By Roy Harrod (auth.)
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Extra resources for Foundations of Inductive Logic
The first and foremost is that this ascription of equal initial prior probabilities is entirely unwarranted. It involves assumptions about nature that we have no right to make. I do not believe that its more sober defenders have any good reasons to recommend it, but rather have adopted it as a counsel of despair. They have felt deeply, and as I contend rightly, that induction must be valid, and have clutched at this principle as the only available resource for vindicating it. But that is not good enough in logic ; we must be patient and think again.
It must presumably be conceded that if the course of events jars sufficiently with the predictions, this will have the negative effect of tending to discredit the original ascription of probability. This is an inductive argument. But just as direct probability theory has nothing to say about why it is ever right or proper to make the initial ascription, so by itself it provides no apparatus for determining the amount by which that ascription is undermined. Direct probability theory is concerned with the consequences of a probability ascription within the hypothesis ; it has nothing to say, ex ante or ex post, about the degree of probability of the hypothesis.
We may indeed find rescue from this apparent contradiction by saying that the tenet in question does not concern empirical matters directly, but concerns knowledge about empirical matters, in fine that it is a higher order tenet ; some may suspect, however, that the possibilities of knowledge in regard to empirical matters must depend in part upon the nature of the empirical matters. We shall return to this problem at a much later stage of our enquiry. Meanwhile we shall abandon further consideration of this denial, and approach the subject in a positive way - namely by analysing the nature of the evidence and the valid grounds for belief that arise in the empirical sphere.