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`Hitherto Hume has been master, only to be refuted in the manner of Diogenes and Dr.Johnson'. So, as we saw in the Introduction, wrote Keynes in 1921 [1]. In the preceding pages, refutations have been offered both of Hume's conclusion about induction and of one of the premisses from which he inferred that conclusion. By their extreme simplicity, as well as some of their other features, these attempted refutations are likely to excite a suspicion that in this book, too, Hume's has been `refuted' only after the manner of Diogenes and Dr.Johnson.
If, however, Keynes meant by that `manner', what he is most likely to have meant by it, this suspicion is certainly false. For Keynes presumably meant to refer to a kind of attempted refutation of philosophical paradoxes, which consists in the (essentially wordless) performance of certain familiar actions. If so, the Johnsonian manner of `refuting' Hume's inductive scepticism would consist, presumably, in one's simply making, or continuing to make, inductive inferences. But it will not require emphasis that that is not what has been done in this book.
Alternatively, `refutation' in the Johnsonian manner might be taken to consist in meeting a philosopher's startling conclusion with a mere emphatic assertion of its falsity. But on this interpretation, too, my attempted refutations are not after the manner of Johnson. For I have not contented myself with asserting, but have endeavored to prove, the falsity of Hume's sceptical conclusion and of his deductivist premiss.
If, again, Johnsonian `refutation' of a philosopher's sceptical theses is taken to consist in the advancing of question-begging arguments against them, then my attempted refutations are still free from the reproach of being Johnsonian. My arguments against deductivism contained no question-begging, even at the only places where they might appear to do so, viz. at the arguments (a) and (d) in Chapter 6 section (iv). For those two arguments, we saw, do not rest on the favorable assessments which it is natural to make of certain inductive inferences, and would not be question-begging even if they did. Then, in von Thun's argument against inductive scepticism, so far from there being any question begged against Hume, the premisses could in fact have been deduced from a thesis which is actually embraced quite clearly by Hume himself (viz. the Regularity premiss (4)).
But the suspicion that my attempted refutations of Hume are in some sense too easy to be effective, will not be easily dispelled. After all, statements of logical probability, even proved ones, are mere `analytic' propositions (as it is often put, and as I have been at pains to emphasize, though in different words). Such insubstantial weapons, it will be thought, cannot inflict much injury on the diamond-hard body of Hume's philosophy of induction.
This thought, however, rests on a fundamental misconception of the nature of Hume's sceptical conclusion, a misconception which it was an essential part of the purpose of Chapters 2--4 to correct. For if it is supposed that proof of mere analytic propositions could not refute Hume's conclusion, that can only be because it is supposed that that conclusion itself is not another proposition of the same kind, but is, rather, a factual one. Yet, that this cannot be so, ought to have been evident both on textual and on philosophical grounds. On textual grounds, because Hume's only argument for his scepticism turns out, on identification, to have been a valid one from premisses none of which are factual. On philosophical grounds, because Hume's sceptical conclusion is certainly universal (it concerns all inductive inferences); and hence it would, if it were also factual, be just one of the propositions (such as `All flames are hot') which it itself says we can have `no reason' to believe.
This point, the non-factual character of Hume's inductive scepticism, is the key to everything else in this book, and in particular to the present question, of the sufficiency of the kind of argument advanced in Chapter 5 for the falsity of that scepticism. If, indeed, Hume's inductive scepticism were a proposition about the relative frequency with which inductive inferences from true premisses have true conclusions, then no proof of a statement of logical probability could be equal to the task of refuting it. But it is not, and could not be, such a proposition. Any argument against it is bound, on the contrary, to be of the same general character as Hume's argument for it, viz. uniformly non-factual throughout. von Thun's argument is such, and even, as it happens, exactly resembles Hume's argument for inductive scepticism, in resting on two judgements of invalidity. (Hume's two are inductive fallibilism (9), and the regularity premiss (4); von Thun's are the judgements of regularity (S1) and (S2) of Chapter 5 section (iii)).
It is especially absurd at the present time to suppose, in effect, that Hume's inductive scepticism is a factual proposition. For, as has been remarked earlier, it is now quite often supposed, as it never was before the twentieth century, that Hume really did prove his sceptical conclusion about induction; which makes the absurdity of the former supposition greater than it would have been before the present century. Yet both suppositions are made, in effect, by some contemporary philosophers, as will shortly be shown. This absurdity issues, moreover, in an attitude to critics of Hume which amounts to one of `Heads Hume wins, tails his critic loses'. For the critic of Hume's inductive scepticism is debarred, on the one hand, from using as his premisses propositions of a general factual kind (concerning the uniformity of nature, say, or the long-run success rate of inductive inferences). He is properly so debarred, because such propositions are not discoverable by experience directly, and if they are inferred from experience, they are unreasonably inferred, unless the falsity of inductive scepticism, which is the very point at issue, is taken for granted. But if, on the other hand, the critic proposes to employ non-factual, analytic propositions, as the premisses of his argument against Hume's inductive scepticism, he finds no better reception, for he is now given to understand that such materials are hopelessly unequal to the task which he wishes them to perform.
The critic of Hume incurs special opprobrium, mixed with condescension, if he proposes to draw those non-factual premisses from the theory of logical probability in particular. For then he has merely added one more to `those numberless critics of [Hume's] ideas who have in the realm of probabilities found an escape from the "scepticism" which he taught' [2]. As one of this host of the damned, who failed to give `the highest possible credit to the philosophical genius of Hume', the critic of Hume even suffers the ultimate mortification of finding himself allied with a mere statesman [3]!
This one-sided attitude to critics of Hume's inductive scepticism, and the absurd interpretation of Hume on which it necessarily rests, were well illustrated by the reception which was accorded by reviewers to D.C.Williams's The Ground of Induction around the middle of this century. A less dispersed example is desirable, however, and Popper furnishes one which is as clear as could be wished.
We saw in Chapter 5 section (i) that there is a certain proposition, the truth of which Popper regards as established by `Hume's criticism of induction' (as well as by his own), and which is simply a special case of what I have identified as being Hume's inductive scepticism (8). This is the statement of logical probability P(Fa, Fb.t) = P(Fa, t).
Now Popper tells us, concerning this comparative equality, that `every other assumption'---and hence, for example, the natural assessment expressed in the contrary P(Fa, Fb.t) > P(Fa, t)---`would amount to [...] postulating that there is something like a causal connection' [4] between individuals. To assert that Hume's conclusion is false, in other words, would be to assert a certain `non-logical, synthetic' proposition, of the nature of a `natural law' [5].
Yet it should be evident that, on the contrary, the inequality P(Fa, Fb.t) > P(Fa, t), is actually a proposition of the same kind as the contrary Humean equality P(Fa, Fb.t) = P(Fa, t). Both are simply statements of logical probability. Nor is there any way in which the comparative equality could be proved to be true, distinct from the (ultimately intuitive) way in which the contrary inequality could be proved to be true. In short, the difference between `=' and `>', which is the only difference between the above two statements, cannot mark a difference between a non-factual and a factual proposition. What Popper ought to hold, therefore, in order to be consistent with the remarks quoted above, is that the great inductive sceptic established---that is, that Hume's inductive scepticism itself is---an immense factual generalization!
This, however, besides having the effect, which is felt to be intolerable, of placing Hume's thesis on a par with those of his critics, would be too obvious an absurdity to be enunciated distinctly. The only alternative is therefore to adopt the lesser absurdity, and the one-sided attitude to Hume's critics, which were described above. Accordingly Hume's inductive scepticism is recognized by Popper as being a statement of logical probability, but its denial, on the other hand, although it too is a statement of logical probability, must perforce be represented as being a temerarious assertion about the nature of the actual universe! Hume's `P(Fa, Fb.t) = P(Fa, t)' is represented as derivable, and as actually derived by Hume (as indeed it was), from premisses purely a priori. But its falsity, on the other hand, is represented as being a proposition of a kind which mere statements of logical probability certainly are utterly incapable of proving.
It should be clear that we are dealing here with an expression of that over-estimation, almost apotheosis, of Hume, which has taken place in the present century, and of which some other expressions are collected below in the Appendix section (iii). To correct that over-estimation, and to set in its proper light the corresponding condescension towards Hume's critics which was illustrated above from von Wright, there is just one fact which it is sufficient, but also necessary, to remember. This is, that it is `in the realm of probabilities' and nowhere else, that Hume's inductive scepticism, no less than what its critics advance, itself belongs.
It will hardly require emphasis that this book does not pretend to make any contribution to the theory of logical probability. On the contrary, the fragments of that theory which I have made use of are so few, and so elementary, that they are certain to appear derisory to the working `inductive logician' in the Carnapian sense. I am content that they should appear so, since they are so.
In order, however, to prevent a misapprehension of the opposite kind, about what is attempted in the preceding pages, it may be necessary here to emphasize, to the majority of philosophers who are not inductive logicians, a point which was made at length in Chapter 1 section (v). For most contemporary philosophers are perhaps likely to feel that even such little technical apparatus as I have employed is necessarily out of place in considering philosophical questions, or at any rate in criticizing a philosopher of the eighteenth century. But the theory of logical probability, if what I have said in Chapter 1 section (v) is true, is not what it may appear to be, a branch of non-standard logic which is the business of no one outside a handful of twentieth-century adepts. It is the theory of the degree of conclusiveness of arguments, and assessments of the degree of conclusiveness of arguments is a prominent part of the business of all philosophers at any time. What Hume, in particular, wrote about inductive inference cannot be considered exempt from criticisms aimed at it from the point of view of `inductive logic' in the Carnapian sense. For despite its lack of technical trappings, Hume's philosophy of induction is not less, though it is not more either, than a rival system of `inductive logic' to Carnap's. I have merely tried to show, without going outside the range of arguments by which such competing systems must be evaluated, that the verdict in this case must be in favor of Carnap.
There is a feeling which is fairly widespread among philosophers, and certainly more widely current than outright acceptance of Hume's inductive scepticism, that that thesis is some philosophical essence so refined as to be irrefutable, and that even to try to refute it is a mark of bad taste in philosophy. This feeling can subsist only so long as one stays at a safe distance from the text of Hume, and leaves the nature the nature and content of his sceptical thesis correspondingly indefinite. But such an over-readiness to credit inductive scepticism with irrefutability is something which we ought perhaps to expect, on general psychological grounds, after science, and intellectual culture generally, have suffered so deep a shock as they did near the beginning of this century. In such circumstances, as I have said in Chapter 8, inductive fallibilism, at the least, is bound to be embraced. But to some minds, the irrefutability, even if not the truth, of inductive scepticism will suggest itself as being a still better insurance against any repetition of such a shock. Much of the philosophy of science of the present century, indeed, appears to be psychologically intelligible only from this point of view; just as much of the philosophy of science of the preceding century is psychologically intelligible only in the light of the Newtonian over-confidence then prevailing.
It may be useful, finally, to draw attention again to the limitedness of what is aimed at in the critical part of this book. I have not attempted to justify induction, or (what perhaps would be the same thing) to refute every possible inductive scepticism. I have attempted to refute just Hume's inductive scepticism, and one of the premisses on which his sole argument for it rests.
[1] See Introduction, p.2 above.
[2] This and the following quotation are from G.H.von Wright, The Logical Problem of Induction (2nd revised edn.), p.153.
[3] Jan Masaryk, author of David Hume's Skepsis und die Wahrscheinlichkeitsrechnung. See on von Wright, op. cit. p.220 n.1.
[4] The Logic of Scientific Discovery (London, 1959), p.367. (Here `casual' is an obvious misprint for `causal'). The next phrase quoted is from p.368.
[5] K.R.Popper, Conjectures and Refutations (London, 1963), p.290.
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