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If there is anything about this argument of Hume which is more admirable than its content, it is the explicitness of it. Almost always, the main obstacle to the evaluation of an argument, and often an insuperable obstacle, is the difficulty of identifying it---of finding out what the argument actually is. How seldom when men argue, in philosophy or elsewhere, can one confidently draw up the structure-diagram and dictionary of their arguments! In the case of Hume's argument for predictive-inductive scepticism, however, one can do so. One can even, as we have seen, substitute for Hume's phraseology at the places where it could nowadays be misleading, other phrases which one can be confident express his meaning.
Admirably explicit as it is, Hume's argument is yet not entirely explicit. Philosophers almost always (even if they happen to be discussing invalid arguments), intend their own arguments to be valid ones, and in this respect Hume was no exception. He certainly was not advancing, for his sceptical conclusion about certain `probable arguments' in his sense, an argument which he regarded as merely a probable one in our sense; that is, an argument of less than the highest possible degree of conclusiveness! Yet it is obvious that his argument is not valid as it stands, either in stage 1 or stage 2. Hume has suppressed, as being too obvious to require expression, certain propositions which are nevertheless necessary for the validity of his argument. One of these will be pointed out in the next paragraph, and a second, less obvious one, in section (iii) below.
In stage 2, Hume appears to infer (g), `The Resemblance Thesis cannot be validly inferred from necessarily true premisses', from (f) alone, i.e. from `The Resemblance Thesis is a contingent proposition'. But if a man, intending his argument to be valid, infers the former proposition apparently solely from the latter, we are entitled to conclude that his stated premiss is not really his only one. He must be assuming, in addition, that no contingent proposition can be validly inferred from necessarily true premisses. This proposition therefore, is a suppressed premiss which we must ascribe to Hume's argument for predictive-inductive scepticism. It may be alternatively but equivalently phrased as: `All arguments from necessarily true premisses to contingent conclusions are invalid'. In the language of Hume, of course, this suppressed premiss would be, `There can be no demonstrative arguments for a matter of fact': a proposition which we know (cf. note 16, Chapter 2 below) that Hume not only believed, but often asserted.
For the conclusion (j), then, Hume's argument has just three premisses which we have noticed so far: the two premisses he stated, (e) and (f), and the unstated one just mentioned. It will prove profitable to ask at this point, how far these premisses, unaided by any other assumptions, go towards establishing the sceptical conclusion which Hume drew (that predictive-inductive inferences are unreasonable). What is the most that these premisses entail about the predictive-inductive inference?
I do not know of any mechanical way of answering this question, but intuitively it is not difficult to answer. What (e), (f), and the first suppressed premiss really do entail about predictive-inductive inferences, but also all that they entail, is the following proposition. `All predictive-inductive inferences are invalid as they stand; and in order to turn them into valid inferences, it is necessary to add to their premisses a proposition which cannot be validly inferred from necessarily true premisses, and which cannot be validly inferred, either, from observational premisses, without such an addition to them as would make that inference circular'.
This is a proposition of considerable complexity. Fortunately it is possible to reduce it to much more manageable proportions, if we break it up into its three natural clauses, and consider each of these in turn.
It can hardly be supposed that the phrase, `as they stand', adds anything to the content of the first clause. That clause, therefore, reduces simply to `All predictive-inductive inferences are invalid'.
Now, given this, the second clause above is redundant, and can simply be omitted. For a proposition can be validly inferred from necessary truths if and only if it is itself a necessary truth. Thus the second clause merely says that the addition to their premisses which is necessary to turn predictive-inductive inferences into valid ones, is not a necessary truth. But this follows from their being invalid inferences (to contingent conclusions) in the first place.
Now as to the third clause. What can be validly inferred from observational premisses, without such an addition to them as would make an inference to the Resemblance Thesis circular, is just what can be validly inferred from observational premisses alone. Now every proposition which can be validly inferred from observational premisses alone is itself either an observation-statement or a necessary truth; and every observation-statement or necessary truth can be validly inferred from observational premisses alone. Consequently, the third clause of the proposition above merely says that the proposition which needs to be added to the premisses of predictive-inductive inferences in order to make them valid, is not either an observation-statement or a necessary truth. The second disjunct here is redundant, and can simply be omitted, for the same reason that the whole of the second clause was. Then the third clause just says that the additional premiss needed to make predictive-inductive inferences valid is not observational. Or contrapositively, that the addition of any observational premiss to a predictive-inductive inference is insufficient to make it valid.
Thus the whole proposition stated above reduces to this: that all predictive-inductive inferences are invalid, and that all the inferences, which result from supplementing the premisses of a predictive-inductive inference by further observational premisses, are also invalid.
This proposition, as distinct from Hume's scepticism (j), which says that predictive-inductive inferences are all unreasonable, I will refer to as Hume's predictive-inductive `fallibilism'. For it is only a judgement of invalidity, though of course a very general one. It says, of the predictive-inductive inference and certain others, no more than that it is possible for them to have true premisses and false conclusions. And since this proposition really does follow from Hume's premisses (e), (f), and the suppressed premiss noticed in the preceding section, I will sometimes refer to it as the fallibilist consequence, as distinct from the sceptical conclusion (j), of his argument.
The thesis of predictive-inductive fallibilism will perhaps appear trivial. It is sure to appear so, and indeed to be so, if the reader, forgetting that `inductive' is being used here in a purely descriptive sense, were to take as part of the meaning of calling an argument `inductive', that that argument is invalid. In fact, however, as will be shown in Chapters 7 and 8 below, the fallibilist thesis is very far from being trivial.
At any rate it is, I affirm, the most that follows about the predictive-inductive inference from Hume's stated premisses, in conjunction with the unstated one noticed above.
This claim meets with some interesting confirmations from Hume himself. For occasionally he writes as though his conclusion were only the fallibilist one. For example, when he represents his conclusion as being just that `nothing leads us to this inference [i.e. the predictive-inductive inference] but custom or a certain instinct of our nature; which it is indeed difficult to resist, but which, like other instincts, may be fallacious and deceitful' [1]. On another occasion he writes similarly, of the `Sceptick', that `all he means [...] is to abate the pride of mere human reasoners, by showing them, that even with regard to principles which seem clearest, and which they are necessitated from the strongest instincts of nature to embrace, they are not able to obtain a full consistence and absolute certainty' [2].
The second of these quotations can weigh very little with us, when we recall the occasion of the pamphlet from which it is taken. For the Letter from a Gentleman was of course a desperate attempt by Hume to prevent public criticism of the `scepticism' of the Treatise from prejudicing his candidature for a chair at Edinburgh University. In such passages, in fact, as is admitted even by the most sympathetic of Hume's biographers and editors (Professor Mossner), the pamphlet is not easily freed from the suspicion of being actually `disingenuous' [3].
Nor can occasional fallibilist versions of Hume's conclusion, such as the first passage quoted above, count for much. For they have to be set against all of the many passages in which Hume expresses his conclusion as being that knowledge of the premisses of a predictive-inductive inference gives us (not just a logically insufficient reason but) no reason, no more reason than we had prior to all experience, for believing the conclusion.
The conclusion, then, which Hume drew in stage 2, is rightly represented as being the sceptical one, that all predictive-inductive inferences are unreasonable. If what was said in the preceding section was correct, however, the most that follows about predictive-inductive inferences from the premisses which we have so far ascribed to Hume, is the fallibilist consequence, that predictive-inductive inferences are all invalid. Now the former proposition certainly does not follow from the latter. Hume, however, as has been said earlier in this chapter, undoubtedly intended his argument to be a valid one. We must, therefore, ascribe to Hume the additional premiss which is needed to make this inference, from predictive-inductive fallibilism to predictive-inductive scepticism, valid. That is the thesis that all invalid arguments are unreasonable. I will refer to this, for obvious reasons, as the thesis of `deductivism'. It is the second suppressed premiss which is needed to make Hume's argument to his sceptical conclusion valid.
Most fortunately, it is possible to verify independently the necessity of ascribing this thesis to Hume. For consider stage 1 of his argument. Here Hume draws, concerning the a priori inference, the same conclusion in (d) as he draws later in (j) concerning the predictive-inductive inference, viz. that it is unreasonable. But the only stated premisses of stage 1, viz. (a) and (b), clearly entail no more than this, that all a priori inferences are such that it is possible for them to have true premisses and false conclusions; that is, that they are all invalid. Yet Hume certainly concluded that they are unreasonable. He must, therefore, have assumed in stage 1 of his argument, as well as in stage 2, though he did not state, that all invalid inferences are unreasonable. (My attribution to Hume of deductivism as a suppressed premiss in stage 2 rested on my reduction of the fallibilist consequence to manageable proportions. Consequently the present discovery of deductivism as a suppressed premiss elsewhere in his argument constitutes a confirmation of the correctness of that reduction).
Hume's argument in stage 2 may therefore be summed up in the following way: from premisses which prove at most the invalidity of predictive-inductive inferences, along with the unstated premiss that an inference is unreasonable if it is invalid, Hume concluded that predictive-inductive inferences are unreasonable.
It is, of course, only in its detail that this account of Hume's argument differs from that which has been given by many other writers. That the conclusion Hume drew about inductive inferences was a sceptical one; that he had a `rationalistic' (i.e. deductivist) conception of what inferences `reason' can sanction; and that his great positive contribution was a certain thesis of non-deducibility (i.e. invalidity)---these three things may be said to be nearly common property among philosophers [4]. Vague as they are, each of them is absolutely correct, if my account of Hume's argument is correct. Their wide currency, therefore, is some confirmation of the more detailed account of that argument which I have given.
[1] Enquiry, p.159. My italics.
[2] A Letter from a Gentleman to his Friend in Edinburgh (ed. Mossner and Price, Edinburgh, 1967), p.19 of the facsimile of Hume's pamphlet of 1745. My italics. This pamphlet swarms with printing errors, and the general sense of the passage quoted suggests that the printer may have mistaken the word `confidence' in Hume's handwriting for `consistence'. The calligraphy of 1745 would have made just such a mistake especially easy.
[3] Ibid., p.xxiv of the editors' introduction.
[4] (Footnote added in June 1972). Much more than this, however, is common to the account which up to this point I have given of Hume's argument and an account of it which was given by the late Professor Dickinson S.Miller in an article in The Journal of Philosophy, vol.46, 1949, esp. p.745. For the essence of Hume's argument is there represented as being from (what I call) inductive fallibilism to inductive scepticism via the suppressed premiss that `all rational inference is deductive'; which premiss the author even calls the thesis of `deductivism'!
Between Miller's treatment and mine there is, indeed, this important difference, that I believed necessary to justify the attribution of the above argument to Hume, whereas Miller apparently did not. Accordingly I have here devoted two whole chapters of a basically textual nature to this end, whereas Miller devotes not one word. He does not, in support of his attribution of the argument to Hume, refer even once to Hume's text. He simply makes the attribution, in the first few lines of his article, and then plunges straight into the philosophy of the matter.
Nevertheless, between the argument which Miller attributed to Hume, and the argument I attribute to Hume, the similarity is strikingly complete: so complete, indeed, that it cannot be unnecessary for me to state that I arrived at my account independently of Miller's. In fact I read Miller's article for the first time on 6 June 1972; more than a year, that is, after finishing the text of this book, and more than two years after publishing (in my article `Deductivism', Australasian Journal of Philosophy, vol.48, May 1970) an account of Hume's argument which is in most respects the same as I have given here.
In the discussion (published and unpublished) which followed the article of mine just referred to, no one pointed out its similarity to the starting-point of Miller's article. This now seems surprising, but the explanation must be, I think, that his article had been overlooked, however undeservedly, not only by me but by almost everyone else. I cannot remember ever having seen, before I read it, a reference to it in a philosophical journal. I learnt of its existence only from the valuable complication by Roland Hall, `A Hume Bibliography' (York, 1971).
That my account of Hume's argument should be essentially the same as that arrived at independently by another philosopher is some additional reason for thinking it a true account. But there is also a second respect in which Miller's article is confirmatory of propositions I had advanced. For it is entitled `Hume's Deathblow to Deductivism', and according to Miller the philosophical value of Hume's argument lies in its being, not a proof of its sceptical conclusion, but an unintended reductio ad absurdum of its deductivist premiss. Now that is the very turn of thought in relation to Hume's argument, which I have said in Chapter 8 section (ii) of this book was characteristic of the first half of the present century. Miller's article (or rather its first page) is thus an especially striking, because unusually explicit, confirmation of what I said there.
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