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Posted by Harvey on July 17, 2003 14:33:27 UTC

Imagine, for a moment, that you are the only sentient creature in the whole universe. That's not a difficult thing to do, as we often have just that feeling. So, while you are the only sentient being around, stop performing computations and ask yourself the question: "is '2 + 2 = 4' true?" The answer is as obvious to me as it should be to you: "no one knows"

No one 'knows', but if you get down to it we don't 'know' much of anything about the way reality is in itself (Kant's Ding an sich). All we have of the world are appearances, and if phenomenalists are correct, we don't even have that (just the effects of our sense impressions). So, we have to start somewhere to make sense of the world, and starting with a more reasonable criteria of knowledge seems to be a better position. That is, rather than get caught up in our level of certainty, we should focus on what seems to be case based on our ability to reason and the evidence that is apparent.

Since scientific realism requires mathematical strutures, or so it seems, it is a reasonable position to suggest that mathematics is an invention that actually reflects a real order that is 'out there'. Are we certain of that? No. There's ways around it (e.g., scientific realism can be false or misleading, science might be reconstructed without mathematical relations, etc).

Does mathematics exist independent of humanity ... :::: The above gedanken experiment should make it clear that that question has no known answer.

Likewise, it should be clear from a review of the term 'knowledge' that we have to be more kind in what we allow to be considered as knowledge. In that sense, it can be shown that mathematical realism can be more than tenable position, it might be the best position with the givens we have access to at this point.

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