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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 make 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 '19 at 10:09
  • What is missing is a "suitable definition of philosophy". – Mauro ALLEGRANZA Jun 25 '19 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. – user20253 Jul 23 '19 at 12:09
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    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 '19 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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Let's separate out two aspects of philosophy. First, there is a broad sense in which philosophy is the study of the application of higher reasoning. This goes straight back to the ancient Greek philosophers in the West (and to other ancient thinkers in other regions of the world): to the Socratic method, or Aristotles system of categorization. Note that for the ancient Greeks math was very much included in this arena. The Greeks saw math as a means of accessing and exemplifying eternal truths about the world.

Second, there is a narrower aspect in which philosophy with the human realm: with morals, virtue, the nature of the self, the rights and duties of people within a social community, etc. This is (in effect) the application of higher reasoning to human conduct and human conditions, with an eye to improving both.

Sciences and maths are clearly philosophy in the first sense, since both are efforts to use higher reasoning to construct models of the universe. We only need to open a journal dealing with any cutting edge in math or science to see people using philosophical methods to try to pin down usable, functional representations. Philosophy in the second sense is akin to what we currently call the social sciences: everything from social theory and sociology to psychology to anthropology. I tend to use the term 'philosophy' for the first sense, and talk about the second sense as 'social theory' or 'moral theory' or such, so in my view, yes, all sciences and maths are offshoots of that greater philosophical focus on higher reasoning, offshoots defined by particular constraints and conventions. Think of science as the philosophy of material substances, constrained by empirical observations, and math as the philosophy of numbers...

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They certainly can be, because they have been. The ancient Greeks thought of mathematics and physics as branches of philosophy. One of Aristotle's works is The Physics, which is followed up by The Metaphysics. He does not treat these topics very differently or put them on separate footings.

But we have since then decided that there is a 'right way' to pursue both of these disciplines, despite there being real philosophical objections to pursuing them that way. They have what Thomas Kuhn would call 'paradigms'. For the sake of effectiveness, and to terminate the circularity of theory-laden definitions, a certain philosophical framework has been promoted above all others by each discipline as it spins off from philosophy and becomes a science. From a philosophical view, the science does not seem to care so much whether it is actually correct, as long as it is effective at moving toward its chosen goal.

This chosen philosophical framework is a philosophical framework. But the job of philosophy would be to continue elaborating and testing it philosophically. That is not welcome to deeply invested practitioners of the science (ask Neil deGrasse Tyson). They want to play out their chosen basis until they find a real problem. At that point, they will fall back and do some philosophical work to find a new paradigm. We see this historically: Things like quantum dynamics and the difficulties in symbolic logic at the start of the last century prompt practitioners to do some philosophy proper in order to address how the results could fit together with previous work. But again, the intention is never to merge back into philosophy long-term, just to get a new set of tools.

So sciences (both natural and 'exact') are wholly contained within philosophy, but they survive by refusing to pursue philosophy most of the time.

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According to some, yes. Physics - or at least the science that makes up physics- may be considered a form of philosophy by some. As another answer on this site helpfully explains, people tried to see sciences like physics as separate from philosophy using the demarcation problem. However, the problem is that this method failed because the criteria for determining if something was 'pure science' or not kept failing by having said criteria being too strong or weak. Some criteria was so strong that some forms of physics - like string theory - did not qualify as science separate from philosophy, which couldn't be right. Some criteria was so weak, things like astrology technically qualified as science. No clear separation could be made and when thinkers such as John Forkosh & Jo Wehler attempted to use verificationist theory to separate sciences like physics from science, criticism came from many people, including other scientific philosophers like Carl Gustav Hempel and mathematicians like Willard Van Orman Quine. Quine (a man who discovered concepts for mathematical set theory & created first-order predicate calculus) concludes in in his paper "Two Dogmas of Empiricism" that it is not possible for scientists to truly escape philosophy or escape ontology/metaphysics as long as mathematics and physics continue to dive into the theoretical:

"Physical objects are conceptually imported into the situation as convenient intermediaries not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer . . . For my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing, the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conceptions only as cultural posits."

Then we have philosopher Paul Feyerabend who argued in that scientific claims are essentially anarchic & that many parts of mathematics and science in the modern world that deal in the theoretical have distanced them from solely depending on the scientific method, but instead an "anything goes" if it logically fits style.

"Is it not possible," asks Kierkegaard, "that my activity as an objective [or critico-rational] observer of nature will weaken my strength as a human being?" I suspect the answer to many of these questions is affirmative and I believe that a reform of the sciences that makes them more anarchic and more subjective (in Kierkegaard's sense) is urgently needed.

Basically, depending on who you ask, math and physics can be branches of philosophy. According to Quine, this branch would be attached to empiricism: The theory that all knowledge is derived from sense-experience. According to Paul Karl Feyerabend and Hempel, modern science would be connected to analytic philosophy (A method of approaching philosophical problems through analysis of the terms in which they are expressed) & possibly epistemological anarchism (a philosophy directly connected to science that literally says the operation of science by fixed, universal rules is unrealistic, pernicious, and detrimental to science itself) due to its chaotic nature that constantly changes our sense of understanding.

Also, as I have mentioned before on Stack Exchange, there is a branch of philosophy called Logicism that is defined by the Stanford Encyclopedia of Philosophy as "a philosophical, foundational, and foundationalist doctrine that can be advanced with respect to any branch of mathematics", so one branch of philosophy is literally connected to any form of math and any advancements in the field of mathematics - meaning there is literally a form of philosophy that is a part of all arithmetic & can only be advanced with new discoveries in mathematics. Here, math is literally a branch of philosophy!

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In essence, your question is like this SE post which asks "how science is related to philosophy". Other closely related question are "is science just a more refined and effective method of philosophy?", "how does one know whether a discipline is a science of philosophy?", and "How should we characterize the relationship between mathematics and philosophy of mathematics?"

If by tree, you mean that math and sciences are types of philosophy, a consensus would be no. A fork and a spoon are two tools for two different tasks. But, to extend the metaphor, a spoon could be shaped into a fork of sorts in the same way that questions that appear in science often mature to the point they become sciences in their own right. In fact, physics which is often considered a model for other sciences (rightly or wrongly), was originally a branch of philosophy; math, physics, and philosophical theory all have different aims, but they are all practices and theories.

To understand why that is, one has to ask questions like "what is philosophy" (which is metaphilosophy), "what is science" (which is philosophy of science), and "what is mathematics" (which is philosophy of mathematics). These involve the general question of definition, the process which is highly philosophical in nature.

Some philosophers, such as W.V.O Quine, believe that how we come to knowledge (which is called epistemology) should largely be just science itself. This is called a naturalized epistemology, and these philosophers theorize that knowledge is on a continuum where the theories of philosophy and the theories of science are very closely related. Other philosophers reject this forcefully. The relationship between mathematics, logic, and philosophy is also a topic of great interest. This problem is known as the foundations of mathematics. See "Where is the border between philosophy and mathematics?".

It should be noted that definitions are notorious in philosophy for being problematic and go back to ancient Greece where philosophers like Plato argued incessantly and stubbornly about definitions. From the article:

When Plato defined a human being as a bi-ped without feathers, Diogenes is said to have plucked a chicken and presented it in Plato's classroom, crying, "Behold, Plato's human being." Plato allegedly replied that his definition would now need to be revised, but this concession to a critic seems to have been an exception rather than the rule.

This question will certainly generate controversial answers because words like 'philosophy', 'science', and 'mathematics' are themselves contentiously defined. For instance, while most people seem to presume there is one thing called science, philosophers of science generally disagree and believe the problem may be unresolvable. This is known as the demarcation problem of science.

Your question, however, is a challenging one, because non-philosophers often are educated very lightly on what science, math, and philosophy are. In my state in the US, for instance, math educators aren't even required to be math majors (which is typical in the US). The best way to come to an answer is to study all three!

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