Question.... (Processes of Logic)

If you'll forgive me for jumping in on what appears almost to be a private argument...."number" is a human abstraction. Yes. But it is also a description of genuinely physical phenonmen.And then we found we could manipulate the ABSTRACTION and get results that could be interpreted back usefully into the material world.I don't actually find that too surprising given that number orignates from the material world.Math IS.

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No, it's just a description of relationships that exist only in our heads. The objects themselves are physical, yes. But the set of objects your counting - the set itself - is something you make up.

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Until we articulate them in bits and bytes, at which point they become realised physically. The notional non-materialism of "number" is mythological and has been since the development of cybernetics in the 40's, IMO.The set you are counting does not exist only in your head. Or at least, it does in much the same way that the 270-degree field of vision you "experience" exists purely within your head. Your idea of your surroundings is "something you make up", and yet is none the less a reflection of the material realities (mostly) to which you are exposed.

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Sure, but then Monopoly IS, too.

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Yes. And when is the last time you heard a dispute about the ontological existence of Monopoly?

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Right, but if you assume that the map is the same as the physical reality, then you confuse the model with the reality. You reify, in other words.

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Hmm, thats not quite what I meant. We have no choice but to treat the map as if it were reality, because the map is our method for comprehending reality. It is not a case of reifying the map, becuase we have no input but the map. You only see a spot about half a centimeter across at any given moment; your perception of your environment is wholly illusory, a synthetic "image" knitted from spot observations, and yet pretty accurate. If you can see a cliff in front of you, you stop moving forward.

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If this wasn't true, how could maps be wrong? We know that some maps are wrong, however, suggesting that maps are simply another kind of mental model. Based on reality, sure, but no more real than any other mental models.

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It is indeed possible to fool the eye and seeing is not believing. However, that does not imply that our perception of reality is wholly false; it is merely qualified. But given the Uncertainty principle, huge amounts of entirely non-illusory physical processes are also known to be understandable only in qualified ways.I can accept that our representation of mathematics is conctructed. But I do not accept that the physical processes we describe are therefore also constructs. Whether you call X times objects on a table X or Y has no impact, no relevance, to the objects.

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I've never heard an argument for the ontological existence of mathematics that couldn't be applied to Monopoly, as well.

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Yes that was rather the point. The only serious position from which this claim can be advanced is the solipsistic fallacy that denies the existence of a material environment.