1 I thank Terence Penelhum, John Heintz, and Mohan Matthen for helpful comments on an earlier version of this paper, read to the Philosophy Club at the University of Calgary.

2 Hume, David, Treatise of Human Nature, ed. by Selby-Bigge, L.A., (Oxford: Clarendon Press, 1888.Google Scholar)

3 Smith, Norman Kemp, Philosophy of David Hume. London: Macmillan, 1941.CrossRefGoogle Scholar

4 Stove, D.C., Dialogue, September 1976, p. 506Google Scholar.

5 Reid, Thomas, Essays on the Intellectual Powers of Man. Introduction by Brody, Baruch (Cambridge, U.S.A.: M.I.T. Press, 1969Google Scholar) All references in the text are to this edition.

6 Prichard, H.A., Knowledge and Perception. (Oxford: Clarendon Press, 1950).Google Scholar

7 Russell, Bertrand, Human Knowledge: Its Scope and Limits (London: Allen and Unwin, 1948).Google Scholar

8 Reichenbach, Hans, “Are Phenomenal Reports Absolutely Certain?”, in Philosophical Review, 1952.Google Scholar

9 Reichenbach's rule of elimination allows one to calculate the probability of C, from A, when C is linked to A by an intermediate term B and only the intermediate probabilities are given. The derivation of the rule of elimination uses the equivalence “[[B v ∼ B] & C] = C“;

(cf. Hans Reichenbach, Theory of Probability. Second edition. Translated by Ernest H. Hutten and Maria Reichenbach (Berkeley and Los Angeles: University of California Press, pp. 76-77).

As it stands the rule does not help us with our problem since we are concerned with the categorical or epistemic probability of our conclusion C, with how willing we ought to be to accept C simpliciter- not relative to some condition A. However it is easy to show how a variant of the rule of elimination applies. (I substitute for Reichenbach's letters.)

10 The puzzle remains when we add other adults to our data. When the probability that adult Paul Newman is not five feet nine inches tall is not .99, it is .8; when the probability that adult Wilt Chamberlain is five feet nine inches tall is not .99, it is .1; when the probability that adult Roman Polanski is five feet nine inches tall is not .99, it is .15; when the probability that Atilla the Hun was five feet nine inches tall was not .99, it was .001, and so on, for Napoleon, Hitler, Peter the Great, tall and short. So what?

11 It might be objected that one need not compute a corrected probability for C in case s is false, just an initial probàbility. However Reichenbach's formula for determining a corrected probability does not allow for this move. One needs the corrected probability of C is case s is false for his formula to work. At this point we may wish to appeal to Jeffrey's rule for determining corrected probabilities in a fallibilistic universe in the light of new evidence. On Jeffrey's rule,

(Cf. Jeffrey, Richard C.. The Logic of Decision (New York: McGraw Hill, 1965), p. 158Google Scholar and elsewhere in chapter 11.)

PROB probabilities are corrected or final probabilities; prob probabilities are uncorrected or initial probabilities. However a similar problem arises for applying this formula to our difficulty. We don't have PROB's unless we have already gone through the whole process of argument in question. Moreover we don't just have one higher order s statement but a whole series of them, each about the preceding statement, estimating its reliability. It is not clear to me how use of Jeffrey's rule may be extended to deal with Hume's problem, to take into account the whole series of higher order s statements, and to determine unconditionally how willing one ought to be to accept C.

12 Chisholm, Roderick M., Perceiving; A Philosophical Study (Ithaca, N.Y.: Cornell University Press, 1957); p. 26.Google Scholar