One could still argue for non-realism/formalism by appealing to ontological minimality, i.e., let’s not assume the existence of mathematical structures or facts unless there are good reasons to, but I feel like the arguments in favor of some types of mathematical realism/platonism (e.g., universe and multiverse views of set theory) are actually fairly strong
What are they, then? (I mean, I am familiar with the standard ones, and don’t find them convincing).
(and most working mathematicians and philosophers of math are realists probably for good reasons). For example one line of argument is that when mathematicians reason about math outside of a formal system, e.g. large cardinals, their reasoning still seem to be coherent and about something real.
What does “seems” mean here? Literally their subjective feeling about what they are doing?
And what does coherence have to do with reality? Surely, you can have coherent fictions.
What are they, then? (I mean, I am familiar with the standard ones, and don’t find them convincing).
What does “seems” mean here? Literally their subjective feeling about what they are doing?
And what does coherence have to do with reality? Surely, you can have coherent fictions.