John Stuart Mill, Determinism, and the Problem of Induction

Abstract Auguste Comte's doctrine of the three phases through which sciences pass (the theological, the metaphysical, and the positive) allows us to explain what John Stuart Mill was attempting in his magnum opus, the System of Logic: namely, to move the science of logic to its terminal and 'positive' stage. Both Mill's startling account of deduction and his unremarked solution to the Humean problem of induction eliminate the notions of necessity or force—in this case, the 'logical must'—characteristic of a science's metaphysical stage. Mill's treatment had a further surprising payoff: his solution to the Problem of Necessity (what today we call the problem of determinism and freedom of the will). Notes 1Skorupski Citation1989: 170]; Scarre not only states but argues for his view 'that Mill took up no position at all on Hume's problem of induction'[2002: 32], and I will discuss his grounds below. 2[I:175, 177/A 5:18]. References to Mill's work by volume and page in the standard edition of Mill's works [1967–1989]; the Autobiography and the System of Logic will be given slashed cites, with A chapter:paragraph and book:chapter:section, respectively, following the uniform citation. Those who do discuss Mill's views on freedom of the will are not always sympathetic. For instance, Carlisle complains that Mill 'would not recognize that a verbal feint does not resolve the conflicting claims of freedom and necessity'[1991: 294]. 3See, e.g., [Green Citation1968. 4Examples of attention to Hume generally are easy enough to come by. In the Autobiography, in the course of describing his formative intellectual influences, Mill takes time out to mention Hume's Essays and History of England[I:11, 71/A 1:5, 3:4]; he later both quotes and complains about the History[XX:47; 19, 135f, 221]. The System of Logic contains a discussion of Hume's treatment of miracles, and of the literature it generated [VII:622–626, 630f/III.xxv.2, 4]; Mill refers to Hume's terminology of ideas and impressions at [VIII:852/VI.iv.3]. But there are also indications of attention to Hume's views about causation and induction specifically. Mill approvingly mentions 'Hume's and Brown's analysis of Cause and Effect'[VIII:838/VI.ii.2]—an analysis hardly distinguishable from Hume's formulation of the Problem of Induction. Or again, Mill suggests that the positivist treatment of causation 'was probably first conceived in its entire generality by Hume, who carries it a step further than Comte'[X:266]. And James Mill's Analysis (about which more below; the younger Mill was quite familiar with it) contains a page-long recapitulation of Hume's analysis of causation [1869: vol. 2, 328f]. 5[VII:184/II.iii.2]; notice how different Mill's understanding of the major premise is from our contemporary take on it: in the inference, (x)(Mx⊃Dx), Mw, so Dw, the conditional can be understood to be vacuously true. (I'm grateful to Josh MacLeod for discussion on this point.) Notice also that Mill has substituted the Duke of Wellington (that is, a then-living person) for Socrates, who appears in the more standard recitations of the exemplary syllogism, but who was long dead. This marks Mill's understanding of the point of inference, which is to make predictions about the unobserved, paradigmatically about the future. 6[VII:186f/II.iii.3], or again, [VII:201/II.iii.6]. A natural response to Mill's complaint, nowadays, would be to reiterate the distinction between soundness and validity: whether the syllogism is valid does not depend on whether it can be known to be sound. While Mill is quite aware of this distinction [e.g., IX:354, 367], on exhibit here is a view of logic as giving guidelines for reasoning; on such a view, usability is a paramount consideration, and categories of, by our lights, would-be valid-but-unusable inference are being stripped of the honorific title. 7Mill summarizes his treatment in the System of Logic in a footnote to his edition of the Analysis[1869: vol. I, 427]: 'I have maintained … that Ratiocination does not consist of Syllogisms; that the Syllogism is not the analysis of what the mind does in reasoning, but merely a useful formula into which it can translate its reasonings, gaining thereby a great increase in the security for their correctness.' A couple of tangential points: First, if syllogisms are data extraction devices, we might wonder how Mill knows that they extract the information stored in a major premise reliably. Mill does not seem to have considered this question explicitly, but there is only one answer he could have given: we have a great deal of experience with syllogisms, and we have learned, inductively, that they are entirely reliable in this regard. Second, we might also wonder about plain old modus ponens, which does not require the quantificational apparatus built into the syllogistic, and of which the Stoics, for instance, were already aware. (I'm grateful to Lanier Anderson for raising this question.) Is a modus ponens not really an inference, either? Again, Mill does not discuss the question, but it is clear what his answer to it would have to be. How do we come to know the conditional premise, p⊃q , of a modus ponens? Not in the way suggested by its semantics: p⊃q is true when p is false or q is true, but if you already know that q is true, then you do not need the modus ponens, and if you already know that p is false, you cannot use the modus ponens. Evidently, you come to know that p⊃q by, say, observing previous p-like circumstances followed by previous q-like circumstances. That is, once again, the major premise of a bit of deductive reasoning records and encodes observations of particulars, and these are the real premises of the reasoning in which a modus ponens is invoked. 8At [VII:307/III.iii.1], [VII:308/III.iii.1], and [VII:572/III.xxi.4]; however, for a later complication, see [IX:482n]. 9There is a delicate question, which I do not want to take up here, as to how uniformly apriorist Church of England apologetics actually were, and as to whether the apologists would have agreed with Mill's classification of their arguments as apriorist. But I think this characterization of Mill's motivations survives the complications the question introduces. 10The idea that arithmetic and logic are empirical sciences is generally regarded as, well, daffy, but it's important not to be dismissive. Notice that a very interesting change has happened when it comes to geometry. When Mill argued that geometry was an empirical science, he sounded just as daffy as when he argued for the same conclusion about logic and arithmetic. But that geometry is an empirical science is now the received wisdom. 11Is this a coherent endpoint? Ravetz Citation1979: 205] complains, of Mach's very similar proposal, that 'banishing the concept of "force" from mechanics as an anthropomorphic relic leaves the field of statics as "the science of nonexistent motions".' Moreover, it's actually an interesting question whether Millian psychology lives up to positivist standards, given the role that 'intensity' (or forcefulness or vividness) of sensations and ideas plays in it. However, I won't pursue these questions here. See also the related discussion of metaphysical accounts of volition at [VII:353ff/III.v.11], especially from the last paragraph of the lengthy quote from Reid [358]. 12Perhaps Malebranchian occasionalism was a more recent relative of this sort of picture; possibly a view ascribed to Descartes by Florka Citation2001: esp. 67, 90, 105f, 107, 116f], on which God has chosen the metaphysical structure of the world, and is thereby responsible for the laws of logic, can also give us some of the flavour of this Comtean stage. 13This is an adaptation of an example due to Jenann Ismael. Let me add a reservation to my earlier agreement that we are still stuck at the metaphysical stage of logic: Mill's positivist aspirations for logic suit a natural way of looking at model theory. So perhaps we have, after all, come a good way along the path that Mill pointed out. 14In the Autobiography, Mill states that his 'theory of Induction was substantially completed before [he] knew of Comte's book', but acknowledges that he 'gained much from Comte, with which to enrich [his] chapters in the subsequent rewriting'[I:217/A 6:14]; later he reiterates that 'much matter derived from Comte' was subsequently 'introduced into the book in the course of the rewriting'[I:231/A 7:3]. In the note to A 7:1 [I:255], Mill returns to the subject of his intellectual debt to Comte, this time insisting once again that 'the first volume [of the Logic], which contains all the fundamental doctrines of the book, was substantially complete before [he] had seen Comte's treatise … it is only in the concluding Book, on the Logic of Moral Sciences, that [he] owe[s] to him any radical improvement in [his] conception of the application of logical methods'. I'm not interested in taking up questions of priority, or of timing and extent of influence: what matters for present purposes is how repeatedly Mill felt that he needed to address the question of what he owed to Comte. His defensiveness confirms how much overlap he took their views to exhibit. 15For a reconstruction of Hume's arguments on the relevant points, see [Millgram Citation2005: ch. 7]. 16I suspect that Mill is also implicitly addressing an objection to his view. For expository convenience I'll put the complaint anachronistically: that logic, the science of (correct) reasoning, is, as now gets said, 'normative', and that therefore it must be a priori, and cannot be, as Mill insisted, an empirical and inductive science. The rarely articulated premise that makes the objection seem inevitable is that the normative has to be a priori. (Anderson Citation2005 points out that this was a widely shared view in the nineteenth century; it is probably scarcely less widely shared today.) My speculation here is that Mill's diagnosis follows Hume's: like other necessities, deontic necessities (shoulds, oughts, and so on) can't be observed, and so they can't be arrived at on the basis of observation, i.e., empirically; if, somehow, you have come to know a statement whose content includes normative force of some kind or another, then you must have come to know it some other way, that is, a priori. Mill's parrying move—parrying because a positive account of the content of a 'should' or 'ought' is still missing—is to remind you that if there are no necessities, and no deontic necessities either, then there need be nothing to know that you cannot come to know empirically. 17[Scarre Citation2002; citations in the running text. Scarre's treatment also appears at [Scarre Citation1989: ch. 4]. Undated references here are to the former. 18This is evidently the point of the remark that 'there was nowhere a lively interest in Hume's treatment of induction before the Green and Grose edition of Hume's works in 1874'[32], as well as of the appendix to the paper supporting Scarre's claim that 'the problem was simply not one of those in the philosophical air when Mill wrote'[46f]. 19These include what we now think of as the New Riddle of Induction (that is, the question of which inductions are the reasonable ones), with which Mill was indeed very concerned [33], or the battle against apriorism, which we mentioned above [38f, 41], or the explanation of why we require very different quantities of evidence in order to proceed with inductions in different domains [37]. 20[X:210f/U 2:4–5]. A related difficulty with Scarre's various claims that in some passage or another Mill is worried about other things, and so not about Hume's Problem of Induction, is a lack of sensitivity to the psychologistic register in which nineteenth-century philosophical debates were conducted. Scarre repeatedly marks the psychologistic formulation of a point of Mill's, and, contrasting it with the antipsychologistic formulation we have been taught to give of Hume's arguments, concludes that Mill is making an irrelevant point (rather than a relevant point in a psychologistic accent). (E.g., 'it was not that Hume's discussions … were unknown … but rather that they were seen as posing a primarily psychological question about the mental processes at work in inductive thinking'[46]; compare the description of Kant as taking 'the main point at issue to be that of the origin of the conception of causation … it is not clear [Scarre tells us] whether Kant fully grasped the fact that Hume was contending that inductive arguments were, strictly, without justification'[1989: 102].) 21E.g., 'this reading would only be a likely one if we were able to ignore Mill's obliviousness of the problem of justifying induction that we find everywhere else in the Logic'[45]. 22Compare Scarre's remarks on 'Mill's … insensitivity to Hume's problem'[36], on Mill's lack of 'awareness of the Humean grounds for scepticism about induction'[38], and Mill's failure 'to see that it may be questioned whether inductive inference is in principle trustworthy'[41]. 23The quoted phrases are from pages 33 and 41; elsewhere Scarre rehearses the standard objection that inductive justifications of induction are circular [36]; he describes Mill as 'a classic case of a man who did not put two and two together'[41]. 24Once we have got past that misunderstanding, of course there is, Mill thought, the philosophical problem of understanding how inductions work, and which ones are successful. His investigation of the topic is still taught today in informal logic classes, under the heading of 'Mill's Four Methods'. 25At one point [45], Scarre comes very, very close to capturing Mill's first response, but he dismisses the train of thought as something that 'might well have convinced Mill that he could solve Hume's problem, had that problem occurred to him'. He follows his discussion with the condescending remark that, 'sadly, of course, it is Mill's view of reasoning, not Hume's, that is defective'. The thought behind that latter remark is likely responsible, by way of the misapplied Principle of Charity, for the former. 26E.g., [Quine Citation1986: 86], and here is a remark from a criticism of Boolos's that captures the spirit of such debates [Boolos Citation1975: 514]: 'Quine has stressed the discontinuities between first- and second-order logic so emphatically that the obvious and striking continuities may be forgotten.' 27See [Priest Citation2004, Priest and Tanaka 2007]. 28Notice that this would not be a satisfactory way of handling a coherentist opponent: what to others looks like vicious circularity can look, to a coherentist, like coherence. That is, the means of sidestepping this problem will vary greatly with just where in the dialectical terrain one is. 29[Mill Citation1869; for the Laws of Association, see ch. 3; quick reviews of some of them can be found at [VIII:852/VI.iv.3] and [IX:177f]. As before, there is no question of our adopting Mill's views; associationism is a defunct research programme. But, as before, that does not mean that we cannot learn a great deal from revisiting Mill. 30[VIII:839/VI.ii.3]; compare [I:177/A 5:18]: 'I perceived, that the word Necessity, as a name for the doctrine of Cause and Effect applied to human action, carried with it a misleading association; and that this association was the operative force in the depressing and paralysing influence which I had experienced'. (Notice that what is involved in the association is said to be the word or the term; perhaps this is meant to allow us to bypass the tricky question of what Mill understood the content of the idea of necessity to be.) Two points are worth emphasizing: First, Mill is quite aware of the standard rendering of the problem of freedom of the will; see, for instance, his discussion of Sir William Hamilton's views on the topic at [IX:437–69] (and n.b. the pointer to his own take on it at 439n). Second, the explanation of the depressing aspect of determinism cannot be complete as it stands. As a matter of psychological fact, necessity is as much associated with logical or mathematical proofs, which no one finds depressing, as it is with the predictability that preoccupies theorists of freedom of the will, and so Mill still owes an explanation for why the further and painful associations arise only in the latter case. 31[VIII:841–843/VI.ii.3–4]; Dickens's Hard Times[1981] captures the popular impression of Mill (in the person of Louisa Gradgrind); notice the dedication to Thomas Carlyle, a former friend of the Mills', and Dickens's informant. (I'm grateful to Stephen Menn for pointing out this connection.) Mill acknowledged the popular impression of him 'as a "made" or manufactured man, having a certain impress of opinion stamped on me which I could only reproduce'[I:163/A 5:12]; compare his description of his teenage self 'as a mere reasoning machine'[I:111/A 4:13]. Alan Ryan, in his capacity as guest editor of a volume of the Collected Works, tersely sums up this widely shared understanding of Mill's concern: 'In his youth, Mill had obviously been very vulnerable to the accusation that his character had been made for him, and not by him, and that he was an artefact of James Mill's designing'[IX:lxii]. 32For a very perceptive rendering of the relations between father and son, see [Carlisle 1981: chs. 1–2, and on this point, esp. page 70]. 33I'm grateful to audiences at HOPOS 2006, the University of Konstanz, the University of London, the University of Alberta, Brigham Young University and the Institute of Advanced Study at Hebrew University for helpful discussion, and to Steve Buckle, Ben Crowe, David Schmidtz, Dana Nelkin and John Skorupski for comments on an earlier draft.

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