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When deal with fundamental notions, many mathematicians and some philosophers agree that Philosophy is not an appropriate framework for mathematical frameworks' developments.

Is the attempt to separate between Philosophy and Mathematics may be considered as some kind of Philosophy?

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    "Nothing to do" is factually false, and it is hard to think of any philosopher or mathematician who would assert that. Historically, the development of modern mathematical frameworks (first order logic, set theory, axiomatic method) by Frege, Hilbert, Russell was very much motivated by philosophical reflections and often done by philosophers and philosophizing mathematicians. However, the methodological autonomy of mathematical practice from philosophical incursions is vigorously defended by some naturalists, e.g. Maddy. – Conifold Mar 21 '20 at 7:54
  • Not very clear... since Ancient Greek science, mathematics was separated from philosophy. This does not mean to deny that there are interesting philosophical problems emerging from mathematics. – Mauro ALLEGRANZA Mar 21 '20 at 11:23
  • @MauroALLEGRANZA Plato's Academy taught mathematics as a branch of philosophy. Archytas, Pythagoras and Aristotle spring to mind as adept at both, there must have been many others. – Guy Inchbald Mar 21 '20 at 17:42
  • Please look at StackExchange forum, It separates between Philosophical and Mathematical discussions even about fundamental notions like Infinity, Set, Natural numbers and so on, so "nothing to do" is not clearly false. – doromshadmi Mar 22 '20 at 9:28
  • @Conifold, moreover, please look at your comments to my question at philosophy.stackexchange.com/questions/54825/… in order to see how you actually tend to separate between philosophical and mathematical questions. – doromshadmi Mar 22 '20 at 10:01
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'seperate' 'between'

Fields Arranged By Purity from XKCD, edited by a fan to include epistemological philosophy

The usual perspective is that philosophy deals with 'meta' concerns. When mathematicians do meta-mathematics it becomes philosophically significant.

But once the tools and methodology of a discipline are accepted, it ceases generally to be of concern philosophically, at least in terms of epistemology. This is an issue of structure, that philosophy and theory of knowledge attempt to stand outside of certainties and consider definitions and assumptions. There is also the practical concern, that to get to the areas of development and innovation in physics and mathematics takes typically not only degrees but a career dedicated to the subject.

Demarcation, the attempt to delineate what is and is not within a field, is intrinsically philosophical because it is dealing with definitions.

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