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principle of insufficient reason.pdf

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when we have no reason to prefer any one value of a variable p over
another in some range R, we should assign equal epistemic probabilities to equal ranges of p that are in R, given that p constitutes a
“natural variable.”4
Collins offers a three-fold defense of his principle: First, it is widely used;
second, it is often our only means of assigning probabilities; and third, physicists
have empirically confirmed it. While all three arguments seem superficially
plausible, I regard them as ultimately unpersuasive, for various reasons which
I shall elucidate here. I therefore address each of them in turn, adopting the
same order in which they are presented in Blackwell, for the purpose of casting
doubt on the principle. Afterward, I will briefly outline three counter-arguments
against it. By the end of the paper, I hope to have drawn attention to what I
see as serious problems in Collins’ restricted PoI.
We henceforth begin with his first supporting argument: If statisticians already use some form of the PoI in order to work with probabilities, then we may
feel comfortable in perpetuating that tradition by applying it to the fine-tuning
argument. Collins cites philosopher Roy Weatherford for support, who insists
that “the Principle of Indifference is the major theoretical justifications [sic] for
the equiprobability of alternatives in dice games and is therefore the principal
source of initial probability in such cases.”5 Yet I find Weatherford’s suggestion highly implausible. Are we really unable to justify uniform distributions
in dice games without appealing to some recondite philosophical principle? I
readily grant that our intuition may play some significant role in motivating
our exploration of uniform distributions in certain probability models, but it
cannot and indeed does not justify any eventual decision to assign such distributions. Rather, the accuracy of uniform distributions is verified empirically, by
observing, to extend Weatherford’s illustration, the results of dice games, and
our high rates of prediction of the outcomes thereof. Now, nobody can deny
that many successful probability models have been constructed using uniformly
distributed random variables, but we ought not misinterpret those assignments
as being justified by a generalized principle based on intuition. So I disagree
with Collins that the predictive success of uniform distributions in particular
contexts (e.g. dice games) justifies using uniform distributions whenever we’re
not sure what else to do. In short, I can find no empirical support for treating
the uniform distribution family as a catch-all for situations where we have only
meager information.
Yet one might point out that the recognition of key common features of
such contexts where uniform distributions are successfully applied is precisely
what enables us to generalize the PoI. In the second prong of his defense of his
restricted version, Collins provides an example case regarding a twenty-sided die.
4 Collins, Robin. “The Teleological Argument: An Exploration of the Fine-tuning of the
Universe,” The Blackwell Companion to Natural Theology, ed. William Lane Craig and J.P.
Moreland, ISBN 978-1-405-17657-6, p234.
5 Weatherford, Roy. Philosophical Foundations of Probability Theory, 1982, ISBN 0-71009002-1, p30. http://books.google.com/books?id=B809AAAAIAAJ