Reflexivity, Objections, and Limits

7.1 The concept of progress

T5 says that the concept of progress is itself polyfunctional and that the metaphilosophical debate about philosophical progress is a divergence case. I now make that out, and then say what the reflexive application does and does not show.

The concept of progress, as applied to an inquiry, has at least five functions, each articulated by one of the accounts surveyed in §6.1. F₁, accumulation: the concept marks an inquiry that has more knowledge than it had (Bird 2007). F₂, understanding: it marks an inquiry that grasps more dependence relations than it did (Dellsén 2016). F₃, convergence: it marks an inquiry whose practitioners increasingly agree (Chalmers 2015). F₄, problem-solving: it marks an inquiry that has solved problems it had not solved (Kuhn 1962; Laudan 1977). F₅, practical yield: it marks an inquiry whose results have made a difference to what can be done.

In mature natural science these coincide, and they coincide for a reason. What is discovered is understood; what is understood and discovered is agreed, because the methods that produce discovery are public; what is agreed and understood solves the problems that motivated the inquiry; and what solves those problems can be applied. The coincidence is so tight that philosophers of science have been able to debate which function is the concept of progress, each side citing cases in which its favoured function is present, without noticing that the cases they cite are cases in which all five are present. That is the signature of a coincidence range.

Philosophy is a divergence case. By F₁, F₂, and F₄, it progresses: the record of §6.3 is accumulated knowledge, is understanding, and is the solution of problems by decomposition. By F₃ it does not: the headline questions do not converge. By F₅ the verdict is mixed and depends on what one counts, as §6.5 argued. The five functions, which coincide in science, come apart in philosophy, and the metaphilosophical dispute is the predicted result. Chalmers weights F₃; Dellsén, Lawler, and Norton weight F₂; Stoljar weights F₁ and F₄; the pessimist, in taking non-convergence to entail non-progress, weights F₃ without argument that F₃ should govern where the functions diverge. The debate has the three-layer structure of §5.1: the parties agree on the facts (what has been established, what is agreed, what is not), disagree at the verbal layer about whether to call it "progress", and disagree at the residual layer about which function of "progress" should govern the evaluation of a discipline whose questions have the structure described in Chapter 4.

What does the reflexive application show? It does not show that the account is true; an account that predicted its own debate could still be wrong. It shows three things. First, that the account is consistent under self-application: it does not, applied to itself, generate a contradiction or a regress, and it does not exempt itself from the structure it attributes to everything else. Second, that the account has content at the reflexive level, since the reflexive prediction could have failed: had the parties to the progress debate shared a single criterion of progress and disagreed about whether philosophy met it, the account would have been embarrassed. Third, that the account's own recommendation, that "progress" for philosophy be understood in the noetic, disentangling way, is a proposal in conceptual ethics and is argued for as one. It is not offered as a discovery that philosophy progresses. It is offered as a decision about what to count, defended by asking what we want the concept of progress to do when we apply it to a discipline, namely to guide the allocation of effort and to evaluate the discipline fairly, and by arguing that F₂ and F₄ serve that end for philosophy while F₃ does not, because F₃ measures the one thing that the structure of the questions makes unattainable.

The rivals do not obviously pass this test. Chalmers's criterion of large collective convergence is a weighting of F₃ presented as a measure, and no argument is given that F₃ should govern in a domain where it comes apart from the others; the intuition that it should is the manifest unity of "progress" carried out of the coincidence range in which it was learned. That is precisely the error the account diagnoses in the first-order aporiai.

7.2 Triviality

Objection. Every concept can be said to have several functions; the account is therefore unfalsifiable, and "polyfunctional" is a label that can be attached to anything after the fact.

Reply. Three things prevent this. First, many concepts are monofunctional or have never been separated by any case: "prime number", "uncle", "kilometre", "even", "bishop" (in chess). These have exactly one application condition, or several that no possible case separates, and they generate no aporiai. The account predicts a correlation between functional load, as defined in §3.5, and the depth and persistence of philosophical problems, and the correlation is there to be checked. A concept used in many contexts is not thereby polyfunctional; "even number" is used in arithmetic, in scheduling, and in games, and has one application condition throughout.

Second, the case-partition criterion of §3.3 disciplines the attribution of functions. One cannot multiply functions by multiplying descriptions; two candidate functions count as one unless a possible case separates their verdicts. This makes "how many functions does C have?" a question with an answer that can be got wrong. The discipline is real, but it is not neutral between the parties, and §7.5 says what that costs.

Third, the account makes predictions, listed in §7.9, that could fail. A theory that could fail is not unfalsifiable.

7.3 Realism

Objection. There is a fact about whether Jones is free, whether Henry knows, whether I survive fission, independent of what functions our concepts serve. The account replaces facts with decisions, and that is not analysis but abdication.

The objection comes in three forms, which deserve separate replies.

The further-fact view. Butler (1736), Reid (1785), Chisholm (1976), and Swinburne (in Shoemaker and Swinburne 1984) hold that personal identity is a primitive fact, which the criteria of memory and bodily continuity track imperfectly, and analogous "simple" views can be held about the other concepts. On this view the functions are evidence for a fact that lies behind them, and where the functions diverge the fact is still there, merely hidden.

Reply. The view must say what fixes the further fact in a divergence case, and it cannot appeal to the criteria, since they diverge. It is therefore a bare posit. What supports the posit is the phenomenology of the concept's manifest unity, the sense that "same person" means one thing. The present account explains that phenomenology without the posit: the concept feels unitary because it is unitary across the coincidence range, where all its functions agree, and the feeling is carried into the divergence region by the mechanism of §3.4. Of two accounts of the same phenomenology, one with a posit and one without, the one without is to be preferred unless the posit does other work. I do not claim that the further-fact view is refuted; I claim that the burden is on it, and that the account shifts the burden by explaining what the view took to be its evidence.

Natural-kind realism. Kornblith (2002) argues that knowledge is a natural kind, to be investigated by cognitive ethology rather than by the analysis of our concept, and the Kripke–Putnam semantics of natural-kind terms (Kripke 1980; Putnam 1975) suggests that for such terms the world, not our practices, fixes the extension.

Reply. Tracking a kind is one function among others, the tracking function of §3.2, and a concept whose only function were to track a kind would indeed have its extension fixed by the kind. But "knowledge" has licensing functions that no kind can settle. Suppose there is a natural kind of reliably produced true belief, and suppose Kornblith is right that it is what the concept of knowledge tracks. The question whether that kind should govern the norm of assertion, or the norm of action under high stakes, is not answered by the kind; it is a question about assertion and action. Natural-kind realism about knowledge is therefore compatible with the account and does not threaten it; it identifies one function and says something true about it.

The point is confirmed by what happens to natural-kind terms themselves when they acquire further functions. "Fish" tracks a folk kind and, since the rise of cladistics, is also expected to track a clade; whales are the divergence case, and the resolution was a division of labour between folk and scientific vocabulary. "Species" is expected to track reproductive isolation, morphological cluster, ecological niche, and phylogenetic lineage, and these coincide for most vertebrates and diverge for asexual organisms and ring species; pluralism about species (Ereshefsky 1998) is disentanglement. "Gene" was expected to track a unit of inheritance, a unit of recombination, and a unit of function, and molecular biology separated them (Griffiths and Stotz 2013). "Planet" is the case already discussed. In each, a natural-kind term with several functions generated the structure of Chapter 4, and it was resolved by legislation where a practice had authority. Natural-kind realism, far from being a counterexample, supplies further instances.

Normative realism. The third form of the objection holds that there is a fact about what the practice of blame should require, and that the account, by calling the residue "normative", has not shown that it lacks an answer.

Reply. This is not an objection but a welcome addition, and §5.7 has already accepted it. If normative realism is true, the residual question of each persistent aporia has an answer, the answer is normative, and philosophy's disputes are objective disputes about it. The account denies only that the answer is a descriptive fact about the concept, supplied by the concept's content. It does not deny that there is an answer.

One further remark. The realist may say: "but surely Smith does not know; that is a fact, not a decision". Agreed. In Smith's case nearly all the concept's functions deliver the same verdict, and the verdict is as determinate as any verdict in the coincidence range. The account does not say that everything in the divergence region is undetermined. It says that verdicts there are function-relative, and that where the functions overwhelmingly agree the relativity is idle. Only in balanced cases is there a residue, and it is in balanced cases, and only there, that the disputes persist.

7.4 Conventionalism

Objection. If the residue is a matter of decision, then philosophy's persistent questions are settled by convention, like the side of the road on which one drives, and it is a matter of indifference how they are settled.

Reply. A convention, in the sense of Lewis (1969), coordinates where any of several options would serve equally well, so that what matters is only that everyone chooses the same one. The residual questions are not like this. The options differ in value: a concept of responsibility that tracks leeway and one that tracks reasons-responsiveness do different things to the practice of blame, and the difference matters to those blamed. The decision is therefore not conventional but evaluative, and evaluative decisions have better and worse answers, constrained by the ends of the practices as §5.7 argued. The Supreme Court's decision that a tomato is a vegetable was not arbitrary; it was reasoned from the purpose of the tariff schedule.

Moreover, the decision is the smaller part of the work. The location of the divergence region, the articulation of the functions, and the exhibition of the costs of privileging each are not decisions at all but discoveries, and they are the larger part of what the record of §6.3 contains. The account is a conventionalism about nothing except the final weighting, and about that it is not a conventionalism but a form of normative pluralism.

The account should be distinguished from Carnap's. Carnap (1950b) held that external questions are practical and, for that reason, not theoretical; he took "practical" to mean not truth-apt. The account holds that the residual questions are practical and therefore normative, and it is neutral on whether normative questions are truth-apt, which is a question in metaethics. Carnap's framework choice was, for him, a matter of expedience; the account's weighting is a matter of what the practices are for.

7.5 Circularity

Objection. The account is stated using the concepts of function, practice, need, and concept, and these are themselves polyfunctional. The dispute between etiological and role accounts of function (Wright 1973; Cummins 1975) is a stable aporia of exactly the kind the account describes. The account therefore presupposes what it explains.

Reply. It does, and to that extent the presupposition is a mark of consistency rather than a defect. The account is not a foundationalist project; it does not claim to state the structure of philosophy's problems from a standpoint outside them. It uses "function" in the role sense, says why (§3.2), and defends the choice in the currency appropriate to a weighting: by asking what the notion is needed for and arguing that the role sense serves that need. That is exactly the procedure the account recommends for any polyfunctional concept in its divergence region. A theory of polyfunctional concepts that could be stated only in monofunctional ones would be in an odd position; a theory that is in the same condition as its objects and handles that condition by its own recommended method is in a good one.

That disposes of the objection in the form in which it is usually pressed. It does not dispose of it in the form that matters, and I have not found a way to. The trouble is not that "function" is polyfunctional. It is that my own two treatments of it diverge, and that I legislated between them in half a line. Definition (3.1) individuates a function by a practice and by the end that practice serves: F is a function of C in P if deployments of C in P contribute to P's achieving E and participants have reason to pursue E. The case-partition criterion of §3.3 individuates functions extensionally, by whether some possible case makes two application conditions deliver different verdicts. The two agree wherever practices with different ends make different demands on some case, which is most of the time. They come apart when two practices make genuinely different demands that no case discriminates, and there (3.1) counts two functions and §3.3 counts one. §3.3 says which wins — "for the purposes of the theory", a single function under two descriptions — and that phrase is a piece of legislation for a divergence region, performed on the account's own central term, and passed over without argument.

I paid for it in §4.4. Korsgaard's argument for agential unity and Schechtman's for social recognition are arguments at the level of (3.1): the practices are distinct and the ends are distinct. My criterion overrules them, and six functions of "person" become four. Whether that is a discovery about the concept or an artefact of my choice of criterion I cannot settle from inside the account, because the choice of criterion is what is at issue.

What I can do is say why I chose as I did and be exact about what the reason is worth. An extensional criterion is what makes the account predictive: it ties the count of functions to the construction of cases, and so to (P1) and (P4) of §7.9, and it is the whole of the reply to the triviality objection in §7.2, since it is what stops functions being multiplied by multiplying descriptions. A criterion pitched at the level of (3.1) would let the count follow the theorist's taxonomy of practices, and a taxonomy of practices is not something a case can check. That is an argument from what the notion is needed for. It is not an argument that the notion is the right one, and I do not have one.

Two consequences follow, and I would rather state them than have them found. The first is that §7.2's answer to triviality is conditional. Against a critic who grants case-partition the account is disciplined, and the count of functions is a matter of fact that can be got wrong. Against a critic who individuates functions by practices it is not disciplined, and the reply to triviality reduces to the observation that my criterion yields predictions and his does not — a reason to adopt mine, not a reason to think it true. The second is that the objection from circularity is therefore answered in its first form and not in its second, and I do not claim otherwise.

What would settle it is a case and not an argument. Construct a possible situation in which agential unity or social recognition delivers a verdict that forensic reidentification, prudential anticipation, and characterisation do not, and the practice-level individuation is vindicated on extensional grounds, (3.1) and §3.3 agree after all, and the objection lapses. Make the attempt seriously and fail, and the burden moves to the theorist who wants the extra functions, who then owes an account of what they are doing that no case can show. I expect the second outcome. I cannot demonstrate it, and that expectation is carrying more of Chapter 4 than an expectation should carry.

7.6 Demotion

Objection. The account reduces philosophy to lexicography plus ethics: it maps the uses of words and then hands the interesting question to moral philosophy. This is a handmaiden's role, and it is not what the great philosophers thought they were doing.

Reply. Four things.

First, no other discipline maps the divergence regions of load-bearing concepts in advance of the world's arrival there, and §6.5 argued that this work has a practical value that does not depend on convergence. It is not lexicography. Lexicography records how words are used; the construction of divergence cases discovers how they could be used and what would follow.

Second, the work is hard, creative, and cumulative. The record of §6.3 is the work of the best minds of the tradition, and each entry required the construction of a case no one had thought of, the articulation of a function no one had named, and the demonstration that a thesis everyone had accepted was true of one function and not of another. That is not a handmaiden's work.

Third, the residue is philosophy's too. The ethics of blame, of assertion, of medical decision, of legal liability, is moral and political philosophy. To say that the compatibilism debate is, in its residue, the ethics of blame is not to hand it to another discipline but to another part of the same one, and to say which part.

Fourth, and most importantly, the account restores rather than demotes philosophy's oldest self-understanding. Socrates did not tell Cephalus what justice is; he showed him where his concept ran out. Aristotle's method, stated at the opening of the discussion of akrasia, is to set out the appearances and the reputable opinions, to work through the puzzles they generate, and to preserve, if possible, all of them, or failing that the most and the most authoritative (Nicomachean Ethics VII.1, 1145b2–7). That is the aporetic method with an explicit prioritisation rule. His recurrent observation that "being", "good", and "cause" are "said in many ways" (Metaphysics Γ.2, 1003a33; Nicomachean Ethics I.6, 1096a23) is the recognition of polyfunctionality, and his practice of resolving puzzles by distinguishing senses is disentanglement. The account is not a reduction of philosophy to something less than it thought it was. It is a description of what it has, at its best, always done.

The image of the handmaiden also assumes that the sciences do the real work and philosophy tidies after them. The cases of §7.3 show otherwise. The sciences generate their own divergence cases, for "planet", "species", "gene", "mass", and "death", and when they do they need exactly the work the account describes, and do it badly without philosophy.

7.7 Success stories

Objection. Philosophy has converged on some things: on Turing's analysis of computability, on Frege's logic, on Tarski's treatment of truth in formalised languages, on the rejection of justified true belief. If the account were right, convergence should not happen. Since it does, the account is wrong, or at least incomplete.

Reply. The account predicts convergence in exactly three circumstances, and the success stories fall under them.

Coincidence over the extended range. Sometimes a concept's functions coincide not only in the environment of acquisition but over every case anyone can construct. "Effectively computable" is the paradigm. Turing (1936), Church (1936), and, by other routes, Gödel, Herbrand, Kleene, and Post gave formalisations that turned out to be provably equivalent, and the equivalence is what convinced the community that the informal concept had been captured (Church's thesis). The concept had several functions, what a clerk could do by rote, what a machine could do, what could be defined by recursion, and they coincided over the whole range. Explication was therefore unique up to equivalence, and the community converged. The account predicts convergence here, and predicts that it will take the form it took: multiple independent explications, discovered to agree.

Authority of a single practice. Sometimes one practice has authority over the concept and legislates. Set theory is the paradigm. Russell's paradox was a divergence case for "set" (§4.6), and the iterative conception (Boolos 1971) was a disentanglement; but what produced convergence on ZFC was that the mathematical practice's function, fruitfulness for classical mathematics together with apparent consistency, dominated, and the community accepted the legislation. Alternative set theories persist at the margins as a reminder that it was legislation, and philosophy's remaining set-theoretic disputes, about the justification of the iterative conception and about absolute generality, are the divergence region where mathematics does not need an answer. Tarski's treatment of truth is similar: by confining the definition to formalised languages and separating object language from metalanguage, Tarski legislated for the practice of formal semantics, which then converged, while explicitly declining to legislate for the philosophical dispute (1944, §§17–19).

Decomposition. Sometimes convergence is convergence on a component of disentanglement: that a case exists, that it separates two functions, that a thesis is true of one and not the other. The rejection of justified true belief is of this kind. Philosophers converged on the claim that Gettier's case separates justification from whatever knowledge requires, which is component (b) of §6.2, and did not converge on what to put in its place. The account predicts exactly this.

The success stories therefore confirm the account. Philosophy converges where the functions of a concept coincide over the extended range, where one practice has the authority to legislate, and on the components of disentanglement; and it does not converge on the headline question of a polyfunctional concept whose practices have no common authority. Austin's image of the sun throwing off sciences (1956) is the image of the first two cases: a concept's functions collapse into one, or one practice takes the concept over, and the question leaves philosophy because it has stopped being aporetic.

7.8 What the account does not cover

The account is a theory of persistent conceptual aporiai in the sense of §2.1, and I have tried throughout to mark its edges. Here I collect them.

Factual metaphysical questions. Whether God exists, whether there are abstract objects, whether the universe had a beginning: the parties to these debates take themselves to be disagreeing about how things are, and the account does not say they are wrong. It has something to say about existence questions where a distinction between existing and being fundamental has been drawn (§4.6), but the class as a whole lies outside it.

Questions with a metaphysical residue. In some aporiai the decomposition leaves a residue that is metaphysical rather than normative, and here the account explains the structure of the disagreement but not its content. The problem of consciousness is the clearest case. Chalmers's (1995) distinction between the easy problems and the hard problem is a disentanglement of the functions of "explain", mechanistic and predictive explanation on one side and something like rendering intelligible on the other, and the account predicts that verdicts on zombie and knowledge-argument cases will track which function of "explain" is salient. But the residual question, whether there is a further fact of phenomenal experience over and above the functional facts, is not a question about what a practice should require; it is a question about what there is, and it has the shape of the further-fact dispute of §7.3 rather than of the ethics of blame. The account says that the dispute has this shape. It does not say who is right. The same holds for the debate between A-theorists and B-theorists of time, which McTaggart (1908) initiated by disentangling two functions of temporal vocabulary and which has a metaphysical residue, and for external-world scepticism beyond the point where the certainty function of "knows" has been demoted.

Formal and mathematical questions. Questions settled by proof are not persistent, and the account has nothing to add to the epistemology of proof.

Questions of interpretation and history. These may be permanently contested but do not present aporetically.

The problem of induction. I am uncertain whether this falls inside or outside. "Justified", applied to inductive inference, has a function of licensing inference and a function of guaranteeing truth, and Hume's argument decorrelates them; Strawson's (1952, ch. 9) dissolution and Reichenbach's (1938) pragmatic vindication are prioritisations of the licensing function. So far the fit is good. But the residue, whether nature is uniform, is not obviously normative, and I leave the case open.

I regard candour about these limits as a strength. An account of philosophy's problems that claimed to cover everything philosophers have ever disputed would be suspect on that ground alone.

7.9 What would refute it

The account makes the following predictions, each of which could fail.

(P1) There is no persistent conceptual aporia, in the sense of §2.1, whose theses fail to map onto distinct functions of the central concept by the case-partition criterion. The discovery of an aporia around a demonstrably monofunctional concept would refute T1.

(P2) Competent users do not stably disagree about verdicts in a concept's coincidence range. Stable, informed, unforced disagreement about whether an ordinary perceiver in good conditions knows what she sees, or whether an ordinary agent acting on her reasons is responsible, would refute (3.4).

(P3) No headline question of a persistent aporia has been or will be settled by convergence without either decomposition or legislation by an authoritative practice. A case of convergence on such a question by discovery alone would refute T4.

(P4) Framing effects on verdicts in divergence cases track the salience of the concept's functions, not arbitrary features of presentation. Experimental findings that verdicts in balanced divergence cases vary with features unrelated to any function of the concept, and do not vary with manipulations of function salience, would refute (3.6).

(P5) No disentanglement is reversed. Since the case-partition criterion entails that functions once separated cannot be re-merged, the discovery of a case that re-merged them would show the criterion to be wrong.

Two empirical studies would test the account directly. The first is a decomposed survey: present professional philosophers with the headline question of an aporia and with its decomposed components, and predict a stable split on the headline together with near-consensus on the components. For free will the prediction is that respondents will divide on compatibilism in roughly the proportions of the PhilPapers surveys while agreeing, at rates above ninety per cent, that Frankfurt cases separate leeway from guidance control, that reasons-responsiveness is compatible with determinism, and that leeway in the unconditional sense is not. The second is a salience manipulation: present the same divergence case under framings that foreground different practices, a courtroom frame and a laboratory frame for a causal-selection case, a first-person and a third-person frame for a personal-identity case, and predict that verdicts shift in the direction of the function the frame engages. Williams (1970) and Nichols and Knobe (2007) have in effect already run versions of the second, and the results are as predicted; a systematic programme would put the account to a sharper test.