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One of the most important problem is the question of logic and its relation, or lack thereof, to mathematical logic. Once mathematicians started to develop their own method of logic, in the 19th century, mathematicians gradually came to be almost universally regarded as the experts on logic, probably to the chagrin of philosophers interested in or working ...


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'seperate' 'between' 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, ...


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There are many geometries. Most of us are familiar with the Euclidean, having Descartes' coordinate grid superimposed on it. This grid naturally leads us to think in terms of points. Set theorists are apt to follow that convention. But the real world is closer on a large scale to the Minkowski spacetime geometry of Relativity theory, modified on a minute ...


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"Impossibility" assumes a fixed logic frame, preceding the possible existence of any universe. Logicians consider Logic itself to be contingent -- IE there are potentially infinite versions of logic. So "impossible" carries its own caveat: "within X logical reference frame". https://math.vanderbilt.edu/schectex/logics/


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What you call "physical reality" was called by Kant noumenon or thing-in-itself. We can't know it, we don't know it, we have no access to it. Its counterpart is phenomenon, what we can perceive and cognize, which is subjective for every individual. Reality is just a structure of ideas, based on perception, that exists in each individual mind. Therefore, a “...


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Math is based on logic and logic is based on physical experience. Therefore there is no difference between physical and mathematical "truths" other than the level of abstraction. You could of course make up alternative logics that are not based on experience, but these wouldnt lead to any useable "truth". If mathematically I define bananas to be the same as ...


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The proof of physical truth is your own consciousness. Your direct awareness of some phenomena cannot be proved by any external or material means. In this sense, your direct conscious experience of Sun in undemonstrable (and all people know this). At the same time you have no doubt that you are experiencing the Sun. And you don't need any proof because you ...


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Mathematics largely deals with formal systems. For example, much of modern mathematics can be constructed in terms of set theory. Once the formal system is established, mathematical "truths" are derived based on the formal rules of the system. If we consider chess as another example of a formal system, then a true statement is loosely equivalent to a ...


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Yes. Reading Kripke's works is very different than reading a math book on set theory, principally because his interests are in "meta" issues, and his works (books), are comprised of his lecture series, in many cases. But if, you do have an understanding of Philosophy of Language and Logic that's derived from your understanding of Frege, Russell, and ...


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The reason for this difference is due to relativity. By relativity I mean "the state of being judged in comparison with other things and not by itself." Physical reality is based on physical world and we know that it is ever changing. Therefore we cannot establish physical truths. Unfortunately we are not even aware that if there is another, that ...


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