To my perspective that infinities are equal is a unfounded intuitiion. Reading a surreal proof on how w+1 is strictly greater than w is partly amazing how you can have claims about infinities without relying on intuition (ie can actually proove stuff). Then a law like “infinity + infinity = infinity” starts to feel like “positive + positive = positive”, “positive” is not a number but a quality. There is additional structure in “2+2=4″ than that positivity is preserved.
In the same way that if one option has negative utlity and one options has positive utility you can safely choose the positive one without regard to the actual magnitude so it is also safe to choose a transfinite positive over a finite positive.
If the theory doesn’t treat finites in a special way (is finiteness-ambivalent) then the core material should transfer for applicable parts to the transfinite domain.
To my perspective that infinities are equal is a unfounded intuitiion. Reading a surreal proof on how w+1 is strictly greater than w is partly amazing how you can have claims about infinities without relying on intuition (ie can actually proove stuff). Then a law like “infinity + infinity = infinity” starts to feel like “positive + positive = positive”, “positive” is not a number but a quality. There is additional structure in “2+2=4″ than that positivity is preserved.
In the same way that if one option has negative utlity and one options has positive utility you can safely choose the positive one without regard to the actual magnitude so it is also safe to choose a transfinite positive over a finite positive.
If the theory doesn’t treat finites in a special way (is finiteness-ambivalent) then the core material should transfer for applicable parts to the transfinite domain.