A stupid question about infinity
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Feb25-12, 01:23 AM
this underscores, in my opinion, that sets are not, perhaps, the "ideal" concept for expressing things we wish to be undeniably true. they are just the best we've come up with...we may hit upon a better idea at some point (or: what i feel is more likely, come up with a different primitive concept that has sets as one possible variant).
Sounds like you would be interested in topos theory.
personally, i believe that ideation is subtler than the symbolism we come up with to express it. that "what is out there" and "what we expereience in here" does not admit of a complete description.
This is more the difference between first order and second order logic rather than set theory versus alternatives.