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[uCan-Post]
May I humbly suggest that there is no such thing as “thinking mathematically,” any more than thinking biologically or thinking astronomically or thinking anatomically or thinking chemically or thinking automotively, etc. Mathematics is the study of the existence and properties of the objects of mathematics, the same idea as every other science and field of knowledge. I think it is very sad that we do not recognize that convincing is not the same as explaining. Proof in mathematics is about verification, substantiation, corroboration, validation, justification, authentication, certification. It does NOT explain.
Consistency does not EXPLAIN. I have been reading and thinking about explanation for many decades and wish many others would realize that we have no science of explanation but badly need one and take the need seriously. We need to clarify the meaning of explanation and conditions for explanation and stop substituting conviction for explanation.
I admire your efforts and your works. I do not mean this as a criticism of you specifically.
Thank you,
George Frank
P.S. Erlina is a very pleasant musical name.