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It is commonly accepted that Aristoteles was a philosopher and George Boole was a mathematician. When I look at a boolean formula and compare it with an Aristotele's text, it is clear to my eyes which one is mathematics. However, both of them try to be rigorous as possible following certain rules, and the difference between mathematics and philosophy cannot be just a matter of notation. I can see that in the case of Boole rules are defined more strictly and precisely, but this intuitive observation isn't enough for my curiosity.

So, can anyone explain in a formal way when a rigorous reasoning is considered mathematics and when it is not?

  • Comments are not for extended discussion; this conversation has been moved to chat. – user2953 Mar 9 '18 at 13:28
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We cannot find a "formal" and rigorous criteria to separate philosophy from mathematics.

Disciplines are the product of human and historical activities, and thus they change over time.

Aristotle was a philosopher ("the" philosopher) and he was the founder of formal logic: but in his time, and up to the end of 19th Century, formal logic was part of philosophy and not of mathematics.

Ariastotle, despite the fact that his work shows a good understanding of the math of his time, was not a "professional" mathematician, like Euclid and (later) Archimedes.

With Georeg Boole and his Mathematical Analysis of Logic (1847) (but Leibniz was already on this path) logic enetered into the mathematical domain, and the focus of the discipline shifted from formal logic to mathematical logic.

  • What about taking as formal criterion: Mathematics is where you can prove general statements, philosophy is where you can present arguments for general statements, but you cannot prove them. I leave aside the problem of undecidable mathematical statements. – Jo Wehler Mar 8 '18 at 22:54

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