Odin wrote:
Mathematics is a human construct, it is a special type of language. 1 + 1 = 2 simply because of how those symbols are defined.
Case in point.
However, there is at least a bit of a problem with this point.
Warning! Technical monologue!
Kurt Goedel proved that there exist propositions of mathematics which are true, but cannot be proven. That is to say, there exist mathematical statements which assert something in a way that cannot be concluded from the definitions of mathematics that is in fact true. In his case, he proved that mathematical statements could describe the provability of other mathematical statements (a nested metalanguage), and that no matter how we formulated math in general, it is always possible to have a statement which asserts the impossibility of its own proof, but the nonexistence of its own proof implies that it is a true
metamathematical statement. Some mathematical philosophers have interpreted this as a refutation of the linguistic interpretation of mathematics: if math were simply language, then each mathematical statement would be reducible to the base assumptions of mathematics (say, the Peano Axioms); i.e., given a mathematical statement, it is simply an elaborate way of rephrasing our own definitions. However, this is just not the case, by Goedel's proof. Consequently?
Something to think about. Goedel's proofs are what got twoshots into maths in the first place.
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