The Phenomenon: Aporetic Clusters

2.1 What a persistent problem is

Not everything that has been called a philosophical problem is the subject of this dissertation. The account I defend is a theory of a specific class of problems, and the first task is to say which.

I shall call a problem a persistent conceptual aporia when it satisfies four conditions.

(2.1) Longevity under scrutiny. The problem has been considered by competent inquirers over a long period, with each generation in possession of the arguments of its predecessors. This excludes problems that are merely new and problems that persist only because no one has attended to them.

(2.2) Stability of the position space. The range of positions taken on the problem has been stable: the same handful of options recurs, refined but not replaced, and the distribution of informed opinion across them does not trend towards one. This excludes problems on which the profession has in fact converged, whether by solution or by abandonment.

(2.3) Aporetic presentation. The problem presents as a set of claims each of which commands wide assent when considered on its own and which are jointly inconsistent. This is Rescher's notion of an aporetic cluster, discussed in §2.3. It excludes problems that are simply hard questions with no particularly plausible candidate answers, such as many questions in the history of philosophy or the interpretation of texts.

(2.4) Case-dependence. The inconsistency is exhibited, and was historically discovered, by means of cases: situations, actual or imagined, in which the claims deliver conflicting verdicts. This excludes paradoxes whose inconsistency is exhibited by pure derivation from the claims alone. (Whether the boundary between these is sharp is a question I return to in §4.6, where I argue that the set-theoretic paradoxes, which look like pure derivations, are in fact case-dependent in the relevant sense.)

The problems of knowledge, free will, personal identity, and causation, as they are pursued in analytic philosophy, satisfy all four conditions; so, I shall suggest, do the problems of truth, liberty, moral rightness, and existence. By contrast, several kinds of question that have been called philosophical do not, and it is worth being clear that they are not my subject.

First, there are the questions that have left philosophy. Austin's image is apt: philosophy has been the "initial central sun, seminal and tumultuous", which from time to time throws off a portion of itself to take station as a science (Austin 1956, 232). Cosmology, the theory of matter, the psychology of perception, and the theory of computation were once philosophical questions and now are not, because the concepts involved acquired a single dominant function, that of prediction or proof, and with it a decision procedure. Chalmers (2015) counts these as philosophical progress and he is right to, but they are not persistent aporiai; they are aporiai that stopped persisting for a reason the present account will identify (§7.7).

Second, there are questions that are straightforwardly factual but hard, such as whether God exists or whether there are abstract objects. The parties to these debates take themselves to be disagreeing about how things are, and I shall not argue that they are wrong to. The account has something to say about some of these debates, in particular about existence questions where a distinction between existing and being fundamental has been drawn (§4.6), but as a class they fall outside it.

Third, there are formal results that were once philosophical questions, such as whether every truth of arithmetic is provable. These were settled by proof, and their settlement is agreed. They are not persistent.

Fourth, there are questions of interpretation and history, which may be permanently contested but do not present aporetically.

The subject of the dissertation, then, is the class of problems that present as case-dependent aporetic clusters and that have proved stable under long scrutiny. I shall argue that this class is unified by a single mechanism, and that the mechanism explains why its members behave as they do.

2.2 The evidence of persistence

That the problems in question are old is not in dispute. The Theaetetus ends with the rejection of three accounts of knowledge, including the one that would later be called justified true belief, and offers no fourth (Plato, Theaetetus 201d–210a). The ancient debate on fate and responsibility already contained the position that was later called compatibilism: Chrysippus's image of the cylinder, which rolls because it is pushed but rolls as it does because of its own shape, was offered precisely to reconcile universal causation with responsibility (Cicero, De Fato 42–43). Locke's chapter on identity and diversity introduced the case of the prince and the cobbler and the distinction between the man and the person, and Butler and Reid replied with objections that are still made (Locke 1690, II.xxvii; Reid 1785, Essay III). Hume gave two definitions of cause and treated them as equivalent (Hume 1748, §VII.ii); Lewis's "Causation" opens by observing that they are not (Lewis 1973, 556).

That the problems are not merely old but persistent in the sense of (2.2) is what the survey evidence adds. The PhilPapers survey of 2009 asked professional philosophers in leading departments to state their positions on thirty questions (Bourget and Chalmers 2014). The 2020 survey repeated the thirty and added others (Bourget and Chalmers 2023). Two features of the results matter here.

The first is the absence of consensus. On no question of the thirty did a position command the near-unanimity that is routine for settled questions in the natural sciences. On the questions at the centre of this dissertation, the leading positions attracted pluralities, not majorities, and the minority positions were held by substantial fractions of the profession.

The second is stability. Where the two surveys can be compared, the distributions moved little. The free will figures cited in §1.2 are the clearest example: 59 per cent for compatibilism in 2009, 62 per cent in 2020, with the survey's own warning that the populations differ and the comparison is only properly made through its longitudinal analysis. Read with that caution, the picture is of a profession that moved a little and divided as before. Such stability across a decade of intensive work is, on the face of it, remarkable. It is not that no arguments were produced. The decade saw the maturation of the manipulation-argument literature, new work on the semantics of ability, a wave of experimental studies of folk judgements, and a good deal of conceptual engineering under the heading of "revisionism". None of it produced anything that could be mistaken for convergence.

Two cautions are in order. Survey respondents in 2020 were not the same individuals as in 2009, so stability of the aggregate is compatible with individual change. And the survey categories are coarse: "compatibilism" covers positions that differ considerably. But the coarseness cuts in the direction of my thesis rather than against it. If the profession were converging, one would expect the coarse categories to show it. They do not.

There is a third source of evidence, less quantifiable but, to anyone who has worked in these fields, unmistakable: the phenomenology of the disputes. The parties to a persistent aporia do not experience one another as ignorant or irrational. They know the arguments. They can state their opponents' positions in terms their opponents accept. They can predict what the reply to any new argument will be, and they are usually right. The experience is not that of an unsolved problem, on which the evidence is not yet in, but of a solved problem whose solution the other side refuses to accept, coupled with the uneasy awareness that the other side has exactly the same experience.

2.3 Rescher's structure

The most careful structural description of persistent philosophical problems is Rescher's. In The Strife of Systems (1985) and again in Aporetics (2009) he argues that philosophical problems characteristically take the form of an aporetic cluster: a set of theses each of which is individually plausible, indeed such that we have good reason to accept each, but which are jointly inconsistent. A solution to the problem is then a choice of which thesis to abandon. The several philosophical positions on a problem correspond to the several possible abandonments, and the choice among them is governed by a priority ordering over the theses, an ordering that in turn reflects the cognitive values of the philosopher: the weight given to simplicity, to fidelity to common sense, to systematic power, to economy of ontology, and so on. Philosophical diversity, on Rescher's account, is thus neither a sign of irrationality nor a sign that the questions are empty; it is the natural consequence of rational agents with different priority orderings confronting the same inconsistent set.

The description fits. Consider the four problems that will occupy Chapter 4.

Free will. (F1) We are sometimes morally responsible for what we do. (F2) Moral responsibility requires that the agent could have done otherwise. (F3) Our actions are the deterministic consequences of prior states of the world together with the laws of nature. (F4) If determinism is true, no one could ever have done otherwise. The theses are jointly inconsistent. The libertarian rejects (F3); the hard determinist or hard incompatibilist rejects (F1); the classical compatibilist rejects (F4) by reinterpreting "could have done otherwise"; the Frankfurtian compatibilist rejects (F2).

Knowledge. (K1) Knowledge is justified true belief. (K2) Smith has a justified true belief that the man who will get the job has ten coins in his pocket. (K3) Smith does not know it. Here the profession has in fact converged: nearly everyone rejects (K1). But the successor cluster, formed when (K1) is replaced by any of its proposed repairs, does not converge, as §4.2 shows.

Personal identity. (P1) Identity is a one–one relation: nothing can be identical to two distinct things. (P2) Psychological continuity, appropriately caused, is what makes a future person me. (P3) In a case of fission, two future persons are each psychologically continuous with me. (P4) What matters in my survival is that there be a future person who is me. Again inconsistent. The no-branching theorist qualifies (P2); the closest-continuer theorist (Nozick 1981) modifies it differently; the four-dimensionalist (Lewis 1976) reinterprets (P1) by counting two persons all along; Parfit (1984) rejects (P4).

Causation. Hall (2004) states the cluster explicitly. (C1) Causation is transitive. (C2) Causation is local: causes are connected to their effects by spatiotemporally continuous processes. (C3) Causation is intrinsic: whether c causes e depends only on the intrinsic character of the process connecting them. (C4) Counterfactual dependence of e on c suffices for c to cause e. (C5) Omissions can be causes. Hall shows that no single relation satisfies all five, and concludes that there are two concepts of causation, production and dependence, which divide the theses between them.

The structural description also fits Chalmers's observation (2015, §3) that philosophy's distinctive results are negative or conditional: it is agreed that (K1) fails, agreed that (F2) and (F4) cannot both be held with (F1) and (F3), agreed that (C1) to (C5) are jointly unsatisfiable. What is not agreed is which thesis to give up. That is exactly what Rescher's picture predicts.

2.4 Three things the structure does not explain

Rescher's account is a description, and an accurate one, but it is not yet an explanation. Three questions remain, and I take the failure of the description to answer them as the mark of what a genuine theory of philosophy's problems must do.

The source of plausibility. An aporetic cluster is not just any inconsistent set. If I believe that all swans are white and also that there is a black swan in Perth, I have an inconsistent set, but no aporia; I simply give up the first belief. What makes a cluster aporetic is that each member is compelling, so that no abandonment is comfortable. Rescher registers this by requiring that the theses be "individually plausible", but plausibility is a fact to be explained, not a primitive. Why is (F2), the principle of alternate possibilities, compelling? Why is (P1), the one–oneness of identity, compelling? Why is (C4), the sufficiency of dependence, compelling? An answer of the form "because we have strong intuitions in their favour" relocates the question. A theory of the aporia should say what it is about these theses, and about our relation to the concepts they concern, that makes them compelling even after we know that they cannot all be true.

Selectivity. Aporetic clusters form around some concepts and not others. There is no aporia of the prime number, of the uncle, of the kilometre, or of the chess bishop. There are aporiai of knowledge, cause, person, freedom, justice, truth, meaning, and existence. What distinguishes the two lists? It is not abstractness: "prime number" is abstract. It is not vagueness: "kilometre" is precise and "heap" is vague, yet neither generates a persistent aporia of the kind at issue (the sorites is a paradox of a different structure, as §3.6 argues). It is not importance alone: "uncle" matters to a great deal of social life. Rescher's account, which locates the source of diversity in the philosopher's cognitive values, has no resources to explain why those values are engaged by some concepts and not by others.

Case-dependence. The inconsistency of an aporetic cluster is typically not visible on inspection. It has to be shown, and it is shown by constructing a case in which the theses deliver conflicting verdicts. Before Gettier, (K1) to (K3) were not an aporetic cluster, because (K2) and (K3) had no referent; the cluster came into being when Gettier constructed Smith. Before Frankfurt, (F2) was not under pressure from within the compatibilist camp; it came under pressure when Frankfurt constructed Black and Jones. Hall's five theses were made inconsistent by cases of late pre-emption, double prevention, and omission, not by any derivation from the theses themselves. This is a striking feature. In mathematics, inconsistency is exhibited by derivation; in empirical science, by observation; in philosophy, by the construction of possible situations. Rescher's account treats the aporetic cluster as given and asks how to resolve it; it does not ask why the cluster had to be constructed, or why the construction typically requires cases that are rare, exotic, or physically impossible.

To these three I add a fourth, which is really a feature of the phenomenology noted in §2.2 and which will matter in Chapter 5: the disputes seem substantive to their parties and often seem verbal to observers, and both appearances survive reflection. Rescher's account sides with the parties. The deflationist sides with the observers. Neither explains why the other appearance is so stable.

2.5 The role of cases

I take the third of these questions to be the key to the other two, and I close this chapter by looking more closely at what a philosophical thought experiment does.

The recent epistemology of thought experiments has been concerned mainly with the status of the verdicts they elicit: whether these are intuitions with a distinctive evidential standing (Bealer 1998; Chudnoff 2013; Bengson 2015), whether they are ordinary judgements about counterfactuals (Williamson 2007, ch. 6), whether they are used as evidence at all (Cappelen 2012; Deutsch 2015; against them Climenhaga 2018), and whether they are trustworthy given their sensitivity to demographic and framing variables (Weinberg, Nichols, and Stich 2001; Machery 2017; in defence Nagel 2012; Sosa 2007b). These are important questions, but they presuppose an answer to a prior one, which has been comparatively neglected: what is the case for, as distinct from the verdict? Why does eliciting a verdict about Smith, or Jones, or the divided person, tell us anything about knowledge, or responsibility, or identity?

The standard answer is that the case is a probe of the concept. We possess the concept of knowledge; we cannot state its application conditions directly; so we apply it to a case and record the result, as one might probe a black box with inputs. The verdict is data about the concept's extension, and an analysis is a hypothesis that fits the data.

This answer is correct as far as it goes, but it omits the feature of the cases that makes them philosophically productive. The cases that generate persistent aporiai are not random probes. They have a very specific design. Each is constructed so that features which ordinarily co-occur are made to come apart. Smith's belief is well-grounded and true by luck: in ordinary life, well-grounded beliefs are true because they are well-grounded, and the two features coincide. Jones acts on his own reasons and could not have done otherwise: in ordinary life, agents who act on their own reasons are agents who could have done otherwise, and the two coincide. The divided person is psychologically continuous with two future people: in ordinary life psychological continuity is one–one, and continuity and identity coincide. Suzy's rock shatters the bottle and the shattering does not depend on her throw, because Billy's rock was on its way: in ordinary life, what produces an effect is what the effect depends on, and the two coincide.

In each case the thought experiment is a divergence constructor. It specifies a possible situation in which two or more properties, which are correlated across the range of cases from which the concept was learned, are decorrelated. It then asks whether the concept applies. And the answer it receives is, characteristically, either a split verdict, or a firm verdict that on reflection turns out to have chosen one of the properties over the other.

Once this is seen, the three unexplained features of §2.4 come into focus together. The case has to be exotic because it must decorrelate properties that are correlated in the ordinary world; if they were easily decorrelated, ordinary experience would have done it and the concept would already have been refined. Aporiai form around these concepts and not others because these concepts track several correlated properties at once while "prime number" tracks one; the concept of a prime number cannot be put into a divergence case because there is nothing for its single application condition to diverge from. And each thesis of the cluster is compelling because each articulates one of the properties the concept tracks, and the concept does track it: (F2) is compelling because our concept of responsibility does, across the ordinary range, apply only to agents who could have done otherwise, and (F1) and the Frankfurtian rejection of (F2) are compelling because it also applies, across the same range, to agents who act on their own reasons, and in the ordinary range these are the same agents.

To turn these observations into a theory, I need an account of what it is for a concept to "track several properties at once", of why a concept should do so, and of what the properties have to do with the practices in which the concept is used. That is the work of the next chapter, and its central notion is that of a function.