-3

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?

doromshadmi
  • 83
  • 3
  • 3
    "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](https://plato.stanford.edu/entries/naturalism-mathematics/#HetNat) from philosophical incursions is vigorously defended by some naturalists, e.g. Maddy. – Conifold Mar 21 '20 at 07:54
  • 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 09:28
  • @Conifold, moreover, please look at your comments to my question at https://philosophy.stackexchange.com/questions/54825/are-mathematical-results-influenced-by-the-way-we-reason in order to see how you actually tend to separate between philosophical and mathematical questions. – doromshadmi Mar 22 '20 at 10:01
  • Separating X and Y is a very long distance away from X and Y having "nothing to do" with each other. For example, physics and chemistry have separate journals, departments, methods, etc., yet have very much to do with each other. You can improve the question by rephrasing it to remove this unnecessary distraction. – Conifold Mar 22 '20 at 10:16
  • @Conifold from my own experience with hundreds of mathematicians around the gloge over the past 15 years, I can ensure you that when discussed about fundamental notions that do not fit their agreements, they are almost immediately direct you to Philosophy by saying "Philisophy is not my framework" . So it is actually not hard at all to think of any philosopher or mathematician who would assert that, because many mathematicians doing it very frequently. Just try to develop a mathematical framework, which does not follow mainstream mathematicians' agreements, and see what actually happens. – doromshadmi Mar 22 '20 at 10:30
  • @Conifold I agree with your remark so I have changed "nothing to do" to "is not an appropriate framework". Yet my previous comment is based on my own experience with hundreds of mathematicians around the globe over the past 15 years. – doromshadmi Mar 22 '20 at 10:40
  • "Philosophy is not my framework" is much better, there is nothing controversial about philosophy not being someone's framework when they are not doing philosophy. Voevodsky developed a new mathematical framework just recently, the Univalent Foundations, and it is largely motivated by internal mathematical considerations. Nonetheless, his papers are very philosophical about developing it based on those considerations. And this is a rule for fundamental frameworks, in mathematics, physics and other fields. This is what methodological autonomy means. – Conifold Mar 22 '20 at 10:44
  • @Conifold isn't "there is nothing controversial about philosophy not being someone's framework when they are not doing philosophy" actually asserts that Philosophy and Mathematics can't be done in the same framework (where such an assertion may be some kind of philosophy)? – doromshadmi Mar 22 '20 at 10:56
  • The word "framework" is very vague. They can have distinct (small time) frameworks, and be brought together in a (big time) framework, which is what typically happens. Of course, most working mathematicians do not deal with big time issues, hence they tend to emphasize the former. Indeed, many are often annoyed by "too much philosophy", or at least indifferent to it. But emotional reactions are not a philosophy. Maddy's is the closest kind of philosophy to what you are looking for that I can think of. As she puts it, when it comes to mathematics proper "*philosophy must give*". – Conifold Mar 22 '20 at 11:05
  • Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/105833/discussion-between-doromshadmi-and-conifold). – doromshadmi Mar 22 '20 at 12:38
  • Does this answer your question? [Can mathematics and physics be thought of as branches of philosophy?](https://philosophy.stackexchange.com/questions/64144/can-mathematics-and-physics-be-thought-of-as-branches-of-philosophy) –  Jan 30 '23 at 01:13

1 Answers1

0

'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.

CriglCragl
  • 19,444
  • 4
  • 23
  • 65
  • To be more concrete, is the rejection by modern mathematicians of, for example, http://www.internationalskeptics.com/forums/showpost.php?p=13028612&postcount=3430 is actually some kind of philosophical response? – doromshadmi Mar 23 '20 at 06:32
  • @doromshadmi: That makes me think of Russell's paradox. Investigating and choosing axioms is exactly philosophy. – CriglCragl Oct 14 '21 at 16:56