Is mathematics invented or discovered?

Can language be spoken in a mall?
“Like, yeah?”

:wink:

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I’m not confusing tokens and classes, I’m pointing out that the distinction is important. We think all instances of a word being the “same word” and forget the underlying reality that one was ink on paper and the other was compressions in the air that have now ceased to be. We all know the difference between “Otis the dog” and “things that are dogs” but we have trouble with the physical form by which a three is stored on a server somewhere and things that are threes, and confuse the two.

Fair enough. Though I don’t think we have a very clear or evidence-supported idea of at what point something becomes a thing that perceives rather than merely a thing that reactions to forces.

But I also don’t think we know the stuff of the universe even does separate into bits that can be counted or added. We know things about what it is possible to perceive the universe doing, but that’s built from perception, it doesn’t precede perception. If we think there is such a thing as noumena (in any sense of “is” and “thing” that we can even approach discussing) then I don’t think we have any more reason to believe it must be subject to addition than we did to think that light has to be a wave or a particle. Our intuition is just useless in this case.

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Agreed. I already made that point with Quine’s rabbits (still can’t find an ur-text though!).

Nevertheless, a materialist is more than content with the idea that things exist sans any necessity of conscious perceivers of them, and (presumably) - given that they are also happy with the big bang model - hence (unperceived) things getting bigger, hence addition.

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