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"Humans are apes" can be distilled into a mathematical statement if you have a Turing test like criterion to arrive at certain abstract essentials to define or identify humans and apes respectively, then to state "Humans are apes" you just need to list all the matching equalities between them one by one, even possibly infinite amount of ...


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A mathematical statement is any statement that measures relationships. 1+1 = 2 and 12+12 = (√2)2 say the same thing, but measure different features of the world. Any natural language measurement statement can be translated into mathematics by removing specificity, and any mathematical statement can be instantiated in natural language by supplying specificity....


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Many fields that we now call "sciences" were originally thought of as branches of philosophy. For that reason, philosophy is often called the "mother of sciences." A good way of conceptualizing it is that philosophy deals with open questions --ones to which there is no universally acclaimed, uncontroversial answer. All disciplines pose ...


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What would be some problems if we would define them to be branches of philosophy? When we use the term -- 'branch', we must be able to distinguish one branch from other branches. In other words, we must be able to demark them. This is not possible in the case of some subjects. IMHO, it would be good for us to consider a thing that is subtler and that ...


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Extended from the original XKCD comic strip, which is in the frame.


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You can still praise God by stating "God is not limited by anything other than God" i may call "God is Almighty" but then don't be overwhelming by saying God unlimited can be impossible. This concept of "infinity" must be understood properly. On real life we can say infinite, unlimited as "Unreachable All at Once" It's ...


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Here's a mad idea. If you had an unnatural number of eyes you might for example count earth 3 as alien 2. Then alien 2 x 9 is not the earth 2 x 9. I suppose, in other words that the truths about natural numbers would vary if the algorithm for counting varied and I suppose it could. But then you could say that the earth way of counting is the one your talking ...


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There is no infinite, there is no "unlimited". There is only "not limited by something" Infinite asserts thing can exceed beyond itself without additional assertion from outside which is impossible. It's the way old philosophers trying to praise God is unwittingly trapped by impossibilities that injure the understanding of God's self. Any ...


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Accounts of impossible worlds come in many flavors, but none seems to require that natural numbers obey the same laws in all possible worlds unless these laws count as "logical" to some (required) extent. Or one might posit numbers as dwelling in their own world(s), wherefore the question of variation becomes the question of something like the set-...


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There're several major schools of realism views towards math. Platonism long ago already believed math objects as real forms existing independently of our physical world. Modern Structuralism instead regard internal structures as real. Formalism and Constructivism (including Intuitionism) usually regard math as merely symbolic rules or subjective mental ...


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The Dirac belt trick is simply experimental evidence that our universe has three macroscopic spatial dimensions. If our universe had more than three macroscopic spatial dimension then the belt trick would not work (although there are more direct ways of demonstrating this e.g. seeing how the volume of a sphere is related to its radius). And the belt trick ...


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Not sure if this helps with your confusion/skepticism, but natural language is full of under-determined sentences, e.g. Today is Tuesday. That statement is true if where you're at right now (time and space) is a Tuesday and false otherwise. Words like 'today' are known as indexicals in linguistics and the philosophy of language. Think of that formalized as ...


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You will interesting commentary here: https://mathoverflow.net/questions/352298/could-groups-be-used-instead-of-sets-as-a-foundation-of-mathematics?r=SearchResults The "received views" generally ignore such possibilities because of history and folklore. Category theory and its child homotopy type theory are changing that situation. But, they do not ...


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A paraconsistent logic is a logic that does not validate the principle of explosion ("from a contradiction, anything follows"). A paraconsistent plurality of worlds will therefore be open to nontrivial worlds in which there are true contradictions. Cantor identified both God and "inconsistent multiplicities" as examples of absolute ...


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Whether imaginary numbers are 'real' is a topic as old as they are. They have been found to causally implicated in physics though. Group theory is abstract algebra, capable of expressing types of geometry as special cases, just as algebra allows us to use different types of number lines. It's like a mapping that can let us link different types of mathematics,...


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It sounds to me like you are talking about structuralism. Structuralism is the philosophical view that mathematics is the study of abstract structures (i.e., patterns) as opposed to the objects and relations that instantiate these structures. Accordingly, mathematics studies the abstract structure of the objects and relations that realise a given structure ...


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Zalamea’s research may be interesting — I’m thinking of Synthetic Philosophy of Contemporary Mathematics as there’s a fair bit of analysis of the work of Grothendieck and other recent abstract/pure mathematicians, and also a pretty broad-ranging review of lots of other works that could be starting-points for investigating the philosophy of contemporary maths....


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Analytic philosophy can be argued to have diverged from the Continental tradition with logical positivism and the Vienna Circle. Which Wittgenstein was associated with, and is considered to have done some of the most important work to develop, with his Tractatus. The 'linguistic turn' is considered to have begun to the influence of his later work, primarily ...


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