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People speak disparagingly about blowing one’s own trumpet. But who else can be relied upon to blow it? So here is my effort to explain how uncritically accepting mathematical folklore about proofs can lead of computationalism about mind: https://link.springer.com/article/10.1007/s11229-022-03812-w#Abs1

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It is not actually clear what the relevance of the precise definition of understanding is to the phenomenon of computerized mathematics. Can we not be a bit selfish and, instead of asking whether computers will understand mathematics, focus on the less philosophically fraught question of whether computers will help us understand mathematics in new ways by producing explanations that instill novel insights?

The conjectures that (1) they will and (2) all this computerized reasoning™ stuff will be required to do that seem like relatively concrete empirical claims (and hard ones to dispute, at least to me). (One can remove the answer of "they already have" by demanding the "explanations" occur in natural language and not graphs and datasets, I think.)

But I guess I can see a partial counterargument to the above selfishness! If one meets, e.g., a new graduate student, both "I don't care at all if you understand these new ideas, I just care if you can explain them to me" and "I don't care at all if you can explain these new ideas to me, I just care if you understand them yourself" would be inappropriate attitudes to take. So maybe both questions are worth studying in tandem.

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Thank you Michael, wonderfully illuminating. Hillary Putnam abandoned the computational theory of the mind for me good reasons. Why reduce intelligence to the how and abandon the why, to goal achievement rather than goal imagination, to be providing answers rather than discovering questions?

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