On Pascal's Wager and mathematical proofs

On Pascal's Wager and mathematical proofs on Young Republic:

A: If you look at my previous email on Pascal's Wager, you'll find a proof (given some conditions) that the expectation is somewhere between minus and plus infinity, and that you can't hope for anything better unless you break one of the conditions.

B: Since probability is at best a model of reality (albeit an accurate one most of the time), I'd say it's flawed to push it to its breaking point like this. I'm not saying your proof is wrong, I'm just saying the assumptions are questionable. In general when math returns an answer of "undefined" for what ought to be a practical problem it means that the model isn't applicable anymore.

A: Well, which assumption did you find questionable? It isn't that it's undefined, but that it's somewhere between minus and plus infinity. What my proof showed is that unless you can better define the conditions, there is nothing meaningful you can say about the expectation value of a generalised Pascal's Wager. Maybe you can better define the conditions. I'd like to see you or anyone try!

B: I found the assumption that math is a suitable means of dealing with the problem questionable. I emphasise that math is an abstract tool for thinking about things and should not be taken as literal truth - we do not live in a universe of Platonic ideals. As I said, when you run into infinities when doing the math, it's often viewed as a mathematical oddity and a sign that the model is being pushed too far. Examples include mechanics (structural, fluids) and even basic stuff like the E and M inverse square law (at distance zero, is the intensity of radiation really is infinite?).

Mathematically, I think that the proof looks all right: if the events you mentioned have finite measure and the attached r.v. X = "afterlife utility" has values +/- inf over the set of events in question, then the integral/sum over the sample space does yield "inf-inf = undefined." I would in fact stress that the computed answer is actually any value between +/- inf /inclusive/, but then I'm just a math pedant. I am also an engineer by training, so my instinct there is to chuck the math when it stops making sense.

Just a note: since human minds may not actually be able to perceive infinite utility or disutility, it may not even make sense to define X = +/- inf (notice that monotonically increasing to some finite upper bound makes some sense in that we can always define event A as "worse" or better than disjoint event "B" but means that there is indeed a finite E(X) ). In either case, I still feel the whole exercise is pretty pointless. Pascal's Wager seems to me a stupid question, a thought experiment, and probably rhetorical.