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I found a quote that seems to answer my question in the negative. "Resnik maintains that holistic considerations may license the introduction of new entities, new methods, and new fundamental laws into a theory, but that they do not extend to the more global theories, where mathematics is singled out as the most global theory we possess." From The ...


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As I see it, the whole point of holism is to understand that real world objects are indeed more than the sum of their parts, something that arithmetic typically overlooks. If I were to cut you into slices (and for the avoidance of doubt I have no intention of doing so) then the parts would add up to your original body weight, although your performance as a ...


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It's worth emphasising that when you type out 1+2+3+4=10, this is in the first instance a sequence of symbols. A conventional interpretation of these symbols might be something like an affirmation that numbers are metaphysical objects, that equality is a kind of identity claim, and that the addition sign is the description of a function relation on the ...


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Long comment When in mathematics we write 1+2+3+4=10 we are not making some sort of "metaphysical claim": we are asserting that when we evaluate the left-hand side expression (we "compute" 1+2+3+4) the process will terminate after a finite number of steps and the resulting value of the process will be the same as the right-hand side. Thus,...


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Your professor is right: The objects of study of physics and mathematics are completely different. Physics seeks to understand the universe, the reality we perceive, and because of this uses the scientific method. Mathematics, on the other hand, seeks to understand mathematical structures, and the method it uses to establish its truths is logical reasoning. ...


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What I believe your professor meant by saying "physics describes our universe while mathematics describes any potential universe" is that mathematics always studies a more general case of anything while physics just studies a special case of that anything. Your professor probably wanted you to focus on the word " any" rather than ...


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You are asking about a very rich field called measurement theory. The standard textbooks are the three volumes of Foundations of Measurement by Krantz, Luce, Suppes, and Tversky (Volume 1 here).


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Here is my way of looking at "the unreasonable effectiveness of mathematics". In the real world, counting macroscopic objects like pebbles or people is useful because in the real world, neither of these two things can spontaneously pop into or out of existence. Counting them has meaning. Then we discover that we can represent those counts ...


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Partial answer: A computer does not implement mathematical, economic or any other type of concepts. It is our reason which gives the input and output symbols of mathematical or economic sense. For example, your money in the bank is just represented by a nanometer-scale-size magnetized surface. Do computers implement an economic concept in such physical fact? ...


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It's a great question. How do finite, imprecise, error-prone real-world objects, such as an abacus or a computer, touch the infinite perfect realm of mathematics? Try this analogy. Suppose you have an infinite group, with a⊙b defined for every pair of elements. Now suppose you take a finite subset S of the group elements, and define a new operation ⊗, ...


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Well, that will depend on your ontological point of view regarding mathematics itself. A necessary prerequisite is that you can somehow formalize the "immaterial entity" you are trying to investigate. For platonists like Roger Penrose or Gödel mathematics is independent of the human mind, mathematical truths are objective statements about abstract ...


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