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- Jul 31, 2014
space is the syntax of sentences that deal with the objects in visual space.The axioms, for example, of Euclidean geometry are masked rules of syntax.">Remember that in Urpflanze msg #305 LW sees that "The geometry of visual
There are many people who take mathematics to be a branch of logic. That would be "logicism" as a philosophy of mathematics. For such folk, Euclidean geometry starts with the axioms. And I think that's what Wittgenstein was assuming in that quote. His "syntax of sentences" would mean the application of logic to the grammatical rules (i.e. the axioms).
I personally look at it differently. I see geometry as the part that happens before there are axioms. So there is some use of intuition in that step. Of course, mathematicians idealize, so they produce axioms that fit an idealization of reality.
Regards,
Neil - << Previous post in topic Next post in topic >>