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Anto's avatar

Hey, that's very interesting, to me! :)You talk about a mutual society based on recongnition of each other's utility/humanity and equally exchanging?

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Peter Gerdes's avatar

Three comments:

First, infinite values in pascal's wager have been studied at length in philosophy (tho IMO no compelling new arguments).

Second, infinite values do nothing to resurect the argument in Pascal's wager.  At best they allow one to conclude that either belief or non-belief in god is the utility maximizing strategy (no ties) but without the argument that the utility given to belief is larger you lose all the features that made the argument interesting.

Third, infinite utilities really aren't utilities in the standard sense.  Utilities (in the Von Neumann and Morgenstern sense) must be chosen from something very much like a real field (field with ordering) though it might be possible to do in something like a division ring.  Infinite cardinalities simply don't form such a structure (though there are real fields with 'infinitary' values...take a non-standard model of the integers and extend it in standard way to a field).  Worse, I believe you have to draw your probabilities from the interval [0,1] in the same real field as you draw your utilities to maintain the nice features of utility (probabilistic mixtures of outcomes take on all values between the outcomes...i.e. probability is at least as discriminating as utility).  This means  you can always pair an arbitrarily large utility with a sufficiently small probability so it is outweighed by an arbitrarily small utility with high probability.

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