Academian comments on VNM expected utility theory: uses, abuses, and interpretation - Less Wrong

21 Post author: Academian 17 April 2010 08:23PM

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Comment author: Academian 18 April 2010 12:17:48AM 0 points [-]

No, I mean that there are no infinite sets in first-order Peano arithmetic. The class "natural number" is not an object in Peano arithmetic.

Comment author: JGWeissman 18 April 2010 12:23:03AM -1 points [-]

First-order Peano arithmetic does not explicitly refer to sets, infinite sets, or natural numbers, but it describes them.

Comment author: Academian 18 April 2010 12:37:04AM *  -1 points [-]

Correct. Nor does "There is no time of death" refer to a set. You can model it as quantifying over a "set of times" if you like, just as Peano arithmetic can be modeled as quantifying over a "set of numbers", but this does not mean the theory refers to sets, or infinity.