Hume Studies

141 HUME AND DEMONSTRATIVE KNOWLEDGE Little could be clearer than that Hume's sceptical arguments concerning induction and causation depend to some considerable extent on his contention that there can be no demonstrative arguments for matters of fact. An understanding of his use of the terms 'demonstration', 'demonstrative reasoning' etc., would seem to be a prerequisite for a satisfactory appraisal of those arguments. What is almost as clear, however, is that these terms have so far evaded much critical discussion and, with one notable exception, it seems to be assumed that we know well enough what they mean. That exception is David Stove, whose book on Hume contains, among many good things, a boldly provocative discussion of these terms in relation to the sceptical argument. Stove has interesting things to say about the terms: I don't think that he is quite right, but then neither is he straightforwardly wrong. I shall present his account, and the one to which he is opposed, and then, after criticising both, I shall try to show why the truth lies elsewhere, and why we begin to approach Hume correctly only when we temper our fascination with the purely formal structures of argument. Inductive scepticism is, of course, that scepticism which claims that there can be neither knowledge nor reasonable beliefs about unobserved matters of fact. Thus inductive arguments, those arguments which attempt to ground beliefs in unobserved matters of fact are, under this scepticism, claimed to 142 be bad arguments. Deductively valid arguments are, of course, often good, but it seems that they are unable to be utilised in justifying beliefs in unobserved matters of fact. The problem of induction is thus that of explaining how these non-valid inductive arguments can be forceful, and Hume's scepticism about induction resides in his believing and arguing, or appearing to believe and to argue, that they cannot. Hume himself does not, however, use the terms 'inductive', 'deductive' and their cognates. Some translation has therefore been employed in getting from his writings to the rough and ready sketch of the problem of induction as presented above. Stove spends some considerable time on this, and there is surely nothing wrong with his careful glossing of Humes 'moral' and 'probable' arguments by our term 'induetive ' . There are, however, good reasons to tread carefully where 'demonstrative' is concerned. Stove's remarks here are somewhat contentious, and before giving his version of what Hume's term means, I shall present what may be accounted the standard view. While Hume does not use the term 'deductive', he does make freguent use of 'demonstration' and its derivatives, and he uses these in such a way as to suggest that a gloss via our term 'deduction' will not be far off the mark. Consider, for example, the following passage: Our foregoing method of reasoning will easily convince us, that there can be no demonstrative arguments to prove, that those instances, of which we have had no experience, resemble those, of which we have had experience. We can at least conceive a change in the course of nature; which sufficiently proves, that such a change is not absolutely impossible. To form a clear idea of anything, is an 143 undeniable argument for its possibility , and is alone a refutation of any pretended argument against it. (T 89) His point here seems to be that as alternative states of affairs remain possible, and are thus compatible with all the evidence upon which is based the hypothesis about continuing uniformity, it cannot be claimed that the persistence of such uniformity is established by argument. A similar account will be given of the following passage from the Enquiry: When a man says , I have found, in all past instances, such sensible qualities conjoined with such secret powers: And when he says , Similar sensible gualities will always be conjoined with similar secret powers, he is not guilty of a tautology, nor are these propositions in any respect the same. You say that the one proposition is an inference from the other. But you must confess that the inference is not intuitive; neither is it demonstrative.... (E 37) It is tempting to understand Hume here as once again...