Philosophy of Mathematics

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Specifically in Mathematics perhaps it is difficult to make a distinction between Mathematics as a discipline and Philosophy of Mathematics on the one hand, and Applications of Mathematics on the other. A testament of the foundational characteristics of this discipline (together with Logic). Pure Mathematics is concerned with Mathematics as a distinct discipline for no ulterior purpose. This page covers Historical developments, Foundations, including Set theory and Methamathematics. There are overlaps with Formal Logic.

Foundations of mathematics

Closely overlapping with Mathematical Logic, Formal Logic, Metamathematics. Also Abstract Mathematics. Tendency to see the foundations of logic migrating from Philosophy into Mathematical Logic. The four pillars (could arguably also be part of Pure Mathematics and Mathematical Logic): Set Theory, Proof Theory, Model Theory, Computability and Recursion theory. Other themes are Algebraic Logic, Type Theory. See also Number Theory

Mathematical reasoning intimately dependent on rigorous logical reasoning, thus concepts of Truth, Statements, Sets, Functions important.

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