That makes sense. I wasn’t really familiar with surreal numbers, but they indeed seem to be an ordered field extending the reals, and yet also including whatever large cardinals one cares to postulate in one’s foundations.
It looks like there’s a little bit of work already on using surreal numbers for probabilities and utility values, proving a surreal version of the vNM theorem and applying it to various Pascal’s-Wager-type scenarios. This seems like a solid direction if one really does want maximal expressive power in one’s degrees of infinitude.
That makes sense. I wasn’t really familiar with surreal numbers, but they indeed seem to be an ordered field extending the reals, and yet also including whatever large cardinals one cares to postulate in one’s foundations.
It looks like there’s a little bit of work already on using surreal numbers for probabilities and utility values, proving a surreal version of the vNM theorem and applying it to various Pascal’s-Wager-type scenarios. This seems like a solid direction if one really does want maximal expressive power in one’s degrees of infinitude.