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Essay / Discussion of the rhetorical approach of the Thomassonian...
We have already discovered that an ontology must, at the very least, take into account that mathematics is about tangible, physical things (even if those things turn out to be simply relations of things). The functionalist claim seems to approach mathematics as a purely linguistic matter, even though what mathematics describes is certainly not. We then have to ask ourselves if what the mathematics describes is really there. It seems that mathematical language, expressions such as a2 + b2 = c2, are purely constructed terms in the same way that we would be willing to say that English is. Perhaps we could then lean towards an intuitionistic approach like that described in JR Brown [2]. An intuitionist, or constructivist, suggests that mathematical concepts|that is, in our terms, relationships| have no existence until a human mind creates them [4]. However, in suggesting this we run into major problems. First, intuitionism seems to want to reject certain claims of mathematics and logic already accepted; namely, claims such as the Law of the Excluded Middle. Indeed, an intuitionist holds that only until a statement is proven or disproved does it have a true or false truth value. Proposals such as those of Goldbach