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PROBABILITY AND HUNIE ' S INDUCTIVE SCEPTICISM BY D. C. Stove Oxford at the Clarendon Press, 1973, pp 132. As a piece of philosophical literature, the book is a pleasure to read. Meticulous conceptual and logical clarity is matched by a clean smoothness of writing style. The structure of the whole work is clearly and carefully presented. Stove makes three contributions to the discussion of Hume's inductive scepticism: (i)to the clarification of Hume's argument and conclusion (s) , (ii) to the assessment of the force of the argument, (iii) to the achievement of historical perspective on Hume's present influence. I shall discuss these in order. As for the book as a whole, Stove offers us a complete structural diagram of Hume's argument for inductive scepticism. This presents in beautifully clear form the structure of an argument whose extended forms span three separate works , each offering surface- differing partial versions, and scores of pages of text. Or rather, as Stove says, what he presents is the best composite of the three versions. This in itself constitutes an important piece of textual detective work, but Stove complements this with a detailed discussion of the most appropriate version of Hume's terminology. All of this is careful· thorough exposition and constitutes an important contribution to understanding Hume, a contribution which could stand apart from the remainder. Stove pushes his final refined english version of Hume's argument a step further and rewrites it in terms of statements of logical probability. Thus the conclusion Stove attributes to Hume: (1) All predictive-inductive inferences are unreasonable 2 5 becomes: (i) If the inference from e to h is predictiveinductive then P(h,e.t) = P(h,t) where P (A, B) is read as "the logical probability of A given B" which is to be understood, according to Stove's discussion, as "the degree of conclusiveness of the argument from A to B", t represents the class of logical tautologies and (i) is to be so read as to represent the class of all judgements of this form. Similarly, (2) All invalid arguments are unreasonable becomes and becomes (ii) If e does not entail h then P(h,e.t) » P(h,t) (3) All predictive-inductive inferences are invalid (iii) If the inference from h to e, is predictiveinductive then P(h,e..t) P (Fb. Fa,t) But this last line contradicts i where h is taken as Fb_.Fa_ and e as Fa_. What makes Stove's argument so simple and strong, yet relevant, is the strength of the form in which he casts Hume's conclusion 1, i.e. as i. All Stove has to rely on is the coherence among statements of logical probability -the 2 7 coherence transmitted by the principles of logical probability. The fact is, as Stove points out, once you accept the principles of logical probability then any statement of logical probability will commit you to an indefinitely large class of other such statements; moreover these are so connected, as Stove's argument shows, that if one makes a sceptical judgement at one point one may be bound to accept credulous judgements at others. This is the trap in which he catches Hume (and, to the extent that other sceptics must embrace Stove's formulation of Hume, those sceptics also). Stove accepts Hume's fallibilist conclusion 3, and so iii and accepts Hume's argument to 3, as he reconstructs it, as both valid and from true premises. He avoids accepting the sceptical conclusion by arguing (successfully, I think) that a necessary, though suppressed, premise is the 'deductivist ' premise 2, cf. ii, which Stove also rejects and on the same grounds as he rejects i. But this leaves the possibility of an inductivist program open again for fallibilism, as opposed to scepticism,and is compatible with any reasonable inductivist position. (Contrary, then, to popular conception, what is acceptable in Hume's arguments i_s_ compatible with inductivism.) And Stove, one suspects »has his own inductivist program in mind, which involves using the logical theory of probability centrally (and the inverse Bayse formula in particular). This book is quite limited in scope, it establishes only...