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Sunday, April 11, 2010

The Q-device

In a blog post dated 2010 Mar 17, mathematician and philosopher Alexander Pruss expressed some interesting ideas regarding probability and countably infinite samples in an attempt to show an absurdity which would, in his judgment, lend support to the claim that the existence of what he and others call "actual" infinite collections of physical objects is impossible.[1] He suggests a set of hypotheses which, taken together, appear to violate our intuition regarding probability. While I do not believe this constitutes evidence against actual infinities, I find the argument interesting in another way which I shall discuss here. In particular, I maintain that we ought not assign probability values under certain conditions whereby the probability measurements in question are insufficiently interpreted. Paul Castell calls this position abstention,[2] and Pruss's ideas yield an opportunity to give an example of how we might find reason for adopting it.