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Alfred Tarski in his next study (Some Methodological Investigations on the definability of concepts, TARSKI, Logic, Semantics, Metamathematics. Papers from 1923 to 1938. Clarendon Press, Oxford, 1956, 296-308.) describes the parallelism between concepts and theorems:

  • axiom - primitive concept,

  • theorem - defined concept,

  • proof and its rules - definition and its rules.

I always thought this was mysterious, and I might have noticed myself.

My question would be that, apart from Tarski's study, there are other sources, research in this direction. Or what could be the deeper reason for far-reaching parallelism?

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    $\begingroup$ (Just a comment as I don’t have time for a full answer now.) This is a huge and deep connection that’s been extensively explored informally and formally by many logicians since, between maths, computer science, and philosophy; the keyword for modern writings on it is the Curry–Howard correspondence. Among other authors, Per Martin-Löf has written extensively on the mathematical–philosophical aspects. $\endgroup$
    – Peter LeFanu Lumsdaine
    Commented Apr 8, 2019 at 10:41

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