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principle of insufficient reason.pdf

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Some notes on R. Collins’ indifference principle
Ben Wallis
2010 Jul 30
In June of 2009, Wiley-Blackwell published The Blackwell Companion to
Natural Theology, an impressive collection of ten carefully-crafted Christian
apologetic treatises. In the third of these, philosopher Robin Collins cites the
“fine tuning” of physical constants at which cosmologists occasionally express
marvel, and incorporates related scientific observations into a rigorous argument
for the existence of God. I do not intend this paper to address that argument in
its entirety. Instead, I mean only to reject one specific element of his case, called
the principle of insufficient reason, or, more commonly, the principle of indifference (hereafter PoI). The following, then, is a very rough sketch of rebuttals
to Collins’ defense of the PoI, as well as some of my own arguments against it.
The PoI has been discussed in some fashion or another as early as the eighteenth century, and perhaps even before then.1 In modern language, and in
its broadest form, it states that if, for some random variable Y , we have only
knowledge of its sample space, and no other relevant information, then we ought
to assign to Y a uniform distribution. In recent years philosophers and statisticians have occasionally revisited the PoI in academic literature, attempting to
find some consistent and defensible formulation; of the textbooks I’ve encountered, however, most are either silent on the issue,2 or in some cases dismiss it
as problematic and controversial.3 In Blackwell, Collins attempts to justify his
own version, which he calls the restricted principle of indifference, and which
states that
1 Hacking, Ian. “Jacques Bernoulli’s Art of Conjecturing,” The British Journal for the
Philosophy of Science, vol.22, no.3, (Aug. 1971), pp209-229.
2 A sampling of textbooks which are silent includes DeCoursey, Stat. & Prob. for Eng.
App. w. Mic. Excel (2003), Grinstead, Intro. to Prob., 2nd rev. ed. (1997), Khuri, Adv.
Calc. w. App. in Stat., 2nd ed. (2003), Montgomery, App. Stat. & Prob. for Eng., 3rd ed.
(1997), Mukhopadhyay, Prob. & Stat. Inf. (2000), Ross, Intro. to Prob. and Stat. for Eng.
and Sci., 3rd ed. (2004), Rowe, Multiv. Bayes. Stat., Models for Source Separ. & Signal
Unmix. (2003), Ryan, Mod. Eng. Stat. (2007), Soong, Fund. of Prob. & Stat. for Eng.
(2004), Wackerly, Math. Stat. w. App., 7th ed. (2008), Wasserman, All of Stat., A Concise
Course in Stat. Inf. (2003).
3 For example, one textbook remarks on the PoI thusly: “The principle of insufficient reason sounds fine. But there are real problems. Would you say it is equally probable that
a car is red or not red? Or that it is red or blue or green or some other color? The
principle quickly leads to a lot of paradoxes.” Hacking, Ian. An Introduction to Probability and Inductive Logic, 2001, Cambridge University Press, ISBN 0-521-77501-9, p143.