May 9, 2007

Probable But Still Unjustifiable

I am attempting to construct an argument against the widely accepted thesis that one may justifiably believe that p based on evidence that makes p probable but which does not guarantee that p. In short, I wish to argue that any belief based on evidence that makes p probable, but with a probability less than 1, is unjustified. My argument utilises a lottery-type analysis†. Imagine a lottery composed of n tickets in which n is large enough to make the following claim putatively true, according to the standard probabilistic analysis, of some particular ticket, t1: S may justifiably believe that her ticket, t1, will lose. For example, most probability theorists would hold that in a lottery of 1,000,000 tickets in which one ticket must win but only one ticket can win, S may justifiably believe that her ticket, t1, will lose. (Of course, S does not know that her ticket will lose, but on the view I wish to impugn she may still justifiably believe that her ticket will lose. You may make n as large as necessary to motivate the relevant intuitions.)

I take it as a truism that a subject may not justifiably believe a set of inconsistent propositions which she recognises to be inconsistent. My argument will take the form of a reductio beginning with the assumption, “S may justifiably believe that her ticket, t1, will lose”, and concluding with the negation of the aforementioned truism. Assuming that the first premise is the least plausible of all the premises in my argument, then my argument should establish that my first premise ought to be rejected. I would greatly appreciate any feedback concerning the structure, validity or soundness of my argument, or questions regarding any of my assumptions or steps. My reductio runs as follows:

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