what do we mean by philosophy of physics or math what does it tell us about them ? Does it tell about how these disciplines of knowledge develop? For example to develop math we use axiomatic approach and for physics we use scientific method.

  • I'd say that philosophy-of-x tends to be to steering the wheel, digesting the foundations of the science and pushing the boundaries while trying to understand which topics should be more relevant and researched. – Yechiam Weiss Apr 1 '18 at 15:07

The axiomatic method is what people think of when they hear the term philosophy of mathematics. It's an important idea nevertheless it's not the only idea in the philosophy of mathematics, and because of this - it's over-rated; for example, cohomology is an important notion in mathematics; and it has an axiomatic formulation, but this tells you very little about what cohomology is, and why it's important; its use-value, that is as used by mathematicians in the world of mathematics gives a much better indication of what it is; use gives ontology here. Robert Langlands, who is famous for the Langlands programme, said:

Our difficulty is not the proofs, but learning what to prove

In fact, a major part of his work is reformulating non-abelian class field theory, an important part of number theory; it's usually called the Langlands programme but I have also heard it referred to as the Langlands philosophy.

I also think its a mistake to think that the philosophy of mathematics, physics and science more broadly must only reflect on the problems of these subjects, or their inter-relationships or their foundations; these subjects are embedded in society, and an important part of philosophy is to investigate the relationship of these subjects to the larger society.

For example the notion of algorithm is a mathematical concept and today we have such things as algorithmic trading, predictive policing and other ways in which the use of algorithms affect the wider society. The recent scandal with Cambridge Analytica highlights some of the dilemmas that a philosophy of algorithms might help frame.

  • So you are saying that discovering the development process of these disciplines of knowledge is one of the area of their philosophy but not the only one there are many other things when we say their philosophy. – Remy Apr 1 '18 at 13:40
  • And when you say that when we think of philosophy of math axiomatic system comes to mind. The scientific method is equivalent to axiomatic system in physics which has its own philosophy what does that tell us about the scientific method. – Remy Apr 1 '18 at 13:50
  • @remy: yes to your first comment; but no to your second - the scientific method is not equivalent to the axiomatic method. – Mozibur Ullah Apr 1 '18 at 16:25
  • By saying equivalent i meant to be their role in those disciplines that is to develop not that they are same process – Remy Apr 1 '18 at 16:41
  • @remy: ok, thanks for your clarification. – Mozibur Ullah Apr 1 '18 at 16:52

Philosophy of science is completely superfluous for the working physicist - according to Feynman's ironic statement

The philosophy of science is as useful to scientists as ornithology is to birds.

To explain why muons reach the earth before decaying, you need some knowledge about time dilation from the Special Theory of Relativity. And to prove that a^n+b^n=c^n, n > 2, has no non-trivial solution, you must understand the sophisticated mathematics of Wiles proof of the Shimura-Taniyama-Weil conjecture. In both cases, philosophy of physics and philosophy of mathematics did not contribute any piece of insight to the answer.

Nevertheless, in mathematics there are certain foundational questions around set theory and some philosophizing along the lines "Which ontological state do mathematical objects have?" But these questions do not find a generally accepted answer. In addition, most working mathematicians care about such issues at most on Sunday morning, when other work is done.

Possibly this answer sounds a bit harsh. Please note: I do not deny that one can find philosophy of science an interesting subject. And that this type of philosophy can be a satisfying occupation. My point is to stress the irrelevance of this field to the working scientist as Feynman stated above.

  • It's muons not myons. You don't need philosophy to to spell correctly either. – Mozibur Ullah Apr 1 '18 at 11:52
  • Thanks, I corrected the "muons". I apologize, being not a native speaker I used the German term. – Jo Wehler Apr 1 '18 at 11:57
  • Your summary seems correct to me. Philosophy is a global study and once it is called 'philosophy of something or other' it ceases to be itself. Philosophy cannot be solved or understood piecemeal. – user20253 Apr 1 '18 at 12:12
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    @JoWehler is completely clueless. Special relativity and general relativity are two theories that were motivated by deep philosophical insights. Einstein himself acknowledged it and emphasized the importance of philosophy of physics in foundational work. – sure Apr 2 '18 at 7:47
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    @JoWehler en.wikipedia.org/wiki/… You don't need this quote in any case, if you understood special relativity and general relativity, or the contribution of Einstein to the foundation of QM. – sure Apr 2 '18 at 8:36

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