Appendix

[ Acknowledgements | Introduction | Part One | Part Two | Part Three | Appendix ]


(i) Other arguments in Hume closely related to the argument diagrammed in Chapter 2 above

In this book the only part of Hume's philosophy with which we are concerned is his attack on inductive inference. This attack, we know, takes the form of an argument for a sceptical conclusion concerning one particular kind of induction, viz. predictive-inductive inference. And Hume repeats this argument a number of times.

In reading Hume on `the understanding', however, one is reminded of the argument about the predictive-inductive inference far more often than is accounted for by actual repetitions of it on Hume's part. There are frequent `echoes' of the content, and even of the structure, of that argument. There must then be in Hume other arguments, which are rather closely related to his argument about the predictive-inductive inference, which are the sources of these echoes of it. What are they?

The main one is the argument of the section `Of the idea of necessary connexion' (Treatise Book I Part III section xiv, Enquiry section vii).

In both books this section follows the discussion of inductive inference, and Hume's argument about the origin of the idea of necessary connection is in fact a kind of ontological version of his earlier argument about the predictive-inductive inference. Thus it is obvious, I suggest, that Hume's failure to find an `impression' of necessary connection corresponds, in some sense, to his discovery of the incurable invalidity of the predictive-inductive inference. And stage 1 and stage 2 of Hume's argument about the predictive-inductive inference correspond to his regularly seeking that elusive `impression', first in a single instance of the conjunction of two observable properties, and then in `several instances'.

To explain clearly and fully what the connections are between Hume's argument about the predictive-inductive inference and his argument about necessary connection, as distinct from perceiving more or less distinctly that such connections exist, would not be easy; and it would hardly be possible without entering deeply into the subject of causation. Fortunately it is not necessary for me to attempt such an explanation. Hume's argument about the predictive-inductive inference (and by implication his attack on inductive inference in general) is so clear and self-contained that it can perfectly well be considered on its own, as it has been considered in this book.

The other source of echoes of the argument about the predictive-inductive inference is this. As soon as he has advanced that argument, Hume immediately propounds, both in the Treatise and the Enquiry, a certain minor variant of it. The original argument concerns, of course, conjunctions of two observable properties (such as flame and heat). The variant concerns conjunctions of an observable property with the power (sufficient) to produce a certain other observable property. With this variation the argument proceeds, through stage 1 and stage 2, just as before.

This variant of the argument about the predictive-inductive inference will be found in the Treatise from p.90 (the middle of the second paragraph) to p.92 (at top); and in the Enquiry from p.36 (near foot) to p.38 (end of first paragraph). There is even a micro-version of it (too short, however, to have any internal structure, or even for its purpose to be clear if we did not have the other, longer versions to help us) in the Abstract: at p.294, second paragraph, the last two sentences.

`Power' being akin to `necessary connexion', the two arguments mentioned above are of course connected not only with the argument about the predictive-inductive inference but also with each other.


(ii) Treatise Book I Part II sections xi--xiii

These are the sections `Of the probability of chances', `Of the probability of causes', and `Of unphilosophical probability'. In the text of the present book these sections, or at any rate everything that is peculiar in them, have been totally neglected. They are discussed here in order to show that, in a book with the subject of the present one, that neglect is (despite what the titles of these sections might lead one to expect) altogether justified.

The `probability' with which this book is concerned is, of course, the logical probability which is to be ascribed to what Hume calls `probability'; that is, to what he calls `probable arguments'; that is (if what was said in Chapter 2 above was correct) to inductive inferences. For it is to be remembered: that the whole of Book I Part III of the Treatise is entitled `Of knowledge and probability'; that all of that Part (except section i, `Of knowledge') is about `probability', in Hume's (wide) sense of that word; and that what it is in fact about (except for sections xi--xiii) is the degree of conclusiveness of a typical inductive inference, viz. the predictive-inductive inference; along with a topic which (see the preceding section of this Appendix) is closely related specifically to that kind of inductive influence.

What sections xi--xiii are about, Hume announces (as we saw in the text) at the beginning of xi. They are about `some other species of reasoning' (p.124), other, that is, than the predictive-inductive inference. Of these `other species' the most important for Hume, he makes quite clear (p.130), is the inductive inference to an unobserved instance from the `frequent', as contrasted with the `constant conjunction' (p.139) of two observable properties. (The class of inferences, that is, of which our paradigm was: `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'). This kind of inference is the main subject of section xii. The subjects of sections xi and xiii are other kinds of inferences again; and still other kinds are very briefly discussed at the end of xii, p.142. The differentia, however, of all of the kinds of inference which were to be discussed in sections xi--xiii was this: that unlike the predictive-inductive inference, they are all `attended with uncertainty' (p.124). For as we saw in the text, Hume begins section xi by clearly announcing a change in his application of the word `probability'. Up to this point (and consequently, in those sections which occupied us in the text of this book), he had used that word, he says, `to comprehend all our arguments from causes or effects' (p.124, my italics), all `arguments from experience' (Enquiry, p.56 n.). Now, however (that is, in sections xi--xiii), he proposes to give it a narrower application, by confining it to just such of the former class of inferences as are `attended with uncertainty'.

As to what was Hume's purpose in discussing these other kinds of inference, it will suffice to quote again the opening paragraph of section xi. `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 derived from the same origin' (p.124). Hume's purpose, then, was to illustrate and confirm, by reference to other kinds of inference (mainly the inference from frequent conjunction), `principles' which he has enunciated distinctly at length already: viz. in connection with the predictive-inductive inference. But this means that sections xi--xiii are not central to Hume's philosophy of inductive inference. The essence of that philosophy has been given in his account, not completed, of the one kind of inductive inference which is `entirely free from doubt and uncertainty' (p.124), and the treatment of which by Hume occupied us to the exclusion of all others in the text of the present book.

This estimate of sections xi--xiii, as an inessential part of Hume's philosophy of inductive inference, is quite certainly one which was shared by Hume himself. In the Abstract, `[...] wherein the chief argument of [the Treatise] is further Illustrated and Explained', Hume's subject is of course the predictive-inductive inference (and the related idea of necessary connection); the materials of section xi--xiii, on the other hand, are nowhere to be seen. In the Enquiry the thirty full pages which these sections occupy in the Treatise shrink to the mere three pages which make up section vi of that book. And it would not be easy to say in what way the Enquiry would have been the worse, if those three pages had been omitted altogether.

But sections xi--xiii are not only an inessential part of Hume's philosophy of induction. They are, philosophically considered, altogether unrewarding intrinsically. Commentators on Hume have without exception failed to extract from them anything of philosophical interest. Their best aids, in dealing with these sections, have been brevity or even silence, and mere paraphrase or (still more non-committal) quotation. And there are ample reasons for this state of affairs.

The most important single reason is that, in sections xi--xiii, the kind of interest which Hume displays, in the inferences he is discussing, is an empirical, psychological interest, rather than a logico-philosophical and evaluative one. The philosophical passages in these sections seem to me, indeed, to be confined to two short ones: pp.126--7 and pp.139--40. And even the first of these is abruptly broken off by Hume saying `the question is [...]'---a certain factual one. There was, of course (though we were not concerned with it), a psychological side to Hume's discussion of the predictive-inductive inference too; but it did not there blot out the philosophical side of his subject. In sections xi--xiii it does.

Another reason, almost equally important, for the difficulties which commentators have encountered in dealing with sections xi--xiii is their downright obscurity. This applies to the little philosophy that these sections do contain, but it applies no less to the would-be psychology of which they chiefly consist. I at any rate have not be able to understand Hume's detailed account of the psychology of the inference about the ships (in xii), or of the inference about the die (in xi).

As an illustration of the obstacles which lie in the way of such understanding, the following sentence will serve. Hume writes, in connection with the die, that `the original impulse, and consequently the vivacity of thought, arising from the causes, is divided and split in pieces by the intermingled chances' (p.129). Nor does the context in which this is said do more than render it a little less obscure than it would be on its own.

The same sentence will serve also to illustrate the fact that very often in sections xi--xiii even Hume's language is curiously embarrassed. Sometimes, for example, as here, his use of the word `chances' is like no other that ever was on land or sea. There is nothing which clearly oversteps the bounds of intelligible English in speaking of an `impulse', or `the vivacity of thought', as being `split in pieces' by something or other; but to speak of this as being done `by the [...] chance' clearly does. And to speak as Hume does of `a mixture of causes among the chances' (p.126) or of `intermingled chances' (intermingled, presumably, again among `the causes'), is little or no better.

It would be very easy to multiply examples of perplexed English in sections xi--xiii, but one more short example must suffice. On p.124, having just introduced his narrowed sense of `probability' which confines it to inductive inferences attended with uncertainty, Hume begins a new paragraph thus: `Probability, or reasoning from conjecture [...]'. Now, given the context just referred to, the supposition is unavoidable that Hume has managed to say here the precise opposite of what he meant; that is, that he meant reasoning not `from' but `to' a conjecture. And if so he has made the most unpromising beginning imaginable for a discussion of inferences.

Hume himself was well aware, at least by the time he reached the mid-point of these three sections, that he was making extremely heavy weather of it all. He admits (p.135) the `air of subtilty which attends' his psychological explanation of the inference from frequent conjunction, and again, in the same connection, confesses himself `sensible how abstruse all this reasoning must appear to the generality of readers' (p.138). In between the last two quoted passages he almost desperately makes a fresh start: `Here is almost the same argument in a different light' (p.137). And on p.139 he is actually back at his very starting point. For he here recapitulates the two `principles which we have found to be sufficiently convincing even with regard to our most certain reasonings from causation' (i.e. the conclusions (d) and (j) in our diagram of the argument about the predictive-inductive inference), and says of them: `But I shall venture to affirm, that with regard to these conjectural or probable reasonings [i.e. the subject-matter of sections xi--xiii] they still acquire a new degree of evidence'. That is precisely what, in the very first paragraph of these three sections, Hume undertakes to establish. Yet it is also what, fifteen pages later, he recognizes he must still `venture to affirm'!

Sometimes, in these sections, indeed, the clouds do part. But the result is not always to light up something of value. For example, Hume's psychological account of the `ship' inference leads him to affirm, in all seriousness, that `a man, who desires a thousand pound, has in reality a thousand or more desires [...]' (p.141). This proposition is certainly a reductio ad absurdum of something in Hume's premisses; but it must be doubted whether it would be philosophically rewarding to try to find out what.

There is, as the reader may have noticed, one passage from these sections of which I have made use in the text above (Chapter 2). This is the italicized pair of sentences from p.139. But of course these are simply that recapitulation, referred to in the last paragraph but one, of the conclusions (d) and (j) of the two stages of Hume's earlier argument which is the subject of this book; except that, in order to comprehend the kind of inference under discussion in section xii, (j) now says that `even after the frequent or constant conjunction' of observable properties, `we have no reason', etc.

We have now seen some of the difficulties which lie in the way of philosophical consideration of sections xi--xiii. I propose next to set down briefly whatever in those sections seems to me to be, in spite of the difficulties, both clear, and of at any rate potential philosophical interest.

First, the general topic of the three sections is clear. It is those species of the genus, `inductive inferences', which are `attended with uncertainty', or in different words, which no one mistakes for valid inferences.

Second, the topic of section xii is clear. It is that particular species, among induction inferences attended with uncertainty, of which the inference about the ships is a paradigm; in other words, the inductive inference to a new instance from the frequent but not constant conjunction of two observable properties.

Third, the topic of section xi is---I believe, but here one must be more tentative---the Bernoullian inference to a singular conclusion, of which the following may serve as a paradigm: `This is a fair die marked in the usual way, and it is about to be thrown, so, this throw will not result in a "four"'. (The major premiss here may alternatively be phrased as, `The chance', or again `The factual probability', `of throwing "four" with this die = 1/6').

One of the reasons why this suggestion must be made with some tentativeness is that it is inconsistent with the view taken above of what the general topic of sections xi--xiii is. If I was right in arguing, in the text, that `probable arguments' in Hume's wide sense are simply inductive arguments, then, since his sense of `probability' in xi--xiii is quite certainly just a narrower sense than his earlier one, the arguments considered in xi--xiii, whatever their differentia, must still belong to the genus `inductive arguments'. They must still be, consequently, `arguments from experience'; that is, their premisses would have to be observational. But the above Bernoullian inference is not inductive, since one of its premisses is not observational. An assessment of the chance (or factual probability) of throwing a `four' with a certain die, is not an observation statement.

The same difficulty arises with at least one of the kinds of inference under discussion in section xiii. At least, if what Hume calls reasoning `from general laws' (pp.146 ff.) is what that name suggests, it too would not be a kind of argument from experience, since its premisses would not be observational.

I do not know how to resolve this inconsistency. But it would be an utterly insufficient ground for rejecting my thesis that, in the sections which concerned us in the text of this book, Hume meant by `probable arguments', inductive arguments. For (to mention only one reason) it is possible that the topic of section xi is not the above Bernoullian inference. Hume may instead have had in mind the inference, to the next throw of a die, from the observed relative frequency of `four' with that die. This is really a totally different kind of inference, of course, and the topic of xi, if this were it, would reduce to the topic of xii, since this inference about the die is just the `ship' inference over again. But, it is interesting to notice, Hume does appear to suggest in the first paragraph of xii that (because `chance' is unreal) the inference discussed in xi does somehow reduce to that discussed in xii. And the topic of xi, on this interpretation of it, really would be an inductive inference.

The topic of xi having been at least tentatively identified, the next question is, what are the kinds of inference which are the topic of the remaining section, xiii? But to this I am unable to return any answer definite enough to be worth setting down. Section xiii defies any treatment other than silence, paraphrase, or quotation.

One thing is clear, however, about the kinds of inferences discussed in xiii. That is that they are inferences which it is usual to regard as `unphilosophical'; that is, as unscientific or unreasonable. For Hume begins xiii by contrasting the subject-matter of it with the inferences about the ships, and (on my interpretation of xi) to the Bernoullian inference about the die, he writes (p.143): `All these kinds of probability are receiv'd by philosophers, and allow'd to be reasonable foundations of belief and opinion. But there are others, that are deriv'd from the same principles, tho' they have not had the good fortune to obtain the same sanction'.

We now have clearly in mind the kinds of inference which are the topics of at least some of these sections. We are, surely, entitled to assume that Hume's interest in these inferences was, at least partly, evaluative. We may, therefore, properly ask: what were some of the evaluative conclusions which Hume reached on these topics? The answer must be that in sections xi--xiii there is nothing which one can point to as being an evaluative conclusion of Hume concerning even one of the kinds of inference under discussion there. It was not so, of course, in the earlier sections, concerning the predictive-inductive inference; there Hume's evaluative conclusion (viz. scepticism) stood out perfectly plainly. But here Hume is far too absorbed in displaying the ability of his `system' to explain various empirical psychological `phenomena' (p.154), to draw any evaluative conclusion at all, sceptical or otherwise.

What Hume's assessment was, of the degree of conclusiveness of the inferences here discussed, is nevertheless perfectly clear of course. It is the same as his assessment of the predictive-inductive inference: that is, it is a sceptical one. For, for one thing, it will hardly be suggested that Hume regarded the inductive inference from mere frequent conjunction, for example, as being more conclusive than that from constant conjunction. Again, although the natural assessments of the former inference, and of the Bernoullian inference about the die, are of course favorable, Hume makes it quite clear that he does not share that assessment. Inferences of those two kinds are, as he says (p.143), `receiv'd by philosophers, and allowed to be reasonable foundations of belief and opinion'; and it is not only by philosophers, of course, that they are so `receiv'd'. The unreasonable inferences discussed in section xiii, Hume says, although `deriv'd from the same principles', simply `have not had the good fortune to obtain the same' favorable assessment (p.143, my italics). Clearly Hume does not believe that between, say, the inference about the ships, and certain `unphilosophical' inferences, there is a real as distinct from a supposed difference in degree of conclusiveness.

Granted that Hume's assessments of the inferences discussed in xi and xii are sceptical ones, does he argue for these assessments here, and if so how? Hume says, concerning the Bernoullian inference about the die, that `here we may repeat all the same arguments' (p.126) which he had employed concerning the predictive-inductive inference; and, at the middle of p.139, he appears to say the same concerning the inductive inference about the ships. At both of these places, in fact, he intimates that he is actually about to repeat that argument, presumably mutatis mutandis. But he does not do so. What he immediately goes on to say is, indeed, a recognizable variant of stage 1 of his argument about the predictive-inductive inference. But in the next paragraph in each of these places (viz. the top half of p.127, and the last paragraph begun on p.139), where one would therefore expect an adaptation of stage 2 of that argument, there is no recognizable variant of stage 2. What the argument of either of these paragraphs is, I am unable to say.

Hume could hardly be said, then, even to have seriously tried to argue for a sceptical assessment of the inferences which he discussed in sections xi and xii. If he had seriously tried to adapt stage 2 of his earlier argument to them, he would have encountered formidable difficulties. But it would take us much too far afield if we were to begin now to explore how Hume might have argued in order to extend his scepticism to those `other species of reasoning'.

Of the actual contents of sections xi--xiii, everything which seems to me both clear and of even potential philosophical interest has now been reported. It will be evident that, unless my report has been grossly deficient, the neglect of those sections in the text of this book was justified. They are so extraordinarily unrewarding, indeed, that some special explanation of the fact seems called for. Such an explanation is not far to seek, if certain things which are said in the text of this book are true.

The fallibilist thesis, it was there said, is an important truth, at least in connection with the predictive-inductive inference. It is so, because the natural assessment of that inference, at least at the `organic' level, is not only favorable but even mistakes the predictive-inductive inference for a valid one. This psychological fact gives the fallibilist thesis something to correct, and imparts even to the sceptical assessment of that inference the merit of avoiding a deeply natural error. In connection with the predictive-inductive inference, too, the assumption of deductivism escapes immediate recognition as a short and sure step to an incredible (sceptical) conclusion, and it does so for the same reason: that the fallibility of the predictive-inductive inference (which is the other premiss needed for the sceptical conclusion) is not genuinely obvious to us.

The case is entirely the opposite, however, with the inductive inference from frequent conjunction, and with the Bernoullian inference about the die. These are inferences `attended with uncertainty': inferences, that is to say, of which the natural assessment, while favorable of course, is not at all such as to mistake them for valid inferences. To assert the fallibility of these inferences would be to assert no more than is, to everyone, totally obvious. Again, to assume the deductivist thesis in connection with these inferences would be self-discrediting, as being a transparent veil for scepticism, and again for the same reason: that the fallibility of these inferences (which is the other premiss for the sceptical conclusion) is genuinely obvious to us.

Contrapositively, then, a man who did assume deductivism, as Hume did, could hardly take a serious evaluative interest in the kinds of inference which are the subject of sections xi--xiii. The predictive-inductive inference is the only inductive inference which pretends to the only high degree of conclusiveness which a deductivist recognizes. And that pretension Hume has already successfully punctured. How could he take seriously the claims to a high degree of conclusiveness of other inferences which do not even pretend to be valid? Such a man could hardly take, in such inferences, any kind of interest other than an empirical and psychological one.


(iii) Some examples of twentieth-century exaggeration of Hume's achievement

Hume has acquired in the present century a reputation far higher than he ever enjoyed before; and at least in connection with inductive inference, if what has been said in this book is true, a reputation even higher than he deserves. To show that this is true, it will suffice to collect some instances in which twentieth-century writers claim to have found in Hume's writings on induction some thesis or argument, which had not been found there before, and which in fact is not there. This is what is done below.

What a writer erroneously attributes to Hume is usually something of which the writer himself strongly approves: as is natural enough in the present century (although in the nineteenth century the temptation was of a precisely opposite nature). But some of these attributions bear so little relation to the text on which they are based as to recall Lewis Carroll's character who

[...] thought he saw an Argument
That proved he was the Pope:
He looked again, and found it was
A Bar of Mottled Soap


(a) Chapter VII of Keynes's Treatise on Probability is a `Historical Retrospect', and on pp.81--3 there is a discussion of the classical theory of probability. Keynes points out that the classical theorists relied heavily, for the assessment of probabilities, on the `Principle of Indifference' which he has in an earlier chapter criticized severely. This reliance, Keynes has shown, was one of the sources of the extravagant claims made for the theory of probability by Laplace and other French writers of `the latter half of the eighteenth century' (p.83 n.1).

Yet [Keynes goes on] the new principles did not win acceptance without opposition. D'Alembert, Hume and Ancillon stand out as the sceptical critics of probability, against the credulity of eighteenth-century philosophers, who were ready to swallow without too many questions the conclusions of a science which claimed and seemed to bring an entire new field within the dominion of Reason.

The first effective criticism came from Hume, who was also the first to distinguish the method of Locke and the philosophers from the method of Bernoulli and the mathematicians. `Probability', he says, `or reasoning from conjecture, may be divided into two kinds, viz., that which is founded on chance and that which arises from causes'. By these two kinds he evidently means the mathematical method of counting the equal chances based on Indifference, and the inductive method is based on the experience of uniformity. He argues that `chance' alone can be the foundation of nothing, and `that there must always be a mixture of causes among the chances, in order to be the foundation of any reasoning'. His previous argument against probabilities, which were based on an assumption of cause, is thus extended to the mathematical method also (p.83).

Both of the quotations from Hume in this passage are from the early paragraphs of section xi of Book I Part III of the Treatise, and it is evidently in that part of the Hume corpus that Keynes finds `effective criticism' of the classical theory of probability. But what does this passage of Keynes say?

Hume's scepticism, as we have seen in the preceding section of this Appendix, undoubtedly did extend to the `other species of reasoning' which he discussed in sections xi and xii. As for justification of extending his scepticism to them, however, we have seen that Hume could scarcely be said even to have tried to supply any. Yet Keynes (in the last sentence of the above passage) represents this extension as a successfully established conclusion. As to how Hume had adapted his argument for scepticism to these other kinds of inference, Keynes does not venture words of his own. He prefers direct quotation from Hume, even when it means quoting a sentence which is not only obscure, but scarcely intelligible English---that `there must always be a mixture of causes among the chances', etc. How this thesis, if it can be called that, accomplishes the extension in question, Keynes seems to think obvious; whereas it could hardly be less so.

And precisely what was the criticism (`effective', at that) which Hume made, whether of the classical theory in general or the Principle of Indifference in particular, Keynes leaves equally unclear. It is impossible to discover from the above passage what it was. Yet it is from this very passage that it must be elicited, if it is to be discovered at all. For Keynes never again refers to this mythical `criticism', and no other writer has lent his name to this particular claim on Hume's behalf.

It ought not to be overlooked that what Keynes's' `Historical Retrospect' implies, about Hume's relation to the classical theory in the second half of the eighteenth century, is anachronistic on its very face. Laplace was not even born until ten years after Book I of the Treatise was published. And at the time when Hume was writing that book, Bernoulli's Ars Conjectandi, which is the earliest work from which the classical theory can possibly be dated, and which is itself relatively free from the pretensions which were later rested partly on it, had been before the world a bare twenty years.


(b) This example also concerns section xi of Book I Part III of the Treatise.

In a 1962 (Fontana Library) edition of Book I, the editor, Professor D.G.C.Macnabb, has appended a footnote to the end of the eighth paragraph. It reads: `Up to this point the section is a masterly non-technical introduction to the calculus of chances'.

This claim is unlike all the others collected in the present section, in that even if it were true, the fact would not be of any importance for the philosophy of induction or of probability. Hume certainly could have written an introduction to the calculus of chances, and it is of historical interest only whether in fact he did so.

But as an example of twentieth-century historiography ad maiorem gloriam of Hume, the above footnote is remarkable, even breathtaking. There is no `introduction to the calculus of chances' in the first eight paragraphs of section xi---neither a `masterly non-technical' one, nor any other. `And this' (as Hume wrote in another connection) [1] `is a matter of fact which is easily clear and ascertained'.


(c) Wherever Hume' attack on inductive inference has been admitted to be at least partly successful, the most common reaction to it has always been one which could be expressed as follows. `True, no inductive inferences can ever attain the highest possible degree of conclusiveness; but some of them are of high logical probability nevertheless'. For as we have seen in Chapter 8, the historical effect of Hume's argument against induction has on the whole been to secure the acceptance of inductive fallibilism, while failing to secure the acceptance of inductive scepticism; and the first and second clauses above respectively reflect these historical facts. This reaction to Hume is not only the common one, but, just because of the almost-universal acceptance of inductive fallibilism, has come to sound, to our ears, distinctly banal. Accordingly I shall refer to it as `the commonplace reaction' to Hume's attack on inductive inference.

If what I have said in the text of this book is true, the commonplace reaction to Hume is also the correct one. Not, of course, that I tried to prove the truth of its second clause (only the falsity of the sceptical contrary of it). But if what I have said is true, the first clause concedes all that is proved by the true premisses of Hume's argument; the first and second clauses together require the rejection of Hume's implicit deductivism; and once deductivism is rejected there is no longer anything in Hume's premisses which would prevent us from making the natural favorable assessment of some inductive inferences---which is what the second clause does.

Now, the common reaction to Hume's argument could not have been the one stated above, if it has been believed that one of the targets of Hume's attack was the thesis that some inductive inferences, although invalid, are nevertheless of a high degree of conclusiveness. For this thesis is the commonplace reaction to Hume's argument (or what is essential in it). It is precisely what most thinkers have believed that they could still claim for inductive inference, even after conceding to Hume everything (viz. inductive fallibilism) which could no longer be denied him. Clearly, then, it has usually been believed, at any rate, that Hume did not have, as one of the targets of his attack, the thesis that some inductive inferences are of high logical probability although invalid.

By the middle of the twentieth century, however, a reaction had begun against the commonplace reaction to Hume. This was to be expected, as inductive fallibilism became a complete commonplace, and even began to made into a truism, while at the same time Hume's reputation was rising to an unprecedented height. Under these circumstances, the thought was almost bound to suggest itself, that the commonplace reaction did insufficient justice to the profundity of Hume's argument against induction. An evasive stratagem which is now so easy (it would then be thought), must surely have been anticipated, and defeated, by Hume himself. Accordingly, it began to be claimed that Hume had in fact forestalled, and a fortiriori that he had had as one of the objects of his attack, the thesis that some inductive arguments have a high though not the highest possible degree of conclusiveness.

Some have tried to save the situation by admitting that all scientific inference is probable inference. But Hume's sceptical attack applies with equal force to probable inference [2].

Can we not, however, argue that while experience yields no certainty as to the future, it may yet instruct us as to what is likely to happen in the future? But this, too, as Hume points out, is `no thoroughfare' [3].

In other words Hume points out that we get involved in an infinite regress if we appeal to experience in order to justify any conclusion concerning unobserved instances---even mere probable conclusions, as he adds in his Abstract (p.15) [4].

It deserves mention that David Hume, who was the first to see that general synthetical propositions cannot be proved a priori, also clearly apprehended that this result of the impossibility of foretelling the future cannot be `evaded' or `minimised' by reference to probability [5].

It will be evident to the reader that if what I have said in the text of this book is true, then what these authors imply must be false. A man could not possibly have been intending to refute the thesis that some inductive inferences are of a high degree of conclusiveness though invalid, if throughout his argument he simply assumed that invalidity suffices to make an inference (whether inductive or of any other kind) unreasonable. The evidence, therefore, for thinking that the authors quoted above are mistaken, is the evidence for thinking that Hume took for granted the truth of deductivism.

That evidence I have given as well as I can in the text, where I tried to show that deductivism enters Hume's argument as a suppressed premiss not just once but twice. (See Chapter 3 section (iii)). And in this respect (as was also remarked in the text), my detailed account of Hume's argument has on its side the opinion, vague but overwhelmingly preponderant among writers on Hume, that Hume's conception of `reason', or of an inference which reason can sanction, was an exclusively `rationalistic' or `deductive' one.

For substantiation of their claim quoted above, Popper and von Wright both refer to the Abstract, p.15 in the original pagination which was reproduced in the edition by Keynes and Sraffa; that is, to a passage which, in the edition by Flew, begins on the sixth-last line of p.293 and ends with the first paragraph of p.294. And this reference furnishes a clue as to how the above mistaken claim for Hume may have originated. For that passage, far from being what Popper says it was, one which was added in the Abstract, turns out to be nothing but the Abstract version of stage 2 of Hume's argument, diagrammed in Chapter 2 above, against the predictive-inductive inference. In it, therefore, if the view taken in this book is correct, Hume's phrase `probable arguments' had the purely non-evaluative sense of `arguments from experience', `inductive arguments'.

Our sense of `probable arguments' on the other hand, as was remarked in the text, is purely evaluative, and in particular it is precisely that which the writers quoted above evidently take to have been Hume's: `arguments of high degree of conclusiveness though invalid'. In order to have at least a partial explanation, therefore, of the exaggerated claims for Hume which were quoted above, one would need to suppose only that their authors mistook Hume's sense of `probable arguments' for our sense of that phrase.

The most likely place for such a mistake to have first crept in is at element (i) in stage 2 of Hume's argument. Yet Hume uses the phrase `probable arguments' at the very outset of stage 2 (in element (e)), where it refers obviously enough to the kind of inferences which were his subject-matter throughout Book I Part III of the Treatise, the Abstract, and sections iv--vi of the Enquiry; which can hardly be supposed to be anything other than inductive inferences. And even the context of element (i) is such as should have made it quite clear that anything inconsistent with deductivism was as far as possible from Hume's mind. For Hume's argument down to (i) and (g) was the result of his asking how one could prove [6] a certain proposition which was necessary for the validity of certain inductive inferences.

The reaction against the commonplace reaction to Hume in its turn provoked some reaction in the 1960s: first from Professor A.Flew [7], then from the present writer [8].


(d) The passage which was quoted in (c) above, in which von Wright claims that Hume's argument cannot be evaded or minimized as it commonly has been, continues as follows:

He [Hume] was aware of the infinite retrogression to which the introduction of probabilities in this connection leads and also of the necessity of interpreting probability as a statistical concept if it is to be of relevance to statements on future events.

To substantiate these two further claims for Hume, von Wright gives two references, one appended to `infinite retrogression', the second to the end of the above sentence. Let us consider the second claim, and its textual backing, first.

It would not be difficult to show that the supposed `necessity of interpreting probability as a statistical concept if it is to be of relevance to statements on future events' is illusory [9]. But to do so is not necessary for my present purposes, which is not philosophical but historical. So for the sake of argument let us concede to von Wright the alleged necessity. The question is, where was it that Hume displayed his prescience with respect to this necessity?

The relevant footnote [10] refers us, yet again, to p.15 (in the original pagination) of the Abstract. But that is (as we have seen in (c) above) just to stage 2 of Hume's argument about the predictive-inductive inference!

Once again, then, at this part of the text Hume's `probable arguments' meant simply `inductive arguments', if what has been said in this book is correct; and if so then von Wright's claim must certainly be mistaken. But the best way to deal with this claim is, as we dealt with Macnabb's claim in (b) above, by direct appeal to the relevant texts. I affirm then, that in Hume's argument, about the predictive-inductive inference there is no sign of an awareness on his part of a `necessity of interpreting probability as a statistical concept', etc.; and the reader is invited to satisfy himself of the fact, by re-reading the relevant passages: which are: Treatises, pp.87--90, Abstract, pp.293--4, Enquiry, pp.35--6.

Now as to the first claim made for Hume in the above quotation. This must be false, if what was said in (c) above was true. If Hume did not forestall the commonplace reaction to his argument, then a fortiriori he did not forestall it by discovering an infinite regress in it.

This claim that if one says that some inductive inferences are of high but not the highest possible degree of conclusiveness, one is led into an infinite regress, is a surprising claim to say the least. But let us, as before, suppose for the sake of the argument that it is true. Our concern is with the still more surprising historical claim, that Hume was aware of this interesting fact (as Carnap, for example, never was). Where was it that, according to von Wright, Hume showed this particular piece of prescience?

The relevant footnote [11] refers us to Book I Part IV section i of the Treatise, `Of scepticism with regard to reason'.

The argument of that section need not be expounded here. It is, and has been generally recognized as being, not merely defective, but one of the worst arguments ever to impose itself on a man of genius. (Hume was not, even so, deceived by it for long: the argument was never repeated after the Treatise). But let us further suppose, for the sake of von Wright's claim for it, that the argument was not defective. What then?

The section is rightly called `scepticism with regard to reason'. For Hume's subject-matter here is not inductive inference, but all kinds of inference indifferently, quite explicitly including valid inference from premisses necessarily true. The `sceptical' conclusion reached here, therefore (the particular nature of which need not detain us), extends indifferently to all inferences whatever.

It is at least misleading, then, to suggest that the argument of the Treatise Book I Part IV section i is an argument against `the introduction of probabilities in this connection': i.e. in connection with inductive inference, the only place where the commonplace reaction to Hume does introduce it.

It is true, however, that the kind of scepticism, whatever it is, which is argued for in that section, would include inductive inference in its scope. But now mark another consequence of endorsing that argument, as von Wright clearly does. The effect of the argument, as we have seen, is to involve all inference in a common ruin. It will thus inter alia obliterate a distinction, on which rests the whole of Hume's own argument in Book I Part III for inductive scepticism, and even his argument for inductive fallibilism: the distinction between valid and invalid inferences. This is also a distinction which is of considerable importance to other philosophers, including von Wright himself.

But apparently Hume must be praised even though the heavens fall.


Footnotes

[1] My Own Life, the last sentence.

[2] A.H.Basson, David Hume (London, 1958), pp.167--8.

[3] N.Kemp Smith, The Philosophy of David Hume (London, 1960), pp.374--5.

[4] K.Popper, The Logic of Scientific Discovery (London, 1959), p.369. Cf. ibid. p.265, starred addition to n.2. And cf. the same author's Conjectures and Refutations (London, 1963), pp.192--3, 289.

[5] G.H.von Wright, The Logical Problem of Induction (London, 1957), p.153. Cf. ibid. p.176.

[6] See the passage of the Abstract, referred to in the last paragraph but one, on which Popper and von Wright base their claim quoted above. It contains the word `prove' twice; `proved' once; and `proof' four times.

[7] In his Hume's Philosophy of Belief (London, 1961), pp.75--6.

[8] In the Philosophical Review for April 1965.

[9] Cf. my review of W.C.Salmon, The Foundations of Scientific Inference, in the Australasian Journal of Philosophy for May 1969, p.88.

[10] The Logical Problem of Induction, p.223 n.16.

[11] Op. cit. p.223 n.15.


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