hajek_dissertation

# hajek_dissertation - 1 Introduction 1 This is not the...

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Unformatted text preview: 1 Introduction 1 This is not the dissertation that in 1990 I set out to write. That one would have been called &amp;quot;Two Dogmas of Conditional Probability&amp;quot;. Realizing that it was overly ambitious, I settled for &amp;quot;A Dogma of Conditional Probability&amp;quot; insteaduntil about three months ago, when I realized that it too was overly ambitious. What remains could be aptly titled &amp;quot;A Hypothesis About Conditional Probability&amp;quot;. I decided that I had better submit it before it devolved to &amp;quot;A Modest Proposal Concerning Conditional Probability&amp;quot;, or worse. This is not to say that I have abandoned the original project. On the contrary, I've become more firmly committed to it, if anything. It strikes me that, by and large, conditional probability has been regarded by philosophers as a relatively uncontroversial and well understood aspect of probability theory. &amp;quot;Conditional probability is simply given by the usual ratio formula, and we know how to understand that .&amp;quot; This encapsulates, I think, an attitude that is prevalent. And I think that it embodies two dogmas. The first is that 'the conditional probability of A, given B' is to be univocally analyzed by the ratio formula, P(A|B) = P(A&amp;amp;B)/P(B). The second is that there is no difficulty in interpreting that ratio; and if pressed for details, people will 1 Large parts of this dissertation will represent my contribution to a paper of the same title, co-authored by Ned Hall, and forthcoming in Eells and Skyrms (eds.) (1993). They are 1 through 5, and 9, although they may receive some editing before publication. I am omitting certain parts of that paper that were written by Hall, but several ideas that I am including (for the sake of smoother exposition and discussion, and for their own interest) are due solely or partly to him; these will all be acknowledged in the main text, or in footnotes. I thank him for letting me use them here. My various other debts to him are also detailed in the main text, and in footnotes. Everything that I have included in the dissertation, with the exception of 5.2, and part of one paragraph in 5.3.1 (and direct quotation), was written by me, although much of it has profited from editorial and stylistic suggestions from Ned Hall, David Lewis, and Bas van Fraassen. As I will indicate again in footnotes at the appropriate places, much of the terminology of 5.2, and part of one paragraph in 5.3.1, is taken from the joint paper, and was written almost entirely by Hall. Again, I thank him for letting me include them here. 2 offer interpretations such as 'the probability of A, upon the minimal revision of P to accommodate B', or 'the conditional betting odds on A, where the bet is conditional on B', as if these were unproblematic....
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hajek_dissertation - 1 Introduction 1 This is not the...

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