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SilasBarta comments on Logical Pinpointing - Less Wrong
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What about Steven Landsburg's frequent crowing on the Platonicity of math and how numbers are real because we can "directly perceive them"? How does this relate to it?
EDIT: Well, he replies here.
I was wondering what he thought about this!
While I greatly sympathize with the "Platonicity of math", I can't shake the idea that my reasoning about numbers isn't any kind of direct perception, but just reasoning about an in-memory representation of a model that is ultimately based on all the other systems that behave like numbers.
I find the arguments about how not all true statements regarding the natural numbers can be inferred via first-order logic tedious. It doesn't seem like our understanding of the natural numbers is particularly impoverished because of it.