JGWeissman 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: JGWeissman 18 April 2010 12:52:05AM 0 points [-]

The standard model of Peano arithmetic is 0={} and S(X)=Xunion{X}; its objects are all finite sets.

The set of all objects in this standard model is infinite, even though Peano arithmetic does not refer to this set.

I fail to see any meaningful sense in which ""There does not exist a time T after the present such that I am not alive" has a "hidden reference to infinity" which is somehow avoided by saying "For any duration N and probability epsilon, there exists a longer duration M such that..."

The difference is that in my version, utility is assigned to states of a finite universe. To the extent that there is a reference to infinity, the infinity describes an abstract mathematical object. In your version, utility is assigned to a state of an infinite universe. The infinity describes physical time, it says that there is an infinite amount of time you will be alive.

Comment author: Academian 18 April 2010 01:05:31AM *  0 points [-]

The difference is that in my version, utility is assigned to states of a finite universe.

That's true. You prefer to assign infinitely many utilities to infinitely many states of possible finite universes, and I allow assigning one utility to one state of a possibly infinite universe.

I think the reasons for favoring each case are probably clear to us both, so now I vote for not generating further infinities of comments in the recent comments feed :)

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