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I am essentially asking whether one could come to intuitively understand how a statement (the use of statement is intentionally vague) fits in with a universe of statements regardless of familiarity. For example, such a person might be able to synthesize a new statement from a set of statements in multiple different ways. They might be able to quickly intuit a set of statements that together are sufficient to synthesize another statement. If such a person were given two theories, perhaps they would be able to see how they might fit together. If such a person exists, I imagine that their understanding of the structure of mathematics would be much more profound than what I described above.

If it is possible for such a person to exist and has existed, is there effective practice that would condition the brain to think in the manner necessary?

PythonCZX
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  • Exemplary question but probably beyond the scope of MSE – tryst with freedom Jan 26 '23 at 21:17
  • Seems more philosophical than mathematical. My guess, for whatever that's worth, is that any attempt to make this precise winds up with Undecidable problems. For instance, if one regards relations in a group as "statements", which seems natural enough, then it is in general Undecidable when a collection of relations yields the same result as some other collection. – lulu Jan 26 '23 at 21:20
  • @MarianoSuárez-Álvarez (1) Rather, I want to know whether it is possible to have an intuition for something that carries over to unfamiliar domains. I mean unfamiliar in the sense that it is unlike things encountered before, not in the sense that one hasn't yet understood. (2) Mentioning a hypothetical person was a mistake, I suppose. I don't care about whether such a person exists, I only mentioned such a hypothetical person to communicate what I meant in the title and to acknowledge the fact that my question is predicated on such a person being able to exist in the first place. – PythonCZX Jan 26 '23 at 22:42
  • But if the answer is still the same, I will concede that the question was asked mistakenly. – PythonCZX Jan 26 '23 at 22:43
  • @MarianoSuárez-Álvarez Fair enough, I'll drop the question then. – PythonCZX Jan 26 '23 at 23:11

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