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Synthetic a priori judgments and Kant’s response to Hume on induction

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Abstract

This paper will make the case that we can find in Kant’s Second Analogy a substantive response to Hume’s argument on induction. This response is substantive insofar as it does not merely consist in independently arguing for the opposite conclusion, but rather, it identifies and exploits a gap in this argument. More specifically, Hume misses the possibility of justifying the uniformity of nature as a synthetic a priori proposition, which Kant looks to establish in the Second Analogy. Note that the focus on the paper is on Kant’s identification of the form that a solution to Hume’s inductive scepticism must take. In making this point, my paper will look to establish two lemmas: (1) Kant identifies synthetic a priori judgments as a means of justifying metaphysical knowledge in a way that circumvents Hume’s dichotomy between matters of fact and relations of ideas; (2) the Second Analogy looks to establish the uniformity of nature of as a synthetic a priori proposition. However, my paper generally abstains from the question of the tenability of Kant’s argument in the Second Analogy. Doing justice to this latter discussion would require more space than I am able to offer here. My paper therefore has a conditional bearing on the philosophical issue of inductive scepticism. If one believes Kant’s Second Analogy to be philosophically cogent, then Kant offers a successful justification of induction against Hume’s scepticism. If not, then at least one can still admire Kant’s identification of the gap in Hume’s argument, which, to a degree, can be exploited independently of Kant’s system.

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Notes

  1. See for instance A766/B794 in the Critique, and 4:257–58 and 4:310 in the Prolegomena. Kuehn (1983) argues that Hume’s problem also was the instigator for Kant’s Antinomy of Pure Reason. References to the Critique of Pure Reason follow the standard A and B paginations for the first and second editions respectively. The translation used is the 1998 Cambridge edition, edited and translated by Paul Guyer and Allen Wood (Kant 1998). References to the Prolegomena to any Future Metaphysics use the pagination of volume 4 of Kant’s Gesammelte Schriften, edited by the Königlich Preussische Akademie der Wissenschaften, Berlin, 1911. The translation used is the 2004 Cambridge edition, edited and translated by Gary Hatfield.

  2. Lewis White Beck’s famous essay, ‘A Prussian Hume and a Scottish Kant’, rather pithily labels the principles that Hume challenges in his account of causation (in the Treatise) and induction as ‘every-event-some-cause’ and ‘same-cause-same-effect’ respectively (Beck 1978).

  3. See Hatfield (2001) and (Watkins 2005, Chapter 6) for some interpretations that do not see the Second Analogy as particularly concerned with responding to Hume’s worry about causation. See Guyer (2008, pp. 9–20) and Chance (2013) for some replies in this regard.

  4. Guyer (2008, p. 123). See also Beck (1978), Walker (1999, p. 14), Waxman (2008), Allison (1994, 2004, p. 246), and Allison (2008b, p. 541). That said, commentators often hold that Kant elsewhere offers such a response to Hume. Walker argues that Kant answers Hume in this respect in ‘On the Regulative Use of the Ideas of Pure Reason’ (A642–704/B670–732), although see (Bird 1999) for a reply. Guyer and Allison see this response in the Introduction to the Critique of the Power of Judgement, which argues that in looking for the particular causal rule to apply, we presuppose that nature as a whole is organised according to a continuous hierarchy of empirical laws, from the more universal to the more particular; see Guyer (2008, Ch. 5), Allison (2001, Ch. 1), Allison (2003, 2008a, Ch. 5, Appendix). Ginsborg (2017, p. 74) argues that this response cannot in itself constitute an answer to Hume’s problem of induction, insofar as the relevant principle of judgement is confirmed by observation, and thus an appeal to it to justify induction would be question-begging. Landy (2015, p. 216) argues that the Second Analogy only adds ‘the specific form’ of the causal laws, but the necessity of these laws has already been established by Kant’s general account of mental representation.

  5. There have been a number of interpretations that see Kant’s account of causation as capable of addressing Hume’s inductive scepticism. One prominent such interpretation is Friedman (1992, 1994), which argues that transcendental laws ground empirical laws by supplying them with the requisite necessity, thus offering a guarantee for the uniformity of particular empirical laws. By contrast, my account only looks to offer a guarantee for general uniformity, while remaining silent on the status of particular empirical causal laws. Another account is offered in Melnick (2006, p. 217), which argues that the uniformity of nature is founded on the homogenous nature of the unfolding of time, which necessitates a homogeneity in the unfolding of events that occur in time; this position is also defended in Longuenesse (2005, pp. 172–177), which relates the conceptual continuity from higher to lower concepts and empirical laws, to the intuitive continuity of time. Buroker (2006, p. 173) finds convincing Melnick’s and Friedman’s arguments for Kant’s being concerned with establishing the uniformity of nature in the Second Analogy. Watkins also argues that Kant’s overall model of causality allows him to establish general uniformity in Watkins (2004, §6, 2005, Ch. 4), although he stresses the metaphysics of Kant’s account of causation, while I emphasise the notion of rule-boundedness.

  6. I do not deny that Kant’s response requires elements of his critical philosophy that go beyond the Second Analogy, but I maintain that the bulk of the heavy lifting is done in establishing the synthetic a priori judgment that is the Causal Principle, which is the task of the Second Analogy.

  7. Kant might, however, have encountered Hume’s argument on the self second-hand by means of Beattie’s discussion of it. Of course, there are a number of possible routes via which Kant might have been exposed to the Treatise (c.f. for example Kuehn 1989), and so any such suggestion must remain speculative.

  8. Here I bracket the distinction between metaphysical necessity and contingency. Hume and Kant would agree that metaphysical necessity goes hand-in-hand with a priority, and contingency with a posteriority. Kripke (1980) would later dispute this (but see Millican 2017, §7 for detailed discussion). Hume of course recognises causal as well as metaphysical (or ‘absolute’) necessity; the former is only knowable a posteriori. Kant, in criticising Hume for failing to recognise the necessity of causation, takes it that Hume’s notion of causal necessity is insufficient in this regard, since Kant takes it to be overly psychologistic in its roots.

  9. Allison (2004, p. 90) very usefully and concisely discusses some of these issues.

  10. MacFarlane (2002, p. 26).

  11. Hanna (2001, p. 125). Hanna offers a detailed semantic account of analytic judgments, whereby to make an analytic judgment is to articulate the decompositional content of a concept Hanna (2006, p. 371).

  12. Allison (2004, p. 91).

  13. Van Cleve (1999, p. 20), Buroker (2006, p. 31).

  14. Hanna (2001, p. 148); see also Anderson (1992, p. 84).

  15. Hanna (2001, p. 150).

  16. An excellent and thorough discussion of Hume’s Fork is available in Millican (2017).

  17. Lightner (1997) and Millican (2017, pp. 37–42). Holden (2014) has argued that Hume in fact endorses the Inconceivability Principle, in line with his reading of Hume as an expressivist about modality, but see the just-mentioned Millican paper for strong criticism of this view.

  18. Millican (2017, p. 38).

  19. Millican (2017, §7).

  20. Here I am convinced that ‘New Hume’ positions such as Wright (1983), Strawson (1989), and Kail (2007) that argue otherwise have been decisively refuted by Winkler (1991) and Millican (2009).

  21. Garrett (2008, pp. 203–206).

  22. Garrett (2008, p. 206).

  23. Indeed, whether or not Hume thinks that synthetic a priori propositions are in general possible, he clearly does not think that the Uniformity Principle in particular could be a synthetic a priori truth. For importantly, he clearly denies that it could be a priori at all (EHU 4.18). Thus, even if one is inclined to maintain that Hume’s Fork can accommodate synthetic a priori propositions, one can still take this paper’s conclusion on board: Kant aims to answer Hume’s argument on induction by showing that the Uniformity Principle (or something like it) is a synthetic a priori proposition, a possibility that Hume missed.

  24. Space and time are necessary but insufficient conditions for the possibility of synthetic a priori judgments. Crucial also is the transcendental unity of apperception, but to go into the details of the Kantian machinery on this point would take us too far afield, and would be somewhat tangential to my paper. For my purposes, it suffices to show that synthetic a priori propositions require a priori intuitions; as I will later argue, Hume rejects the latter.

  25. In this paper, I will be discussing the version that Hume offers in the Enquiry Concerning Human Understanding (rather than the version set out in Book 1 of the Treatise of Human Nature, or the one set out in An Abstract of a Book Lately Published). This is because the Enquiry was the work of Hume’s that Kant referred to in writing his Critique of Pure Reason (Guyer 2008, pp. 5–6). This is also the most polished and complete version of the argument—for details of the differences, see Millican (2012, §3) and Qu (2020, Ch. 3).

  26. Qu (2014, 2020, Ch. 3–4).

  27. In the references to Hume’s texts throughout, ‘THN’ refers to the Treatise of Human Nature (Hume 1739–1740/2007), and ‘EHU’ refers to the Enquiry Concerning Human Understanding (Hume 1748/2007). Arabic numerals refer to section and paragraph numbers (EHU), or to book, part, section, and paragraph numbers (THN).

  28. I take EHU 4 to be making a sceptical point (we lack reason-based justification for our inductive inferences) rather than a psychological one (the process by which we are caused to inductively infer is not one that involves reason). For some defences of the latter reading, see Garrett (1997) and Owen (1999). I offer a case for reading EHU 4 as sceptical in nature in my Qu (2014, 2020, Ch. 3); see also Winkler (1999) and Millican (2002), as well as Millican (2012), which revises his account in a few respects. It is worth noting that Kant, at least, clearly takes Hume’s problem to be genuinely sceptical, whether or not he was correct to do so.

    In correspondence, Peter Millican suggests that Hume himself might be read as providing a quasi-transcendental argument for the Uniformity Principle. One might read Hume as arguing that we do in fact have justified belief about unobserved matters of fact (EHU 5.2), and the Uniformity Principle being justified is a necessary precondition of this—therefore, the Uniformity Principle is justified.

  29. Elsewhere in Qu (2020, pp. 66–76), I have argued that Hume also dismisses the possibility of sensation directly grounding our inductive inferences in EHU 4.16, following Millican (1998, 2002). But this is controversial, and is denied by Garrett (1998), for instance. As the matter is not crucial for my purposes in this paper, I set it aside here.

  30. Probable reasoning includes both what Hume calls ‘probabilities’ and ‘proofs’, and is not Hume’s favoured term in the Enquiry. I use it because it is more convenient that ‘reasoning concerning matters of fact’ and less prone to confusion than ‘moral reasoning’.

  31. Elsewhere in Qu (2014, 2020, Ch. 3–4), I argue that Hume seeks to mitigate this sceptical result by adducing some positive justification for our inductive practices in EHU 5; as such, the argument of EHU 4 is not watertight, and can be circumvented, as I maintain Hume himself aimed to do. However, insofar as Kant either did not seem aware of, or convinced by, any such considerations, I bracket them for the purposes of my paper.

  32. Allison (1981, p. 70) puts it elegantly: ‘transcendental determinations of time, as products of the transcendental synthesis of the imagination, are universal and necessary (a priori) characteristics of objective time or an objective temporal order.’

  33. The sense in which concepts and objects are not homogenous can be somewhat obscure. In my view, it is best understood as due to the fact that concepts are logically ordered, while objects are spatio-temporally ordered.

  34. An anonymous referee poses an interesting question: what is the relation, if any, between pure intuition as the bridge between concepts in synthetic a priori judgments and schemata as the bridge between object and concept? My own view is that these two issues are somewhat orthogonal. For one, schemata are the products of the imagination, while a priori intuitions fall within the province of sensibility. For another, schemata, which allow for concepts to apply to intuitions, are universal to all judgments; meanwhile, among judgments, only those that are synthetic a priori have a priori intuitions playing this bridging function. This corresponds to pure intuitions and schemata having different functions with respect to judgments. The function of a priori intuitions in synthetic a priori judgments is tied to truth: they allow a concept not contained within a subject to be truly predicated of it. Meanwhile, the function of schemata is independent of truth: even false applications of concepts to intuitions will require schemata as a means of bridging the gap between the conceptual and the sensible.

  35. For instance, Landy (2015, p. 215) points out that alterations might accord with the general law of the connection of cause and effect by according with more specific causal laws, thus bringing the B version in line with the A version. Similarly, Watkins (2010, p. 161) claims that Kant ‘often refers to the law of the connection of cause and effect simply as a causal rule, so the content of the principle of the Second Analogy is that every event occurs according to a causal rule’. See also Allison (2004, p. 247): ‘…the difference between the two formulations is merely terminological.’ For a detailed account of the relation between the two formulations, see Longuenesse (1998, Chapter 11).

  36. ‘Same thing’ is somewhat ambiguous here. In Kant’s example of the house, we are observing the same object regardless of order. In Kant’s example of the ship, we are observing the same event only if the order is retained. Perceivings of events are order-sensitive, while perceivings of objects are not. If we changed the former example to involve a burning house, then this would be an event rather than an object, and so the order of perceptual states would matter: if the perceptual states were in a different order, we would be observing a different event (e.g. a house fire extinguishing rather than kindling).

  37. Kant’s position here presupposes that scepticism about the external world (a form of which Hume arguably endorses) is unviable, but Kant elsewhere addresses such scepticism in his Refutation of Idealism.

  38. Here, ‘everything that happens’ refers to changes in objects, that is, objective change.

  39. Longuenesse (2005, p. 166).

  40. That even infants and beasts behave inductively is a point that Hume repeatedly stresses (EHU 4.23, EHU 9.1).

  41. It might in fact be overdetermined: defamation, sedition, and the Protection from Online Falsehoods and Manipulation Act (POFMA) may all be seen to apply.

  42. Friedman (1992, particularly §3 and §5), Friedman (1994, p. 38).

  43. Although, of course, there might be other reasons to establish the necessity of particular laws. As such, my disagreement with Friedman is less on Kant scholarship, and more on the nature of Hume’s sceptical attack on induction (and what would suffice to constitute a response to this attack).

  44. Allison (1994). See also Paton (1951, pp. 275–278) and McFarland (1970, pp. 8–11).

  45. Allison (1994, p. 298).

  46. Kant’s use of the Causal Principle to justify the Uniformity Principle is similar to Price’s attempt in his Review of the Principal Questions and Difficulties in Morals to justify the Uniformity Principle on the basis of the Causal Maxim (every event has a cause) being intuitively known. See Millican (2012, pp. 76–77) for discussion of Price’s attempt.

  47. Hume does suggest that the principle that every event has a cause might be justified by experience, for instance in THN 1.3.3.9, THN 1.3.8.14, and THN 1.3.12.5 (see also EHU 8.15).

  48. Millican (2002, pp. 136–137). Millican (1996) carefully explores such strategies.

  49. Russell (1912, Chapter 6). For other attempts, see for instance Williams (1947), De Finetti (1969), Blackburn (1973), Mackie (1979), and Stove (1986). See also Howson (2000, Chapter 4) for a more formal discussion of such strategies, and (Ayer 1972) for a rejection of such accounts. Millican (1996) has a careful and comprehensive discussion of such attempts.

  50. White (2015). White argues that it is very difficult to construct a world whereby induction goes radically wrong; in most cases, induction will go even (on average) or do well. Thus, on balance, we have a priori reason to think induction reliable, since we are statistically likely to occupy an induction-friendly world. For a recent rejection of this solution, see Barnett and Li (2018).

  51. See Garrett (2015, p. 322), who similarly describes Kant as addressing Hume’s problem of induction by means of offering a third kind of argument—that is, a transcendental argument.

  52. As mentioned earlier, Hume recognises causal necessity (e.g. EHU 8.5), but this should be sharply distinguished from objective necessary connections between causes and effects, which he rejects. Note also that Hume acknowledges uncertain probable arguments (e.g. his ‘probability of chances’ and ‘probability of causes’, e.g. THN 1.3.11–12;EHU 6.4).

  53. Stern (2004, pp. 8–10).

  54. For some discussion of such difficulties, see Stern (2004, pp. 59–63).

  55. This might be contrasted with accounts that see Kant’s response to Hume on induction as residing in the Introduction to the third Critique, such as those defended by Guyer and Allison. For Kant there leans heavily on a teleological conception of nature, which is a philosophical worldview of which Hume is trenchantly dismissive (THN 1.4.3.10-11). For different reasons, Guyer (2008) concedes that this teleological account cannot offer an epistemological rebuttal to Hume’s worries on induction (p. 219), and ‘begs the question against Hume’s worry’ if it addresses it at all (p. 220). Allison (2008a, p. 154) is similarly pessimistic.

  56. Watkins (2004, p. 485).

  57. Although the Prolegomena, in following an ‘analytic’ method rather than the ‘synthetic’ method of the Critique (not to be confused with the analytic/synthetic distinction), does proceed by assuming the possibility of synthetic a priori propositions (4:263).

  58. See Falkenstein (1998) for a careful response on Hume’s behalf to the argument of the Second Analogy, which argues that his notion of ‘exact scrutiny’ (THN 1.3.12.5) can play the role that Kant requires of the a priori causal rules.

  59. Thanks to Peter Millican for raising this issue in correspondence.

  60. Thanks to Peter Millican for highlighting this worry to me in correspondence. Kantians might respond that for appearances, the metaphysical and epistemological questions are identical: since phenomena are partly constituted by the a priori intuitions and concepts we impose on them, the epistemological question of what we can know a priori about appearances also amounts to the metaphysical question of what necessarily obtains in appearances. And one might also raise an ad hominem point: Hume himself plausibly runs together epistemological and metaphysical questions in his own philosophy, for instance with regard to causation. Here, he seems to proceed from the epistemological claim that all we can know of necessary connection is a subjective impression, via his empiricist Copy Principle, to the metaphysical claim that necessary connection can only be such a thing.

  61. This worry is perhaps most prominently raised in Stroud (1968). I lack the space to discuss this issue here, but for an excellent discussion of this and surrounding issues, see Stern’s collection (Stern 1999b). Stern (1999a) in particular addresses this issue with respect to the Second Analogy, while elsewhere (Stern 2008) does so with respect to the Refutation of Idealism.

  62. The centrality of time to Kant’s argument in the Second (and First) Analogy is emphasised in Melnick (2006, p. 203): ‘Kant’s views on the nature of causation and substance… depend… on what he calls a “third thing”, the pure intuition of time…’. Landy argues that Kant’s arguments on our representations of time are directed at Hume in particular (Landy 2015, Chapter 2).

  63. A similar perspective is adopted in (Stern 2008, p. 273), which argues that transcendental arguments can successfully respond to scepticism independently of the framework of transcendental idealism, although he does concede, with respect to the Refutation of Idealism, that a challenge to the argument might require an appeal to a form of transcendental idealism. Stern (1999a) is also representative of such a stance, this time with respect to the Second Analogy.

  64. For very detailed and helpful comments, thanks are owed to Peter Millican, Don Garrett, Lorne Falkenstein, David Landy, and Thomas Moore. For some searching questions which were invaluable to improving the paper, I am also grateful to a reading group at the National University of Singapore and an audience at the Australian Seminar in Early Modern Philosophy 2017 at the University of Sydney.

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Qu, H. Synthetic a priori judgments and Kant’s response to Hume on induction. Synthese 199, 7131–7157 (2021). https://doi.org/10.1007/s11229-021-03107-6

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