[ Acknowledgements | Introduction | Part One | Part Two | Part Three | Appendix ]
Hume certainly thought of himself as having advanced, about inductive inferences, some proposition of a sceptical kind; of a kind, that is, which is shocking to common beliefs, and unfavorable to men's pretensions to knowledge. Nearly all of Hume's readers must also have thought that he did so. I shall therefore take this point as granted. It is safe to assume, further, that Hume did not merely assert this sceptical thesis about induction, but argued for it. The question in this Part of the book is, what was his argument?
It would be idle, of course, to try to answer this question by looking in Hume's writings for an argument for `inductive scepticism' eo nomine. Hume does, indeed, have much to say about different kinds of scepticism, though only one of these kinds will concern us. But he does not use the words `inductive' or `induction' [1]. Where we would find it natural to employ the adjective `inductive', Hume speaks of arguments, or inferences, or reasoning(s) `from experience' [2]; or `from causes or effects' [3]; or even `concerning matter of fact' [4]. The arguments which he discusses under these headings, however, are all (with one possible exception) [5], ones which we would call inductive.
Arguments from experience are, of course, the central topic of Hume's philosophy `of the understanding'. But, it should be observed, Hume never discusses all kinds of inductive arguments together, as a class. Instead, he breaks up this class of arguments into a number of different `species of reasoning' [6], and discusses each `species' separately. And he devotes to just one of these special classes of arguments from experience more attention than he does to all the rest combined.
That one is the kind of reasoning which Hume called `the inference from the impression to the idea' [7], `when' (or `after') `we have had experience'---a `long, uniform' [8] experience---of the conjunction of one observable property with another. The following example, which is based on one of Hume's, will serve us as a paradigm of the class of arguments which he treats under this heading. `This is a flame, and all of the many flames observed in the past have been hot, so, this is hot'. The first part of the premiss here corresponds, of course, to Hume's `impression'; the second part, to a long uniform `experience'; the conclusion, to Hume's `idea'. It would be intolerably cumbrous if I were to continue to refer to arguments of this kind as `inferences from the impression to the idea, when we have had experience'. Instead I will call them `predictive-inductive' inferences. Predictive-inductive inferences, then, constitute that `species of reasoning' which occupied Hume's attention in the greater part of Book I Part III of the Treatise; in the central sections iv and v of the Enquiry; and in the Abstract.
This is also the only kind of inductive inference concerning which Hume ever advanced a clear argument which ends in a sceptical conclusion. For, on the other hand, Hume never discusses explicitly (what it sometimes seems to be thought he discussed exclusively) universal-inductive inferences: the class of inferences, that is, of which `All of the many flames observed in the past have been hot, so, all flames are hot' will serve us as a paradigm. And on the other hand, the other kinds of arguments from experience which he does discuss are treated by Hume at any length only in sections xi--xiii of the Treatise Book I Part III: three sections which have been very much neglected by students of Hume, and on the whole, in view of their defects, justly neglected. In this book, consideration of these sections is relegated to the Appendix. This is the more justified, in that Hume says quite clearly that he has no fresh argument to offer, concerning the kinds of inference considered in those sections, beyond what he has already advanced concerning the predictive-inductive inference [9].
Thus it is not about all inductive inferences, but only predictive-inductive ones, that there exists an argument in Hume which is explicit and clear, and which ends in a sceptical conclusion. What we must first attend to, therefore, is his argument for the limited conclusion which we may call `predictive-inductive scepticism'. For this conclusion Hume certainly does advance a clear argument in the Treatise, and one which, at least by the time he wrote the Abstract, he realized was `the chief argument of that book' [10]; as it was also to be of the first Enquiry. It is this argument which will occupy us throughout this chapter and the next, and, in a generalized form, for the rest of this book.
But Hume's argument for scepticism about predictive-inductive inference was never presented by him as a free-standing one. It was, in fact, always presented as one stage, the second, of a longer argument. The first stage of this longer argument has as its subject-matter a different kind of inference. This is what Hume calls, by way of contrast with the subject of the second stage, `the inference from the impression to the idea', `before we have had' (or `without', or `independent of') `experience'. That is, taking the `experience' (of the conjunction of heat with flame) out of the premiss of the predictive-inductive inference, the class of inferences of which `This is a flame, so, this is hot' will serve as a paradigm. I will call such inferences `a priori' inferences. It will prove to be very important for an understanding of the second stage of the longer argument, i.e. of Hume's argument for predictive-inductive scepticism, that we should take into account this earlier stage of his argument, concerning a priori inferences.
This two-stage argument is the central feature of Hume's philosophy of the understanding, and is to be found fully-fledged at the following places in the texts. In the Abstract, stage 1 of the argument, about the a priori inference, begins at the foot of p.292; stage 2 of the argument, about the predictive-inductive inference, begins with the new paragraph just below the middle of p.293; and the whole argument ends with the second-last paragraph of p.294. In the Enquiry the relevant section is iv, `Sceptical Doubts concerning the Operations of the Understanding'. Part I of this section is an extended presentation of stage 1 of the argument; Part II of the section is an equally extended presentation of stage 2 of the argument. The essential substance of Hume's argument about the predictive-inductive inference (i.e. stage 2) runs from near the top of p.35 to near the top of p.36. But the sceptical conclusion of stage 2 is not explicitly drawn in the Enquiry until the next section v, `Sceptical Solution to these Doubts', pp.42--3. In the Treatise the relevant sections are Book I Part III sections ii--viii, especially vi, `Of the inference from the impression to the idea'. Here stage 1, concerning a priori inference, is dispatched in the first paragraph of the section. Stage 2, concerning predictive-inductive inference, begins with the second paragraph, p.87; is resumed with the new paragraph at the foot of p.88; and is essentially concluded with the second paragraph of p.90.
The account of Hume's argument which I give below is, as it were, a composite photograph of all these different versions. The version in the Abstract is in most respects the best, however, and it is that to which my account of the argument corresponds most closely.
Hume is, of course, a very repetitive writer, and one can find his argument about predictive-inductive inference sketched in many other places in his writings besides those just mentioned [11].
For the identification of an argument as complex as Hume's is, it is almost essential to separate the structure from the content of the argument. The best way to effect this separation seems to be to compile a `dictionary' of the propositional elements of the argument, and to correlate them with the elements of a `structure-diagram' of the argument [12]. This is what is done below for Hume's argument. The representation will be found self-explanatory, except perhaps that it needs to be emphasized that the arrow has no evaluative significance whatever. We are here trying just to identify a man's argument, and p -> q, for example, means simply that p was in fact offered as a ground for believing q.
Stage 1
Stage 2
Stage 1
(a) }
(b) } -> (c) -> (d)
Stage 2
(e) }
(f) } -> (h) } -> (i) }
} } -> (j)
} ----------> (g) }
Even if this account of the structure of Hume's argument is correct, it does not follow at all that the content of his argument needs no elucidation. The opposite is in fact the case. The language of the elements of the above dictionary is substantially that of Hume himself, and at certain points especially that language, as we will see in the next section, is rather deceptively different from what we would use to convey the same meaning. There is, however, one extremely important feature of the argument which, if my representation of it is correct, emerges already.
That is, the way in which the conclusion of the second stage of the argument reiterates or `echoes' that of the first stage. For it can be seen already that the conclusion (d), which in stage 1 Hume drew concerning a priori inference, is in its content the same as the conclusion (j) which in stage 2 Hume drew concerning the predictive-inductive inference. That is, that it is not `reason', which `engages' or `determines' us to make inferences of that kind. What Hume means by saying this, will be determined later; but it is important to observe that it is what he concludes about the a priori and the predictive-inductive inference alike.
In the next section I will `translate' some parts of Hume's terminology into language less likely to be misunderstood. It should be noticed, however, that even the version given above as the original contains one translation of sorts. This is the word `presuppose', in premiss (e) of stage 2. Hume does not use this word. I have used it here not because its meaning is clear. On the contrary I think no word is used by philosophers with more ambiguity, and it will be part of our task in the next section to attach to it just one of its several possible meanings. I have used it because it is the obvious choice of one word which is to stand for a rather remarkable variety of phrases, all equally unclear, which Hume employs when he is stating his premiss (e) [14].
In stage 1 of Hume's argument there is only one matter which calls for clarification. That is, what Hume means when he says, in the conclusion (d), that the a priori inference is not one which `reason' `engages' us to make.
But this question, as we know, arises equally in connection with the conclusion (j) of stage 2, since Hume there says the very same thing about the predictive-inductive inference. We can therefore at the same time deal with one query concerning stage 2, and the only one which arises concerning stage 1. What, then, did Hume mean by saying, of a certain kind of inference, that it is not `reason' (or `reasoning', or `our reason') which `engages' (or `determines') us to make it?
The answer I will give here to this question will be one which I do not offer as final, for in Chapter 4 below I intend to offer a much more specific answer to it.
The reason why (j) and (d) require at least some translation at present is that they appear on the surface to be propositions of a kind which it is certain they really are not. Hume's two conclusions appear to be factual, and in particular, psychological propositions: as though (j), for example, were Hume's answer to a causal question, `What faculty of the mind is it which is at work in us when we make predictive-inductive inferences?'. But to any philosophical reader of Hume it will be obvious that this appearance is misleading. Here, at any rate, Hume's interest in the inferences he discusses is not empirical and psychological, but rather the kind of interest which a philosopher usually takes in inferences: viz. an evaluative, and in some sense, logico-philosophical interest. In the conclusions (j) and (d) as they stand, we have in fact just another instance of what we know to be true in general of Hume (as of most philosophers between the seventeenth and the twentieth centuries): that he asserts logico-philosophical theses in the guise of remarks about the constitution of the human mind.
Instead of an apparently psychological proposition, therefore, (j) should be rendered as a proposition evaluative, in some sense, of a certain class of inferences (viz. predictive-inductive ones). Not just any evaluation would do, of course. For there can be no doubt that Hume intends by (j) an extremely unfavorable evaluation of the inferences which are its subject. After all, (j) is that famous sceptical conclusion which Hume came to about inductive inferences, or rather, about the only `species' of inductive inferences which he discussed both clearly and at length. (If (j) is not Hume's inductive scepticism, there is no inductive scepticism anywhere in Hume).
I therefore suggest, as the interim translation of (j): `All predictive-inductive inferences are unreasonable'. This captures the non-psychological, the evaluative, and the unfavorable meaning of Hume's conclusion in stage 2. The predicate `unreasonable', indeed, cries out for further explanation, and this will be given in Chapter 4. In the meantime we must, accordingly, translate (d) as: `All a priori inferences are unreasonable'.
Hume himself, it is worthy of notice, does not always express his two conclusions in such a way as to give them a misleading psychological appearance, and when he does not, his language comes very close to that which we have just adopted for (j) and (d). Consider, for example, the passage from the Treatise [15], and especially the phrases I have italicized, in which he summarizes the conclusions of both stages of his argument, as follows: `That there is nothing in any object, consider'd in itself, which can afford us a reason for drawing a conclusion beyond it; and, That even after the observation of the [...] constant conjunction of objects, we have no reason to draw any inference concerning any object beyond those of which we have had experience [...]'. The conclusion (d) here is of course the part of this quotation before the semi-colon; the part after it is (j). Both parts are italicized in the original, and the passage shows other signs, as well, of having been written with special care. The result is, as we see, that Hume's conclusions, even though they still refer to `reason', have been quite shorn of their usual pseudo-psychological air, and stand forth clearly in the character which my translations ascribe to them, of (adverse) evaluative propositions about certain classes of inferences.
I now turn to the premisses and intermediate steps of stage 2 of Hume's argument, to consider the meaning of certain words and phrases occurring there.
In premiss (f) of stage 2 Hume says, of the proposition that unobserved instances will resemble observed ones, that is concerns `matters of fact and evidence'. This is not a phrase which a present-day philosopher will be likely to employ, but a general acquaintance with Hume's philosophical terminology leaves no difficulty in translating it. Hume means by it, that the proposition in question is a contingent one.
The translation of Hume's `demonstrative', as applied to arguments in (g), presents hardly any more real difficulty. Yet it is here that the danger of misunderstanding his argument begins to become serious.
Here as elsewhere Hume meant by a `demonstrative argument', a `(valid) argument from necessarily true premisses'. This is the only sense of the phrase which would explain Hume's own argument from (f) to (g); for it will be seen that the only ground which Hume gives for saying that there can be no demonstrative arguments for the Resemblance Thesis (as I will call it), is that that thesis is a contingent proposition. It is also the only sense of the phrase which is consistent with Hume's many variations on the theme that there can be no demonstrative arguments for any conclusion concerning matter of fact [16].
Using `demonstrative' of arguments in this sense was not, of course, on Hume's part, idiosyncratic in the slightest degree. This sense of the word is now somewhat obsolete, but by no means altogether so. It lingers on in the application to mathematics and logic of the title of `demonstrative' sciences; for we still mean to convey by this, at least that the reasoning employed in those sciences is always from non-contingent premisses.
For the most part, however, it is not in this sense that philosophers nowadays apply the word `demonstrative' to arguments or inferences. We almost always mean by it, especially if we use it as Hume so often does, in opposition to `probable arguments', just that the arguments in question are valid. Our sense of `demonstrative argument', then, is purely evaluative, and quite independent of the kind of premisses the argument has. (Our sense of `probable', applied to an argument, is similarly purely evaluative: we mean by it just that the argument in question has a high, though not the highest possible, degree of conclusiveness). But to suppose that Hume used `demonstrative argument' in this sense would be to impute to him an error unbelievably gross and often repeated. For he would then be saying, each time he asserts that there can be no demonstrative arguments for a matter of fact, that there cannot be a valid argument which has a contingent conclusion!
The position is very similar (mutatis mutandis) with regard to Hume's use, in (e), (h), and (i), of the word `probable', applied to arguments. Yet it is in connection with this word that the danger of misunderstanding Hume's argument is at its greatest. What, then, does Hume mean here by `probable arguments'? And by the word which (cf. e.g. note 14 above) he uses interchangeably with `probable arguments', `probability'?
This question is of fundamental importance for everything which follows in this book, and although it is not really at all difficult to answer, special care is therefore required here. The safest way to proceed will be by breaking this question up into two separate questions, each of which is extremely easy to answer, and of which the answers together will give us the answer to the above question.
I ask first, therefore, a different question: what is the main topic of Book I Part III of the Treatise, of the Abstract, and of sections iv--vi of the Enquiry? As a first approximation, the answer could hardly be more obvious. The main topic of these parts of Hume's writings is certain kinds of inference. For one of Hume's purposes obviously was to evaluate those inferences. But even in order to state what Hume's evaluative conclusions were, it must be possible for us to refer, in a neutral, non-evaluative way, to the class of inferences which were the subject of his evaluations. What inferences, then, are the main subject of these parts of Hume's writings?
It will be safest to proceed here by a series of approximations. First, then (just as for Hume a `demonstrative argument' is one from necessary premisses), the arguments which are his main topic in Book I Part III of the Treatise etc., are, evidently, arguments from contingent premisses. Thus he sometimes writes, in the course of stating (h), that arguments for the Resemblance Thesis must be `probable only, or such as regard matter of fact and existence' [17]. Again, in stating (i), he sometimes speaks of `probable arguments, or arguments regarding existence' [18]. Similarly, Hume sometimes uses the phrase `moral evidence' [19] as a name for the kind of inference which he is discussing; and whatever more that may mean, it surely at least means `arguments from contingent premisses'. So far, then, Hume's topic can be characterized as being `arguments from contingent premisses'.
Since, however, Hume cannot be supposed to have had in mind arguments from contingent premisses to non-contingent conclusions, we can safely add a further approximation. The arguments which were his subject-matter were arguments of which both the premiss and the conclusion were contingent.
The next restriction is also obvious. Hume's main topic was not at all `arguments from and to contingent propositions' in general. It falls, rather, within the species of that genus in which the premisses of the arguments are not merely contingent but observational propositions: reports, that is, of actual or possible past or present experiences. His subject is `arguments from experience' [20], `reasonings from experience' [21]. This restriction, that the inferences under discussion are ones with observational premisses, is also part at least of what Hume means by his insistence that those inferences `terminate' [22] in one or more impression.
We have not yet characterized Hume's topic narrowly enough, however, for certainly it does not include every `argument from observational premisses to a contingent conclusion'. The latter class includes the kind of inference which in section (i) above was called the a priori inference (for example, from `This is a flame' to `This is hot'). It also includes, for example, the inference from `This is an orange flame' to `This is a flame'. But the inferences which are the main subject-matter of the Treatise Book I Part III, etc., are certainly very different ones from either of these.
The class of inferences we are seeking is, of course, just that proper sub-class of arguments from observational premisses to contingent conclusions, of which the predictive-inductive inference is a typical, and the most important, member. The next most important member of the class, according to Hume, is the kind of inference which he discusses in section xii of Book I Part III of the Treatise (and in the corresponding fourth paragraph of section vi of Enquiry). This is the class of inference of which the following example, based again on one of Hume's, will serve us as a paradigm: `Nearly all of the many ships observed leaving port in the past have returned safely, and this is a ship leaving port, so, this will return safely'.
Since its typical and most important members are the predictive-inductive inference and the similar (`ship') inference from frequent conjunction, the class of inferences in question can be further characterized as being `arguments from observed to unobserved instances of empirical predicates'. Or, more simply, and finally, as `inductive arguments'.
These characterizations are, of course, like all the earlier approximations to them, entirely non-evaluative of the class of inferences which they pick out. For we have been trying precisely to determine what inferences were the subject of Hume's evaluative conclusions.
That the main topic of Book I Part III of the Treatise, of the Abstract, and of sections iv--vi of the Enquiry is what we call inductive inferences, is obvious enough; and it was in fact taken for granted in section (i) of this chapter. But it was worthwhile to labor to establish the obvious here, because to do so takes us so far towards answering the vital question on which we are engaged, of what Hume meant by `probable arguments' in the argument diagrammed above.
Let us ask, then, the second easy question which now will enable us to answer the question just mentioned. What word or phrase did Hume use to refer, in a non-evaluative way, to the inferences which it was at least one of his objects to evaluate? Not, of course, `inductive inference'; and in fact, as was remarked earlier, Hume uses a variety of phrases for this purpose---`arguments concerning existence', `arguments from experience', `moral evidence', etc. But there is one word and one phrase which every reader of Hume will easily recognize as his favorite synonyms for each of these phrases and for our `inductive inference'. They are `probability' and `probable arguments'.
The whole of Book I Part III of the Treatise, for example, is `Of Knowledge and Probability', and apart from section i `Of Knowledge', all of that part, beginning with section ii `Of probability; and of the idea of cause and effect', has for its main topic what Hume calls `probability' or `probable arguments'. Its main topic, however, is also what we call `inductive inferences'. Therefore what Hume means by `probable arguments', in (e), (h), and (i) of the argument diagrammed above, is simply `inductive inferences'.
Although the textual support for it seems, and I think is, irresistible, this translation is sure to cause some demur, and it is not hard to see why. Our sense of `probable arguments' is evaluative, and even purely so. We use `probable' of an argument to mean `of high but not the highest possible degree of conclusiveness'. Yet according to the above translation, Hume used `probable arguments' in a purely non-evaluative sense. It would be difficult to believe that between his time and ours the word `probable' has acquired its evaluative meaning for the first time. But could Hume have been so insensitive to the element of evaluation in the meaning of the word `probable' as my translation requires him to have been?
Indeed he could have been. For it is in fact possible to prove decisively that he was a great deal more insensitive to the normal evaluative meaning of the words which he chose to use as non-evaluative names for certain classes of inferences than my translation of `probable' as `inductive' represents him as being.
At the outset of section xi of the Treatise Book I Part III, and of the corresponding section vi of the Enquiry, Hume announces a change in his sense of `probability' and `probable arguments': a change which narrows the range of application of those words.
At this stage of the Treatise and Enquiry, of course, the discussion of the predictive-inductive inference, and hence the argument which is diagrammed above, is over. Hume is about to turn his attention to `some other species of reasoning', of which the main one is the inference from frequent conjunction (the inference about the ships). In the Treatise he opens this group of three sections, xi--xiii, with the following interesting paragraphs.
But in order to bestow on this system its full force and evidence, we must carry our eye from it a moment to consider its consequences, and explain from the same principles some other species of reasoning, which are deriv'd from the same origin.
Those philosophers, who have divided human reason into knowledge and probability, and have defin'd the first to be that evidence, which arises from the comparison of ideas, are obliged to comprehend all our arguments from causes or effects under the general term of probability. But tho' every one be free to use his terms in what sense he pleases; and accordingly in the precedent parts of this discourse, I have follow'd this method of expression; 'tis however certain, that in common discourse we readily affirm, that many arguments from causation exceed probability, and may be receiv'd as a superior kind of evidence. One wou'd appear ridiculous, who wou'd say, that 'tis only probable the sun will rise tomorrow, or that all men must dye, tho' 'tis plain we have no further assurance of these facts, than what experience afford us. For this reason, 'twould perhaps be more convenient, in order at once to preserve the common signification of words, and mark the several degrees of evidence, to distinguish human reason into three kinds, viz. that from knowledge, from proofs, and from probabilities. By knowledge, I mean the assurance arising from the comparison of ideas. By proofs, those arguments which are derived from the relation of cause and effect, and which are entirely free from doubt and uncertainty. By probability, that evidence, which is still attended with uncertainty. 'Tis this last species of reasoning, I proceed to examine [23].
The section `Of Probability' in the Enquiry, which is what corresponds to sections xi--xiii of the Treatise, opens with a precisely parallel explanation [24].
Thus, `in the precedent parts of this discourse', and hence in the sections which contain the argument diagrammed above, Hume had used `probability' to `comprehend all our arguments from causes or effects', or all `arguments from experience', as he calls them in the corresponding Enquiry passage. Now, however (that is, for sections xi--xiii in the Treatise, and section vi in the Enquiry), he proposes to confine `probability' and `probable arguments' just to such of those arguments as are `attended with uncertainty'. For the predictive-inductive inference, which is not so `attended', he now adopts the name `proof'.
This passage provides additional evidence that Hume had used `probable arguments' quite non-evaluatively in the earlier sections. For the differentia which he gives of the kinds of inferences to be discussed in sections xi--xiii is not at all evaluative. A kind of inference's being `attended with uncertainty' is simply a matter of how it is evaluated in fact and by men. Hume is, once again, giving an evaluatively neutral name to some inferences which it is no doubt part of his intention to go on to evaluate. But if the new, narrower sense of `probability'---in effect, `inductive inferences generally recognized as uncertain'---is non-evaluative, as it is, then a fortiriori the earlier, wider sense of `probability', viz. `inductive inferences', is also non-evaluative.
But the most striking thing about the passage quoted above is the application which Hume proposes in it for the word `proof'. Now the word `proof', both in Hume's time and ours, is one which when applied to inferences or arguments, is not only evaluative but in the highest degree expressive of favorable evaluation. Yet the class of inferences on which Hume now bestows this name is none other than that of predictive-inductive inferences. That is, precisely those inferences which he has just before been at great pains to reach an extremely unfavorable evaluative conclusion about! No one who has just argued for the conclusion (j) of stage 2 of Hume's argument, about the predictive-inductive inference, could possibly go on to call that kind of inference `proof', unless he were insensitive to the normal evaluative meaning of the word `proof'. There is therefore no difficulty whatever in supposing a fortiriori Hume's use of `probable arguments' was, what my translation made it, entirely non-evaluative.
Hume's choice of names for various classes of arguments, it must be admitted, was not well-advised. Since in the Enquiry, and in the Treatise Book I Part III, his main object evidently was to evaluate, in some sense, various kinds of arguments from experience, he should have first introduced those arguments under clearly non-evaluate names. To introduce them under names already in use with an evaluative meaning was bound to involve him either in the appearance of begging the very question he wished to ask, or in the appearance of self-contradiction; according as the evaluation which he arrived at, of a certain argument, was or was not the same as the evaluation implicit in the name he used for it. Since in the case of most of the `species of reasoning' which he discussed, Hume's evaluation was not the same as that which his name for it conveys, what he says often has the appearance of self-contradiction; as when he calls arguments, of which his evaluation is unfavorable in the extreme, `probable' arguments, and even `proofs'.
Still, this defect is really only name-deep, as it were. On the whole Hume could have hardly done more than he did to make clear to his readers that his senses of `probable arguments' (both the wide and the narrow sense), and his various names for special kinds of inductive inference, were all of them entirely non-evaluative.
The word `inductive' was applied to arguments, in the foregoing paragraphs, in what I believe to be the sense which it has customarily had: that of `arguments from observed to the unobserved instances of empirical predicates'. This is also the sense in which it will be used throughout the remainder of this book. But it deserves to be emphasized that, in consequence, the word `inductive' here has no evaluative meaning whatever. In particular, it is not and will never be part of what I mean by calling an inference `inductive' that that inference has less than the highest possible degree of conclusiveness.
Many contemporary readers will probably find some difficulty in resisting the temptation to read this element into the meaning of `inductive'. Why this is so, and why the temptation should nevertheless be resisted, will appear from Chapters 3, 7, and 8 below. The temptation would not be avoided, but would if anything be strengthened, if I were to adhere, for a translation of Hume's `probable arguments', to the phrase `arguments from observed to unobserved instances of empirical predicates'. The fact is, as we shall see, that Hume's influence on the history of thought has set us here a problem of nomenclature which has no completely satisfactory solution. The best way for the reader (at least if the experience of the writer is any guide) to avoid importing an evaluative element into my `inductive' or Hume's `probable arguments', is for him to keep in the forefront of his mind just the concrete paradigms which have been introduced of this class of arguments; principally, of course, the predictive-inductive inference about the flames.
The last problem of translation concerns the word `presuppose' in premiss (e) of Hume's argument. What did Hume mean by saying that probable arguments presuppose that unobserved instances of empirical predicates resemble observed ones? (Or rather, since `presuppose' was my own word, what did he mean by the variety of phrases, listed in note 14 above, for which `presuppose' was an apt, though unilluminating, paraphrase?) In what sense is it true that predictive-inductive inferences, for example, presuppose that unobserved instances resemble observed ones?
The senses in which an argument can `presuppose' a proposition are many, and they are not often enough distinguished by philosophers. One such sense is this. An argument from premiss p to conclusion q is sometimes said to presuppose a proposition r, in the sense that unless r were true, no one could be in a position to acquire belief in the premiss p. In this sense, the predictive-inductive inference about the flames, for example, presupposes, among other things, that there is such a property as heat.
It is not in this sense of the word, however, that `presuppose' occurs in premiss (e). For in this sense (e) is obviously false; or at any rate would certainly have been thought false by Hume. The last thing he would have wished to maintain is that no one could be in a position to acquire belief in `This is a flame and all of the many flames observed in the past have been hot', unless future flames do resemble past ones! Some of Hume's more optimistic critics appear to believe that something like this is indeed true; but that is an additional reason, if any were needed, for thinking that it is not the above sense of `presuppose' that Hume intends in the premiss (e).
I cannot hope to show, of every sense of `presuppose' except the one I will adopt, that it could not have been Hume's. I must instead proceed directly, and state what I think is Hume's sense of the word. This cannot fail to introduce an element of uncertainty into my account of his argument. But I will be able to show that the risk of error involved is very small.
Sometimes when we say of an argument from p to q, that is presupposes r, our meaning is as follows: that, as it stands, the argument from p to q is not valid, and that, in order to turn it into a valid argument, it would be necessary to add to its premisses the proposition r. I believe that this is the sense in which `presuppose' occurs in premiss (e) of Hume's argument.
My grounds for this belief are two. The first is that when `presuppose' is taken in this sense (and `probable arguments' is translated as `inductive arguments', in the sense stated above), (e) comes out true. For (e) would then say this: `Inductive arguments are all invalid as they stand, and it would be necessary, in order to turn them into valid arguments, to add to their premisses a proposition which asserts that unobserved instances resemble observed ones'. And so interpreted, (e) is true. Consider a typical inductive argument, such as the predictive-inductive inference from `This is a flame, and all of the many flames observed in the past have been hot' to `This is hot'. It is invalid as it stands. Nor could it be turned into a valid argument without the addition of some further premiss which will have the effect of saying that (at least in respect of heat) flames yet unobserved resemble observed flames. This additional premiss could take many non-equivalent forms. Perhaps the weakest of all of them would be the conditional proposition, `If this is a flame and all of the many flames observed in the past have been hot then this is hot'. But the addition, to the original premiss, of some Resemblance Thesis is clearly needed if this typical inductive argument is to be turned into a valid one.
My second ground for thinking that in (e) `presuppose' means what I have suggested, is that when it is taken in this sense (and `probable' is translated as `inductive'), the conclusion which Hume drew from (e) combined with (h) is perfectly explained. For (e) would, again, say this: `Inductive arguments are all invalid as they stand, and it would be necessary, in order to turn them into valid arguments, to add to their premisses the Resemblance Thesis'. The translation of (h) is: `Any arguments for the Resemblance Thesis must be inductive ones'. Together these two propositions entail that any inductive arguments for the Resemblance Thesis would be such that they could be turned into valid ones only by the addition to their premisses of the Resemblance Thesis itself; only, that is, by having their conclusion as a premiss, or in other words, by being circular. But this is precisely what the proposition (i), which is inferred by Hume from the conjunction of (e) and (h), says.
Now, it is very unlikely that any suggested sense of `presuppose', if it were not the one that Hume intended, would both make his premiss (e) true, and so neatly explain the inference Hume made from (e), with (h), to (i). I do not know of any sense of `presuppose', other than the one I have advanced, which fulfills even one of these two desiderata. Consequently there can be little risk of error in supposing that Hume did mean by `presuppose' in (e) what I have suggested he meant.
For ease of reference it will be best if I now bring all my translations together, and state what I take the whole of Hume's argument to have been.
The structure diagram of the argument is of course not changed. It remains as in the diagram:
Stage 1
(a) }
(b) } -> (c) -> (d)
Stage 2
(e) }
(f) } -> (h) } -> (i) }
} } -> (j)
} ----------> (g) }
But the content of the argument, incorporating both my abbreviations (`a priori inference', `predictive-inductive inference', and `Resemblance Thesis'), and my various translations, is now as follows.
Stage 1
Stage 2
[1] With the solitary exception that `induction' occurs once, in the Appendix to the Treatise, p.628. Even here, however, Hume seems to use the word not of argument from observational premisses. (The reference here is to the Selby-Bigge edition of A Treatise of Human Nature (Oxford U.P., 1888). All my page-references to the Treatise, and to the first Enquiry (An Enquiry concerning Human Understanding), Oxford U.P., 1894 are to the Selby-Bigge editions of those works).
[2] An Abstract of a Treatise of Human Nature (in Flew, ed., Hume on Human Nature and the Understanding, Collier Books, New York, 1962), p.293. (All my page-references to the Abstract are to this edition).
[3] Treatise, p.124.
[4] Abstract, p.292.
[5] Viz. the class of arguments, whatever it is, which Hume discusses in section xi of Book I Part III of the Treatise, and in the third paragraph of the corresponding section vi of the Enquiry. See the Appendix below, section (ii).
[6] Treatise, p.124.
[7] The title of section vi of Book I Part III of the Treatise.
[8] The phrases here placed in quotation marks will be found repeated, with minor variations, in all the passages in the Treatise, Abstract, and the Enquiry which are to be specified in the next paragraph but three.
[9] Cf. Treatise, p.126, the sentence beginning `Here we may repeat [...]'. The same thing is implied on p.139, by the passage beginning `And no doubt [...]'.
[10] This quotation is from the full title of the Abstract.
[11] Cf. also section (i) of the Appendix below.
[12] This invaluable device has been borrowed from my friend, and former teacher and colleague, Professor J.L.Mackie.
[13] In the Philosophical Review for April 1965 I published an account of Hume's argument which is very like the one given here, except in one vital respect. This is, that I there failed to distinguish between what later in this book will be called the fallibilist consequence of stage 2 of the argument, and the sceptical consequence which Hume actually drew. I published another account of Hume's argument which is free from this defect in the Australasian Journal of Philosophy for May 1970.
[14] In the following quotations I have italicized the phrase which was silently translated above as `presuppose'.
`[...] all reasonings from experience are founded on the supposition that the course of nature will continue uniformly the same' (Abstract, p.293).
`All probable arguments are built on the supposition that there is this conformity betwixt the future and the past [...]' (Abstract, p.294).
`[...] probability is founded on the presumption of a resemblance betwixt those objects, of which we have had experience (etc.)' (Treatise, p.90).
`[...] all our experimental conclusions proceed upon the supposition that the future will be conformable to the past.' (Enquiry, p.35).
`[...] all inferences from experience suppose, as their foundation, that the future will resemble the past.' (Enquiry, p.37).
[15] p.139.
[16] For example: `[...] whenever a demonstration takes place the contrary is impossible and implies a contradiction' (Abstract, p.293). `What is possible can never be demonstrated to be false [...]' (Abstract, p.294). `Were a proposition demonstratively false, it would imply a contradiction [...]' (Enquiry, p.26). `[...] Whatever is intelligible [...] implies no contradiction, and can never be proved false by any demonstrative argument or abstract reasoning a priori' (Enquiry, p.35). `[...] the only objects of the abstract science or of demonstration are quantity and number [...]' (Enquiry, p.163).
[17] Enquiry, p.35. My italics.
[18] Ibid. pp.35--6. My italics.
[19] Ibid. p.35, and again p.158.
[20] Ibid. p.38 and p.56 footnote, for example. My italics.
[21] Abstract, p.293. My italics.
[22] Enquiry, p.46; cf. Treatise, p.89.
[23] Treatise, p.124. Hume's italics.
[24] Enquiry, p.56, footnote appended to the title of the section.
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