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I think that they can be viewed like that, with some suitable definition of philosophy.

Then mathematics could be defined as one of the branches of philosophy in which theories are built on definitions and axioms and the results are proven and physics can be thought of as some kind of philosophical theory of laws of nature (you know the full Latin name of Newton´s book Principia) that are seeked both experimentally and by constructing mathematical models.

I know this is a naive question, and it reveals my amateurism in the field, but, does this makes any sense to you?

I do not see anything particularly unphilosophical in math and physics, so, what would be some problems if we would define them to be branches of philosophy?

Would then some change be needed in the definition of the scope, range and reach of philosophy?

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    Try to be more specific, we already have a number of threads discussing philosophy vs sciences: Are philosophy and science mergeable today?, How is Philosophy related to Science? A field becomes a science, and splits off from philosophy, when it is sufficiently established, subjectwise and methodologically, to resolve issues more or less uncontroversially. Philosophy deals with issues that can not be so resolved. The two have complementary purposes, and merging them is counterproductive. – Conifold Jun 22 at 10:09
  • What is missing is a "suitable definition of philosophy". – Mauro ALLEGRANZA Jun 25 at 6:43
  • A field that becomes a science does not cease to be part of philosophy, but as a science it may become a specialist discipline that ignores its own wider philosophical context. Thus when we examine the foundations of these sciences they become philosophy again. Mathematics and physics reduce to metaphysics if we study their foundations because this is their root and origin. If we are not interested in foundations and context then the philosophical basis of these sciences may be largely ignored. But ask what a number or a physical object really is and you're doing philosophy. – PeterJ Jul 23 at 12:09
  • It would be pretty old fashioned to include mathematics and physics under philosophy. Such a definition would not be widely accepted, and one wonders what you'd gain from trying to hold to it against the mainstream? – transitionsynthesis Jul 23 at 16:04
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One needs to distinguish between Mathematics and Meta-Mathematics. In my opinion the first is a science and the second is Philosophy. An example of the later is Kurt Godel's incompleteness theorems which have nothing to do with mathematical calculations or practice in particular but have vast relevance to how one thinks about mathematics in the abstract and in the strategy for creation of new systems.

Although I am less familiar with Physics, that field can likely also be split into a scientific branch and a philosophical branch.

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