Sand wrote:
twoshots wrote:
Sand wrote:
twoshots wrote:
Well that's really the problem with this whole debate. Once we define real, the debate becomes trivial.
My point is that mathematics in book or verbal or other symbolic form is a language that becomes "real" in the mind of someone who interprets the symbols. It means nothing to a horse or a dragonfly or someone not involved with mathematics. It's a method of communication of the inter-relationship of patterns that has an internal consistency that is rigid. Nothing more.
But math isn't the language, it's the referent. The two can and must be separated as a consequence of the Incompleteness Theorems, because what is conceived of as mathematics cannot be reduced to trivial relationships among assumptions. Mathematical propositions are more than syntax.
Mathematics is no more the relationships it describes than physics is the forces of nature or chemistry is the interactions of molecules. They are systems of descriptions of these things structured in such a way as to be internally consistent and are a form of communication, not the phenomena themselves. The structures themselves are, of course, independent of humanity but the communication is not.
What math is may be a matter of definition, but if math is distinct from its referent, what is it's referent other than a Platonic ideal? If the language has a referent, this referent could not be a standard empirical physical thing (because we cannot draw conclusions about physical things a priori), since surely whatever its referent is isn't a particular physical thing (I for one have never seen a Jen-you-wine circle).
By distinguishing math from its referent, this introduces an admission that the referent is something. The only way to get around this is to try to say that the referent is self same with the language, which has been shown to result in an absurdity.
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* here for the nachos.
27 Mar 2009, 11:26 am
