Summary: the problem with Pascal's Mugging arguments is that, intuitively, some probabilities are just too small to care about. There might be a principled reason for ignoring some probabilities, namely that they violate an implicit assumption behind expected utility theory. This suggests a possible approach for formally defining a "probability small enough to ignore", though there's still a bit of arbitrariness in it.
Ok, so care to present an a priori pure logic argument for why St. Petersburg lottery-like situations can't exist.
FInite approximations to the St. Petersburg lottery have unbounded values. The sequence does not converge to a limit.
In contrast, a sequence of individual gambles with expectations 1, 1/2, 1/4, etc. does have a limit, and it is reasonable to allow the idealised infinite sequence of them a place in the set of lotteries.
You might as well ask why the sum of an infinite number of ones doesn't exist. There are ways of extending the real numbers w... (read more)