Hume's Probability Argument of I, iv, 1

125, HUME'S PROBABILITY ARGUMENT OF ?,??,? In the Treatise, ?,??,?, Hume presents an follows:' argument which, in the barest of outlines, goes as 1 (Pl) Every proposition has a probability less than one. (P2) If reason were the basis of our beliefs, then we would have no beliefs. (follows from (Pl)) (P3) We in fact do have beliefs. Hence, (P4) Reason is not the basis of our beliefs. The argument has not been particularly well received. D. C. Stove, for example, refers to it as being "not merely defective, but one of the worst 2 arguments ever to impose itself on a man of genius." While not everyone is as unsympathetic as Stove, it nonetheless is difficult to find commentators favorably disposed toward the argument. Various sections of the Treatise are notoriously unclear. ?,??,? is such a section; as such, it is difficult to say just what Hume intended his argument to be. My contention in the present paper is that there are two reasonable ways of reconstructing Hume's argument, both consistent with what Hume writes in ?,??,?. The first reconstruction is clearly unsound; the second reconstruction fares somewhat better. In particular, my contention will be that this second reconstruction, if not sound, is at least valid 4 and contains no obviously false premises. Allow me to make some preliminary comments before presenting these reconstructions. The reconstructions to follow will primarily be concerned with premise (P2) above; in particular, the 126. reconstructions will focus on how Hume can claim that (P2) follows from (Pl). Premise (Pl) is a common 5 sceptical claim, not obviously false, and certainly not unique to Hume. As such, it strikes me that the more interesting part of the argument is Hume's claim that (P2) follows from (Pl), and such will be the focus of the reconstructions (although (Pl) will be discussed toward the end of this paper). Concerning (P2), why does Hume think this follows from (Pl)? His reasoning is contained in the following passage; Having thus found in every probability, beside the original uncertainty inherent in the subject, a new uncertainty deriv'd from the weakness of that faculty, which judges, and having adjusted these two together, we are oblig'd by our reason to add a new doubt deriv'd from the possibility of error in the estimation we make of the truth and fidelity of our faculties. This is a doubt, which immediately occurs to us, and of which, if we wou'd closely pursue our reason, we cannot avoid giving a decision. But this decision, tho' it shou'd be favourable to our preceeding judgment, being founded only on probability, must weaken still further our first evidence, and must itself be weaken'd by a fourth doubt of the same kind, and so on in infinitum; till at last there remain nothing of the original probability, however great we may suppose it to have been, and however small the diminution by every new uncertainty. No finite object can subsist under a decrease repeated in infinitum; and even the vastest quantity, which can enter into human imagination, must in this manner be reduc'd to nothing. (T182) Not for nothing did I claim that this section of the Treatise is unclear. At best, I can discern only the outline of Hume's reasoning, which seems to go as follows: first, when we assign a probability to some 127, proposition, reason dictates that we re-evaluate this probability. In particular, reason dictates that we "add a new doubt deriv'd from the possibility of error in the estimation we make of the truth and fidelity of our faculties." Note that Hume never specifies the object of this 'new doubt.' He might mean a) that our doubt concerns whether the probability we assigned the proposition is correct, or b) that our doubt concerns the evidence on which we based the assignment of that probability. Whatever the case, this 'new doubt' must "weaken still further our first evidence," presumably resulting in a lowering of the probability we originally assigned to the proposition. We then repeat this doubting process, adding new doubts of the same kind in infinitum, "till at last there remain nothing of the original...