explains why items of its kind continue to exist. The function of the heart is to pump blood because past hearts' pumping blood is what explains, through natural selection, why there are hearts now. Applied to concepts, an etiological account says that the function of a concept is the effect its past deployments have had that explains why the concept has been retained and transmitted (Millikan 1984, chs. 1–4; for concepts specifically, Simion and Kelp 2020).

On the role or systemic account (Cummins 1975), the function of an item is the contribution it makes to some capacity of a system that contains it, relative to an analysis of that capacity into the contributions of parts. The function of the heart is to pump blood because pumping blood is the heart's contribution to the organism's capacity to circulate oxygen. Nothing about history is required; a heart that came into existence by chance would have the same function.

For the purposes of this dissertation I adopt a role account, relativised to practices and anchored in needs, as follows.

(3.1) Definition. F is a function of concept C in practice P if and only if (a) deployments of C in P contribute to P's achieving an end E; (b) participants in P have reason to pursue E; and (c) the application conditions of C are shaped by that contribution, in the sense that cases in which applying C serves E are the cases from which C is taught and in which its application is uncontested, and cases in which applying C would defeat E are treated as counterexamples to proposed accounts of C.

Clause (a) makes the function a contribution; clause (b) anchors it in a need, so that not every effect of a concept's deployment is a function of it; clause (c) ties the function to the concept's application conditions, so that the function is not external to the concept but is part of what determines when the concept applies. It is clause (c) that does the work in Chapter 4. A concept's functions, on this definition, are not merely uses to which it is put; they are among the determinants of its extension.

I prefer the role account to the etiological one for three reasons. First, the etiological facts about the history of a concept are almost always inaccessible, and where they can be reconstructed they are often idle: what matters for our present use of "knowledge" is what it does for us, not what it did for the community in which it arose. Second, etiological functions can be lost while the item persists, as with vestigial organs, whereas the functions that matter for the aporiai are ones sustained by present need. Third, and most importantly, the role account makes the normative anchoring explicit through clause (b), and the normative anchoring is what allows the account of Chapter 5 to go through.

That said, nothing I argue is incompatible with an etiological gloss. Typically the role functions of a concept are also etiological functions of it, since a concept that does something we need is a concept we retain; this is the thought behind Queloz's (2021) "pragmatic genealogy", which reconstructs the functions of concepts by asking what needs they answer to and treats the answer as explaining the concept's persistence. I shall draw on that method in §3.3. But I do not require that every function of a concept explain its retention, and I allow that a function may be acquired late, as when a term already in use is adopted by a legal system and shaped to legal ends.

It will help to have a rough typology of functions, though I do not claim it is exhaustive or that the kinds are exclusive. A function may be tracking: the concept's contribution is to pick out a property or kind, whatever it turns out to be, so that inquiry into the kind can proceed (the function that Putnam 1975 and Kripke 1980 made central to natural kind terms). It may be coordinating: the concept's contribution is to align the behaviour or expectations of participants (the function of "same person" in the practice of returning to the same individual for what is owed). It may be licensing: the concept's contribution is to mark the point at which some act is permitted or required (the function of "knows" as the norm of assertion, or of "responsible" as the condition of blame). And it may be orienting: the concept's contribution is to direct an attitude (the function of "same person" in directing prudential concern, or of "cause" in directing the search for an intervention). The same concept may have functions of several kinds, and this, I shall argue, is the normal condition of the concepts that generate philosophical problems.

3.3 Identifying functions

If functions are to do explanatory work, there must be a way of finding out what the functions of a concept are that does not simply read them off from the philosophical positions one wishes to explain. I offer three methods, which in practice are used together.

Genealogy. The state-of-nature method of Craig (1990), developed by Williams (2002) and made systematic by Queloz (2021), asks what concept a community of agents with generic human needs and limitations would have to have, given a specified practical problem. Craig's own answer, for knowledge, is that such a community would need to flag good informants: individuals whose testimony on a question can be relied upon. The method then traces how the concept, once introduced, becomes "objectivised" (Craig's term) as it detaches from the perspective of the particular inquirer and comes to mark a property the informant has regardless of who is asking. The method's strength is that it identifies functions from needs rather than from doctrines. Its limitation, for my purposes, is that it tends to deliver one function, the one built into the specification of the practical problem, and to treat the others as later accretions. I use it to identify core functions and then ask what other practices the concept has been drawn into.

Subtraction. The second method asks what a community would be unable to do if it lacked the concept, or if the concept's application were restricted so as to exclude a class of cases. Haslanger's (2012) ameliorative question, "what do we want the concept to do?", is a version of this, run in the forward direction. The subtraction method has the advantage of surfacing functions that a genealogy, fixed on the concept's origin, may miss. If we lacked the concept of knowledge, we would be unable to flag informants; but we would also be unable to mark the point at which inquiry may stop, or to state the norm that governs assertion, or to state the condition under which one may act on a proposition. Each of these is something we do with the concept, and each, on subtraction, is revealed as a distinct loss.

Case-partition. The third method is the one on which the account most depends, and it is the one that connects the theory of functions to the practice of philosophy. Two candidate functions F and F′ of a concept C are distinct if and only if there is a possible case on which the application condition associated with F and that associated with F′ deliver different verdicts. If no such case exists, F and F′ are, for the purposes of the theory, a single function under two descriptions. This gives an extensional criterion for individuating functions and a corresponding method for discovering them: construct cases, and see where the verdicts split.

The case-partition criterion has three consequences worth stating. First, it means that the question "how many functions does C have?" is not to be settled by introspection or by lexicography but by the construction of cases, which is to say by the very activity that philosophers engaged in these problems have always been engaged in. The thought experiment is not only a divergence constructor, as §2.5 argued; it is a function individuator. Second, the criterion is defeasible in one direction: a function that has seemed single may be split by a new case, as "control" was split into regulative and guidance control by Frankfurt's case (§4.3), but two functions that have been shown to diverge cannot be re-merged by any further case. The number of functions attributed to a concept can therefore only grow over the history of a problem, which is one reason the history of a problem has the shape it does. Third, the criterion prevents proliferation: one cannot multiply functions by multiplying descriptions, since descriptions that agree on every possible case count as one.

3.4 Why one concept acquires several functions

If concepts can have several functions, and if having several functions is what generates persistent problems, one wants to know why concepts should ever be in this condition. Why does a community not simply have one term per function? I identify four pressures, which act together.

Correlation in the environment of acquisition. The properties that serve the several functions of a concept are, across the range of cases actually encountered, correlated, and typically correlated for a reason. A person whose beliefs are safe from error is, in the ordinary run of cases, a person who is a reliable informant, whose beliefs are a good basis for action, and who is creditable for getting things right: safety, reliability, action-worthiness, and creditability come together because all are consequences of competent belief-formation in a cooperative environment. An agent who acts on her own reasons is, in the ordinary run of cases, an agent who could have done otherwise, who is the source of her action, and who is an apt target of resentment or gratitude: these come together because the ordinary exercise of practical reason is one in which alternatives are open and no one else is pulling the strings. The organism I am is, in the ordinary run of cases, the psychological continuant I am, the forensic subject I am, and the object of my prudential concern: these come together because psychology is realised in organisms and organisms do not divide. What produces an effect is, in the ordinary run of cases, what the effect depends on and what we would intervene on to prevent it: these come together because ordinary causal chains are single and uncontested. Given such correlation, a term that tracks any one of the properties tracks the others, and a practice that needs one of the others can adopt the term without cost.

Lexical economy. Learning and communication favour fewer terms over more (Zipf 1949). A term that can be borrowed by a new practice at no cost of confusion will be borrowed rather than a new term coined. Homonymy is costly only where it produces misunderstanding, and correlation prevents misunderstanding: so long as the properties coincide, no one is ever misled by the fact that "knows" is doing four jobs.

Underdetermination of the learned concept. A learner presented with cases from the range in which the properties coincide cannot tell which property the term tracks. This is the situation Goodman (1955) described with "grue", Quine (1960) with "gavagai", and Kripke (1982) with "quus": finite exposure to cases underdetermines the extension of a term over cases not yet encountered. Ordinarily this is treated as a puzzle about how meaning is possible at all. Here it has a different and positive role. Since the learner cannot tell which correlated property is the one, and since for the learner's purposes it does not matter, the term as learned inherits all of the correlated properties as candidate application conditions, and nothing in acquisition selects among them. The learner has acquired a concept that is determinate over the range from which it was learned and multiply determined, which is to say not uniquely determined, beyond it.

There is a suggestive analogy in the machine-learning literature. A classifier trained on data in which two features co-occur learns a mixture of the two and behaves unpredictably on inputs where they come apart; the phenomenon has been called "shortcut learning" (Geirhos et al. 2020). The analogy is imperfect in one instructive respect. When a classifier meets an out-of-distribution input, its output is, from the point of view of the intended task, noise. When a competent human concept-user meets a divergence case, her verdict is not noise. It is firm, and it is firm in a direction that tracks which of the concept's practices the presentation of the case has made salient. That is because the human user does not merely possess a mixture of features; she participates in the practices that the features serve, and can be moved to give one of them precedence. This is the fact that Chapter 5 builds on.

Institutional bundling. Finally, distinct institutions, law, science, morality, medicine, and ordinary life, each take up the same term and shape it to their ends. Hart and Honoré (1959) showed in detail how the law's concept of causation is shaped by the requirements of assigning liability, and how it therefore departs from the concept used in scientific explanation while sharing its vocabulary. Locke observed that "person" is "a forensic term, appropriating actions and their merit" (1690, II.xxvii.26), which is to say a term shaped by the practice of holding responsible, while also being the term by which we track ourselves in anticipation. Each institution adds a function to the shared term, and each function is invisible to the others so long as the institutions' cases coincide.

3.5 Coincidence and divergence

I can now define the notions on which the account turns.

Let a concept C have functions F₁, …, Fₙ, and let each Fᵢ be associated, by clause (c) of (3.1), with an application condition Aᵢ: a condition on cases that specifies when applying C in that case would serve Fᵢ. Then:

(3.2) Definition. The coincidence range of C is the set of possible cases on which A₁, …, Aₙ all deliver the same verdict. The divergence region of C is the set of possible cases on which at least two of them deliver different verdicts. A divergence case is a member of the divergence region.

Five claims about these notions will be relied on.

(3.3) The coincidence range of a concept that has been successfully learned and transmitted includes nearly all the cases in the environment of its acquisition. This is a consequence of §3.4: if the application conditions frequently diverged in the cases from which the concept was learned, the learner would notice, and the community would either coin a new term or fix a priority. A concept with several functions can be learned as one concept only because the functions coincide where it is learned.

(3.4) Within the coincidence range, the concept's verdicts are determinate and robust. All its functions agree, so no framing or emphasis can shift the verdict; the concept behaves as if it had a single application condition, because for these cases it effectively does.

(3.5) Within the divergence region, the concept issues conflicting determinate instructions, one per diverging function. It does not fall silent. This is the point at which polyfunctionality differs from vagueness, as §3.6 explains: a borderline case of "heap" yields no verdict, whereas a divergence case of "knows" yields a "yes" from one function and a "no" from another, each of them firm.

(3.6) The verdict a competent user actually gives in a divergence case is determined by which function the presentation of the case has made salient. The same case, differently described, will elicit different verdicts, and the difference will track the practice the description foregrounds. This is the account's central prediction about the psychology of thought experiments, and §4.3 and §4.4 present the evidence that bears on it.

(3.7) Divergence cases may be actual or merely possible. The world produces them when circumstances change (the discovery of trans-Neptunian objects comparable in size to Pluto; the invention of the ventilator; the possibility of gestational surrogacy; the incorporation of joint-stock companies), and when it does, the community has to legislate. Philosophy specialises in constructing the merely possible ones in advance. The relation between these two activities is the subject of §6.5.

One conceptual question should be addressed before proceeding. When a concept is polyfunctional in the sense defined, is it one concept with several functions and an extension that is undetermined over the divergence region, or is it several concepts that happen to share a word? I do not think this question has an answer independent of our purposes, and I propose to treat the two descriptions as descriptions of two states. Before divergence has been exhibited and the functions articulated, the community has one concept, with one word, one competence, and one uncontested practice of application; the several functions are latent. After divergence has been exhibited and the functions articulated, the community is in a position to have several concepts, and whether it does depends on whether it coins terms, adopts subscripts, or continues to use the one word with an explicit understanding of its ambiguity. The passage from the first state to the second is what Chapter 6 calls disentanglement, and it is one of the principal forms that progress in philosophy takes. The philosophical debate over whether, say, there is one concept of knowledge or two (Sosa's animal and reflective knowledge) is a debate about whether to make the passage. It is not a debate that has an answer prior to the decision.

A final notion. Concepts differ in functional load: in the number of distinct functions they bear and in the stakes attached to each. "Uncle" bears one function, or several that no case has ever separated, and its stakes are low. "Person" bears at least five, and the stakes include the assignment of legal rights, the direction of medical treatment, and the object of a lifetime's concern. The account predicts that the depth and persistence of a philosophical problem should vary with the functional load of the concept at its centre, and that the concepts on Kant's battlefield should be exactly the high-load ones. I take this to be borne out.

3.6 Neighbouring notions

Polyfunctionality has relatives, and the account is best understood by contrast with them. I take them in the order of increasing closeness.

Ambiguity and homonymy. "Bank" has two meanings with no coincidence range: no case is both a financial institution and a riverside. Competent speakers are never in doubt which is meant. Polyfunctionality is, if one likes, latent homonymy, in which the two meanings have not been distinguished because they have never been observed to come apart. The difference is that homonymy is a fact about a word, while polyfunctionality is a fact about the practices a word serves.

Polysemy. "Book" applies to a physical object and to a text; "window" to an opening and to what fills it. Polysemy is the closest linguistic relative of polyfunctionality: related senses, systematically connected, often coinciding. Linguists treat polysemy as a semantic fact about lexical items. The present account explains a species of polysemy, that of high-load concepts, by its practical origin, and it makes a prediction that a purely semantic account does not: that the senses will split exactly where the practices' cases diverge.

Vagueness. "Heap" has borderline cases in which it issues no determinate verdict; the sorites exploits this. Vagueness is a matter of degree along a dimension; a divergence case is a matter of conflict among criteria. In a borderline case one does not know what to say; in a divergence case one knows two things to say and they conflict. Alston (1964) distinguished degree vagueness from "combinatory vagueness", in which a term is associated with several conditions no one of which is necessary; combinatory vagueness is closer to polyfunctionality, but Alston's account, like the cluster account below, treats the conditions as an unexplained list and treats their coming apart as producing indeterminacy rather than structured conflict.

Open texture. Waismann (1945) observed that empirical concepts are not defined for every possible case: we have not said whether a cat that grew to giant size and then revived after death would still be a cat, because nothing in our experience required us to. Open texture is undefinedness for unanticipated cases. Polyfunctionality is not undefinedness but overdefinedness: for the unanticipated case there are too many definitions, not too few, and they conflict. Waismann's phenomenon is real and general; the present account picks out a subclass of it with a specific structure and a specific etiology.

Family resemblance. Wittgenstein's observation (1953, §§65–71) that games share no single feature but are linked by overlapping similarities concerns the criteria of membership within the range of accepted cases. It is a claim about how the extension of a concept hangs together, not about what the concept is for. Polyfunctionality is a claim about roles, and within the coincidence range there is a shared extension, whatever holds it together. A concept can be both family-resemblant and polyfunctional; the notions are orthogonal.

Cluster concepts. The cluster theory of names (Searle 1958; cf. Wittgenstein 1953, §79 on "Moses") and Putnam's (1962) account of "law-cluster" concepts such as "energy" hold that a concept is associated with a cluster of criteria, no one of which is necessary and some weighted majority of which is sufficient. This is the closest structural relative of the present account, and Putnam's discussion of what happens to "energy" when relativity forces the abandonment of one law in the cluster is an account of a scientific disentanglement. The difference is that the cluster theory says nothing about why those criteria cluster, and it predicts that when the criteria come apart the concept will fall silent or apply by weighted vote. The present account anchors the criteria in functions, explains their clustering by correlation, and predicts structured conflict rather than silence, with the verdict tracking salience of function.

Essentially contested concepts. Gallie (1956) argued that certain concepts, his examples were "art", "democracy", "social justice", "religion", and "the Christian tradition", are such that disputes about their proper use are not resolvable by argument or evidence and are not, for that reason, confused. He gave seven conditions: the concept is appraisive; the achievement it signifies is internally complex; that achievement is variously describable, its components differently weightable; it is open to modification in unforeseen circumstances; each party recognises the others' use as contesting the same concept; the concept derives from an exemplar; and continued contestation sustains or develops the exemplar's achievement. Waldron (2002) has complained that the notion is applied too freely. The present account both vindicates and disciplines Gallie. His "internally complex" and "variously describable" conditions are, in my terms, the claim that the concept has several functions differently weighted; his "openness" is the divergence region; his requirement that the parties recognise a common concept is the coincidence range. What Gallie did not supply is a mechanism, and he restricted the phenomenon to appraisive concepts. I supply the mechanism and lift the restriction: "knowledge" and "cause" are contested in exactly Gallie's way, and the restriction to appraisive concepts was an artefact of the examples he happened to choose. The account also gives Waldron his criterion: a concept is essentially contested if and only if it is polyfunctional, its functions are normatively loaded, and the community faces actual or seriously entertained divergence cases.

Interpretive concepts. Dworkin (1986, ch. 2; 2011, ch. 8) distinguished criterial concepts, which are shared by sharing criteria of application, natural-kind concepts, which are shared by pointing at a kind, and interpretive concepts, which are shared by participating in a practice and whose correct application depends on the best account of the point of that practice. His examples were justice, liberty, equality, law, and courtesy. My "function" is close to Dworkin's "point", and my divergence region is close to the region where, on his account, the practice's paradigms give out and interpretation begins. I part company on two points. First, Dworkin holds that there is a uniquely best interpretation and therefore a right answer to interpretive questions; I hold that the plurality of points may be irreducible, so that there need be no fact of the matter about which function should dominate, though there may be better and worse answers. Second, Dworkin classifies concepts as interpretive tout court; I hold that the same concept is criterial in its coincidence range and interpretive in its divergence region. This explains why Dworkin's critics, who insist that "justice" and "law" have ordinary criteria of application that any competent speaker knows, are right, and why Dworkin, who insists that in hard cases only interpretation will do, is also right.

Concept and conceptions. Rawls (1971, §1), following Hart (1961), distinguished the concept of justice, a role in social life specified abstractly as the proper balance between competing claims, from the various conceptions of justice that fill the role differently. The distinction is a version of the present one in which the concept has been identified with one function, adjudication among competing claims, and the conceptions with alternative fillings of it. My account suggests that the concept of justice bears several functions (adjudication, but also desert, need-satisfaction, protection of entitlement, reciprocity) and that the conceptions are prioritisations among them. Rawls's own procedure in the original position can be read as an attempt to derive a priority ordering from a fair choice situation, which is to say as an argument in conceptual ethics.

Manifest, operative, and target concepts. Haslanger (2012) distinguishes the manifest concept, the one we take ourselves to be using; the operative concept, the one that in fact governs our application; and the target concept, the one we ought to use. The distinctions are orthogonal to mine but interact with it. A divergence case typically reveals a gap between manifest and operative: the manifest concept of knowledge was "justified true belief", and Gettier's case showed that the operative concept was something else. The target question, what concept we ought to use, is the normative residue that Chapter 5 argues is what remains of a persistent dispute once the rest is cleared away.

Inconsistent concepts. Eklund (2002) and Scharp (2013) argue that some concepts, truth being the paradigm, are governed by constitutive principles that are jointly inconsistent: the unrestricted T-schema together with classical logic yields a contradiction from the Liar. This is a structural cousin of the present account, located at the level of principles rather than functions. My account relates to it as follows. The constitutive principles are articulations of functions; the T-schema articulates truth's function as a device of disquotation and generalisation (Quine 1970; Horwich 1990). The inconsistency appears only in the divergence region, which for "true" is the region of semantically closed self-reference where the disquotational function comes apart from the function of marking grounded, assertable content (Kripke 1975 makes groundedness the operative notion). Over its coincidence range, the concept of truth is not defective at all, and this explains what an inconsistency account struggles with: why a concept governed by inconsistent principles should have been serviceable for the whole history of human thought and remain so. Scharp's proposal to replace "true" with a pair of concepts, ascending and descending truth, is on my account an instance of disentanglement, and the account explains why that is the right shape for a solution to take.

The following table summarises the contrasts.

Two neighbours remain to be treated where they belong. The notion of a verbal dispute (Chalmers 2011) is taken up in §5.2, because its proper assessment requires the theory of disagreement developed there. And the natural kind model of concepts (Kripke 1980; Putnam 1975; for knowledge, Kornblith 2002) is taken up in §7.3, because it is the basis of the most serious realist objection to the account.