Introduction: The Oldest Thought Experiment

1.1 A case from the Republic

The oldest surviving philosophical thought experiment is small enough to state in a sentence. In the first book of the Republic, the elderly Cephalus offers an account of justice: to tell the truth and to pay back what one has received. Socrates replies with a case. A friend, while in his right mind, lends you weapons; he then loses his mind and demands them back. Returning them would be paying back what one has received. It would not be just (Plato, Republic 331c).

Nothing in the exchange is obscure, and yet everything that this dissertation is about is already present in it. Cephalus's account was not foolish. In every case he had encountered in a long commercial life, the just thing to do had been to honour one's obligations and to return what was owed. His concept of justice had been learned from those cases, and it worked. Socrates did not refute it by finding an ordinary case it mishandled. He constructed an extraordinary one, in which two things the concept of justice normally does together, honouring obligations and doing good rather than harm, came apart. The case did not show that Cephalus had mislearned the concept. It showed that the concept, as everyone had learned it, was silent, or rather that it spoke with two voices, in a region no one had visited.

The pattern has never changed. When Edmund Gettier constructed a believer with a justified true belief who nevertheless does not seem to know (Gettier 1963), when Harry Frankfurt constructed an agent who is responsible for what he does though he could not have done otherwise (Frankfurt 1969), when Derek Parfit constructed a person who divides into two (Parfit 1971), and when Ned Hall constructed an effect that depends on an event no process connects it to (Hall 2004), each did what Socrates did to Cephalus. Each took a concept that works, located a region of possible cases in which the several things it does come apart, and built a case in that region. And each produced the same result: not a refutation but a fork, a set of claims that had seemed to be one claim, each of which now had to be weighed against the others.

This dissertation is an attempt to take that pattern seriously as a datum about philosophy, to explain it, and to draw from the explanation a conclusion about the two questions that the pattern most obviously raises. Why do philosophy's central disputes persist among intelligent, informed, and honest inquirers? And what, given that persistence, does progress in philosophy consist in?

1.2 The scandal

The persistence of philosophical disagreement has been noticed for as long as there have been philosophers to disagree. Sextus Empiricus made diaphōnia, undecidable disagreement among the dogmatists, the first of the five modes by which the Pyrrhonist suspends judgement (Outlines of Pyrrhonism I.164–169). Kant opened the first Critique by describing metaphysics as the battlefield of endless controversies, a discipline that had for centuries been groping about without finding the secure path of a science (Critique of Pure Reason Aviii, Bvii, Bxv). Kant took this to be a scandal in something like the literal sense: a stumbling block to the rational self-respect of the discipline, one he elsewhere applied to the fact that philosophy had still to take the existence of external things on faith (Bxxxix n.).

In our own period the observation has been sharpened by data. Chalmers (2015) asks why there is not more progress in philosophy, and his standard for progress is explicit: large collective convergence on the answers to the big questions, of the kind the natural sciences and mathematics have achieved. By that standard, he argues, philosophy has made little progress, and he supports the claim with the results of the 2009 PhilPapers survey of professional philosophers (Bourget and Chalmers 2014), which found nothing approaching consensus on any of thirty central questions. The 2020 repetition of the survey (Bourget and Chalmers 2023) found the distributions broadly stable. On free will, for example, the proportion accepting or leaning towards compatibilism was 59 per cent in 2009 and 62 per cent in 2020. The authors caution that the two surveys sampled different populations under different parameters and should not be read against each other directly, and supply a separate longitudinal analysis for that purpose; but even taking the headline figures at face value, a decade of intense work on Frankfurt cases, manipulation arguments, and the semantics of ability claims had shifted the profession's collective opinion by three points, and left it divided in almost exactly the proportions in which it began.

Three broad responses have been made to this situation, and it will help to have names for them.

The pessimist accepts Chalmers's standard and concludes that philosophy does not progress. Dietrich (2011) argues, bluntly, that there is no progress in philosophy, that the same problems are debated with the same range of positions as in antiquity, and that this is because philosophical problems are not the kind of thing that can be solved. Brennan (2010) draws a sceptical conclusion about the epistemic standing of philosophical belief; Kornblith (2010) presses the same worry from the epistemology of disagreement; Goldberg (2013) asks how philosophy can be defended in the face of what he calls systematic disagreement.

The revisionist optimist rejects the standard. Stoljar (2017) argues that philosophy makes progress on a great many of its questions once one distinguishes the "boundary" and "topic" questions actually being asked from the vaguer big questions with which they are conflated, and that a reasonable optimism is warranted. Dellsén, Lawler, and Norton (2022) apply to philosophy the noetic account of scientific progress, on which progress consists in increased understanding rather than in accumulated knowledge or convergent belief, and argue that on that account philosophy progresses. Williamson (2007) insists that philosophy's methods are continuous with those of other disciplines and that the discipline can do better if it holds itself to higher standards. Gutting (2009) documents a body of things philosophers now know.

The deflationist denies that the questions were ever the sort of thing that could be answered. In the Wittgensteinian tradition philosophical problems are symptoms of language "on holiday" (Wittgenstein 1953, §38), to be dissolved rather than solved; the real discovery is the one that lets one stop (§133). In the Carnapian tradition the persistent disputes are "external questions", to be settled pragmatically by a choice of framework rather than theoretically by discovery (Carnap 1950b). And in the recent literature on verbal disputes, Chalmers himself (2011) argues that many philosophical disagreements are at least partly verbal and offers a method of elimination for detecting when they are.

Each of these responses captures something. The pessimist is right that the headline questions do not get settled and that this is not for want of effort. The optimist is right that something cumulative happens in philosophy and that the pessimist's standard is imported from disciplines whose questions have a different structure. The deflationist is right that the disputes have a semantic dimension and that the parties often talk past each other. But none of the three, I shall argue, has correctly identified the mechanism that produces the phenomenon they are all responding to. Until one has the mechanism, one cannot say whether the persistence is a failure, what would count as success, or what to do next.

1.3 The thesis in outline

The mechanism I propose can be stated in five theses. I state them baldly here; the rest of the dissertation is their defence.

T1 (Polyfunctionality). The concepts at the centre of philosophy's persistent problems are polyfunctional. A single concept does several distinct jobs in our practices. Each job imposes its own application condition on the concept. Over the range of cases from which the concept is learned and in which it is ordinarily used, these conditions coincide in extension, so that the multiplicity is invisible.

T2 (Divergence). Persistent philosophical problems arise in the region of possible cases where the application conditions come apart. The characteristic structure of such a problem, a set of individually compelling but jointly inconsistent propositions, is explained by T1: each proposition articulates the application condition of one function, each is compelling because the concept does perform that function, and the set is inconsistent only over the divergence region. The philosophical thought experiment is the instrument by which divergence cases are constructed in advance of the world producing them.

T3 (Disagreement). The doctrinal positions in a persistent debate are prioritisations of functions. Once the factual components of the dispute (about which the parties largely agree) and the merely verbal components (which the method of elimination dissolves) are removed, what remains is a normative disagreement about which function the shared concept should serve in the divergence region. This residual disagreement is neither factual in the ordinary sense nor merely verbal. It is a question of what Burgess and Plunkett (2013) call conceptual ethics, and it is rationally stable among competent inquirers for the same reason that reasonable disagreement about the weighting of plural goods is stable: nothing in the concept, as learned from the coincidence range, fixes the weights.

T4 (Progress). Progress on a persistent problem consists in four things: locating the divergence region by constructing cases; articulating the functions whose divergence the cases reveal; disentangling the functions into distinct concepts; and relocating the residual question to the normative domain, where it can be pursued as the practical question it is. This progress is cumulative, is agreed across doctrinal divides, and constitutes understanding of how our practices hang together. Convergence on the original headline question is not to be expected, and its absence is not a failure.

T5 (Reflexivity). The concept of progress is itself polyfunctional, and the metaphilosophical dispute about whether philosophy progresses is itself a divergence case. The account therefore predicts and explains the debate to which it is a contribution. This is not offered as a proof of the account but as a consistency check that the account passes and that its rivals do not obviously pass.

The five theses stand in a definite order of dependence. T1 is an empirical-cum-conceptual claim about a class of concepts. T2 uses T1 to explain the structure of philosophical problems. T3 uses T2 to explain the structure and stability of philosophical disagreement. T4 uses T2 and T3 to say what progress can and cannot be. T5 turns the account on itself.

They are not equal in weight, and it will save the reader effort to know it now. T1 and T2 are the substantial claims, and Chapter 4 is where the dissertation stands or falls. T3 I take to be forced once T2 is granted, so that Chapter 5 is largely a matter of drawing it out and of keeping it clear of relativism. T4 has the most to say outside philosophy and the least novelty within it, since much of it is already the working self-understanding of the fields concerned. T5 carries no weight in the argument at all; it is a check, and a reader who rejected it could hold everything else.

1.4 What the account explains

An account of philosophy's persistent problems should be judged, like any theory, by what it explains. I list here the phenomena that I take to be the explananda and that I shall return to in §4.7 when assessing the abductive case.

(E1) Plausibility of each horn. In a philosophical problem the competing claims are not merely logically possible positions; each strikes reflective people as obviously true until it is set against the others. A theory should explain why each horn is compelling, not just why the horns conflict.

(E2) The indispensability of exotic cases. Philosophical problems are typically forced by cases that are constructed, rare, or physically impossible: fission, teleportation, counterfactual interveners, barn façades, double prevention. Theories of philosophy that treat these as optional illustrations have not understood their role.

(E3) Persistence without stagnation. The headline questions persist, yet the literature is not static: distinctions are introduced, positions are refined, some views are abandoned by nearly everyone (justified true belief as an analysis of knowledge; the unrestricted principle of alternate possibilities). A theory should explain why both are true at once.

(E4) Convergence on decompositions, divergence on headlines. Philosophers across doctrinal divides agree on the distinctions introduced in a debate (regulative versus guidance control; production versus dependence; identity versus what matters) while continuing to disagree about the headline question the distinctions were meant to address.

(E5) Stability of the distribution of opinion. Professional opinion on the headline questions is distributed across the positions in proportions that are stable over time and are not tracking the accumulation of arguments.

(E6) The pattern of experimental findings. Where experimental philosophers have measured folk judgements, verdicts on paradigm cases are robust across cultures and demographics, while verdicts on the exotic cases are sensitive to framing, affect, and abstraction (§4.3, §4.7).

(E7) Why the disputes seem substantive to the parties and verbal to the deflationist. Both appearances are stable and both are held by thoughtful people; a theory should explain how both can be partly right.

(E8) The recurrence of the same structure outside philosophy. Disputes of the same shape arise in law (whether a tomato is a vegetable, whether a corporation is a person), in the sciences (whether Pluto is a planet, whether a patient in irreversible coma is dead), and in ordinary life, and are there resolved by explicit legislation rather than by discovery. A theory of philosophy's problems should say what these have in common with philosophy's and why they, unlike philosophy's, get settled.

I shall argue that T1 to T4 explain all eight. The comparison with the rival accounts is less tidy than a scoreline would make it look, and I do not want to claim more from it than it will bear: the pessimist and the optimist are for the most part not offering explanations of E1, E2, or E6 at all, and it is no criticism of a position that it fails to explain something it never set out to. What can fairly be said, and what §4.7 argues, is that E1, E2, and E6 are the explananda on which the rivals are silent and on which this account has something specific to say, and that E5 and E7 are the two on which a rival and this account make different predictions rather than merely differing in coverage.

1.5 Method and scope

The argument of the dissertation is abductive. I do not claim that T1 is a conceptual truth about philosophy, nor that it can be established a priori. I claim that it is the best explanation of E1 to E8, and I try to show this by developing four case studies in enough detail that the reader can check the fit, by saying what the account predicts and what would refute it (§7.9), and by comparing it with its rivals on the explananda.

The case-study method carries an obvious risk of selection. The four problems I treat at length, knowledge, free will, personal identity, and causation, are among the most discussed in analytic philosophy, and were chosen for that reason: if the account fails there it fails. But I have also tried to indicate (§4.6) how the account extends to truth, liberty, moral rightness, existence, set, and scepticism, and I have tried in §7.8 to be candid about the problems it does not obviously cover. The account is a theory of philosophy's persistent conceptual aporiai, in a sense to be made precise in Chapter 2. It is not a theory of everything that has been called philosophy. Questions that are straightforwardly empirical, questions that are straightforwardly mathematical, and questions whose residue is metaphysical rather than normative fall outside it or at its edge, and I say so.

Two further methodological commitments should be declared. First, I treat the historical record of philosophy as evidence. If the account is right, the history of a persistent problem should display a characteristic shape, the progressive articulation and disentanglement of functions, and I shall argue that it does. Second, I treat the findings of experimental philosophy as evidence, with the caveats that the replication record of that literature demands. The account predicts a pattern in those findings, and I shall argue that the pattern is there.

1.6 Neighbours

Almost everything in what follows has been said of some concept by someone. This section is not a survey. It records the debts I could not have done without, in something like the order of their size, and it is uneven because the debts are. Fuller treatments follow where they belong, most of them in §3.6.

The largest is to Rescher. The Strife of Systems (1985) and Aporetics (2009) supply the structural description on which Chapter 2 is built: a philosophical problem presents as an aporetic cluster, a set of theses each of which we have reason to accept and which cannot all be true; a doctrinal position is a choice of which thesis to abandon; and the choice is governed by a priority ordering over the theses. Rescher also reaches, decades before survey evidence made the scandal quantitative, the conclusion I want to reach: that philosophical diversity is the expected output of rational inquiry and not a symptom of incompetence. I have taken the frame whole.

Where I press him is on the priority ordering. Rescher locates it in the individual philosopher, in the weight one gives to simplicity, to fidelity to common sense, to systematic power, to economy of ontology, and there it hangs unsupported. It tells us that philosophers differ; it does not tell us why they differ about these concepts rather than about "prime number", nor why each thesis of a cluster should be individually compelling, nor why the inconsistency has to be exhibited by constructing a case instead of derived from the theses themselves. On his account the cluster is where the argument begins. My claim is that the cluster has an etiology: its theses articulate the several jobs one concept has been doing at once, and the priority ordering is not a fact about a philosopher's taste but a weighting of the practices the concept serves. That moves the diversity out of the psychology of philosophers and into the ethics of practices, which is the whole of the distance between his conclusion and mine. The case is made in §2.4.

The second debt is to Craig. Knowledge and the State of Nature (1990) asks what concept a community with our needs and our limitations would have had to invent, answers that it would need to flag good informants, and in answering shows that a concept's content can be reached through the practical problem it solves. Williams (2002) turned the method on truthfulness, Queloz (2021) made it systematic, and Hannon (2019) and Simion and Kelp (2020) have carried it into epistemology. The apparatus of Chapter 3 is theirs. Two of the three methods of §3.3 are not mine.

The departure is at one point, and the rest of the dissertation follows from it. A genealogy specifies a practical problem and derives the concept that solves it, so it delivers one function per genealogy, and the concept's other jobs arrive afterwards as accretions on a core. I take the multiplicity to be primary. It is not, on my account, an accident that the programme has an unresolved internal dispute over whether the point of "knowledge" is to flag informants (Craig 1990), to close inquiry (Kelp 2011), or to license assertion (Williamson 2000). Each party has identified a real function; the concept performs all three; and the dispute among them is a small and self-referential instance of the phenomenon the programme was built to explain. I read it as evidence rather than as an embarrassment.

A third debt is narrower and, for one of the four case studies, decisive. Hall's "Two Concepts of Causation" (2004) sets out the aporetic cluster for causation as five theses, shows that no one relation satisfies all five, and concludes that the word carries two concepts, production and dependence, which divide the theses between them. That is this dissertation's thesis for one concept, argued there with more rigour than I shall manage for any of mine. Cartwright (2004) reached a more radical version of the same conclusion and put it in her title.

Described honestly, I am generalising Hall. What the generalisation adds is three things he had no reason to supply, his question being about causation and not about philosophy: an account of why a concept comes to carry two, which for causation is the correlation of production with dependence in ordinary uncontested chains (§3.4); the prediction that the same structure appears wherever a concept is load-bearing for several practices, which Chapter 4 exists to redeem; and a diagnosis of what remains of the dispute once the two concepts have been separated, which Hall does not take up and which I claim is normative. Whether that is a contribution or the dilution of a sharp local result is a fair question to put to me, and §4.5 is where I would want it put, because causation is the one domain in which the diagnosis was reached without my thesis and can therefore be checked against a version that did not begin from it.

With Chalmers the relation is less a debt than a running argument, and it runs in both directions. "Verbal Disputes" (2011) supplies the method I use in §5.2, barring the disputed term to see what disagreement survives, and I use it to reach a conclusion he does not draw: applied to the persistent aporiai the method never dissolves them, because barring the word leaves the practices standing with their demands unreconciled, and what emerges is not silence but a normative dispute over a shared instrument. He allows as much for terms tied to practices with consequences; I claim this is not an exception but the rule for every problem in my class. His question about progress (2015) sets the problem of Chapter 6, and his criterion for progress is the target of §7.1, where I argue that "large collective convergence" is the weighting of one function of "progress" presented as a measure of the concept.

Burgess and Plunkett (2013) named conceptual ethics and argued that the question which concepts we should use is a substantive normative one; Cappelen (2018), Haslanger (2012, 2020), Thomasson (2020), and the volume edited by Burgess, Cappelen, and Plunkett (2020) have since made a field of it. I take that claim and add a historical one to it: philosophy's persistent disputes already were disputes in conceptual ethics, conducted for two and a half thousand years in the idiom of analysis, and the disguise is what has made them look at once interminable and deep. The machinery for saying so precisely is Plunkett and Sundell's (2013) metalinguistic negotiation, on which Chapter 5 leans harder than its citations there suggest.

Gallie (1956) is invoked in these pages more often than the size of the debt warrants. He saw that some concepts are contested in a way that is neither confusion nor resolvable by argument, and his seven conditions describe such a concept unusually carefully from the outside. Description is what they remain. The mechanism is missing, and the restriction of the phenomenon to appraisive concepts was an artefact of the examples he chose rather than a finding about concepts. §3.6 supplies the mechanism, lifts the restriction to "knowledge" and "cause", and gives Waldron (2002), who objected that the label gets attached to anything, a criterion for when it may be.

From Dworkin (1986, 2011) I take one word. His "point" of a practice is near enough to my "function" that a reader should know it was there first; I deny that there need be a uniquely best account of the point, and I hold that a concept is not interpretive tout court but criterial in its coincidence range and interpretive only where its functions diverge.

Eklund (2002) and Scharp (2013) hold that some concepts, truth above all, are governed by constitutive principles that cannot all be satisfied, and Scharp's replacement of "true" by a pair of concepts is disentanglement carried out deliberately. Theirs is the closest structural relative of the present account, and my difference from it is one of charity and of scope: polyfunctionality is not defectiveness, which is why a concept governed by conflicting principles can remain serviceable for the whole history of human thought, as truth has.

Three smaller debts, each load-bearing exactly where it falls. Beebee (2018) proposes that philosophy aims at equilibria rather than at knowledge, which I take to be right and which the account explains: there are several equilibria because there are several coherent weightings, and §5.5 says what distinguishes them. Dellsén, Lawler, and Norton (2022) supply the conception of progress adopted in Chapter 6, and what I add is the content their account properly leaves open, namely what it is that philosophy comes to understand. And Rawls's burdens of judgement (1993, Lecture II) do more work in §5.4 than the citation there implies: the explanation of why the residual disagreement is stable among reasonable people is his, applied to a domain he was not writing about.

1.7 Plan

Chapter 2 characterises the phenomenon. It says what a persistent problem is, reviews the evidence of persistence, sets out Rescher's aporetic structure, identifies three things that structure leaves unexplained, and argues that the role of constructed cases is the key to explaining them.

Chapter 3 develops the theory of conceptual function that the account requires. It distinguishes role functions from etiological functions, adopts a practice-relative notion of the former, gives three methods for identifying the functions of a concept, explains why a single concept comes to bear several, and introduces the distinction between the coincidence range and the divergence region on which everything depends. It closes by distinguishing polyfunctionality from ambiguity, vagueness, open texture, family resemblance, cluster concepts, essential contestedness, interpretive concepts, and inconsistent concepts.

Chapter 4 states and defends T1 and T2 through the four case studies, sketches extensions, and assembles the abductive case.

Chapter 5 defends T3. It distinguishes three layers of disagreement in a persistent dispute, argues against the purely verbal diagnosis, argues that the residue is normative, explains why it is stable, draws the consequences for the epistemology of disagreement, and answers the charge of relativism.

Chapter 6 defends T4. It surveys accounts of progress, sets out the disentanglement account, documents the record of disentanglements in the four case studies, shows that disentanglement is sometimes followed by re-unification at a higher level of abstraction, argues that philosophy's construction of divergence cases has anticipatory practical value, and shows how the account reconciles pessimist, optimist, and deflationist.

Chapter 7 defends T5 and takes the objections: triviality, realism, conventionalism, circularity, demotion, and the apparent counterexamples of philosophy's convergent successes. The objection from circularity it answers only in part, and §7.5 says where the answer stops. It marks the account's limits and states what would refute it.

Chapter 8 concludes with a statement of what, on this account, philosophy is for.