Refutation of the \"Language-Only\" Interpretation of Math (The limitations of science)

by xeno6696 , Sonoran Desert, Wednesday, February 17, 2010, 03:11 (5395 days ago) @ George Jelliss

NOW the whole thing you talked about in dealing with "infinitists" makes sense. Though from what I've seen this seems a wholly semantic argument. -http://mayhematics.com/m/m3_order.htm-I did some more digging (because I was unaware of this debate) and found some more interesting things. -http://en.wikipedia.org/wiki/Infinitism
http://en.wikipedia.org/wiki/Finitism-In terms of mathematics it appears you argue that since we cut off counting at some point then we can consider the system "finite." What then, is the true purpose of mathematical induction when it always asserts that if a statement is true for n + 1 then it is true for all n? Or do you simply prove for n - 1 and then assert for all numbers n? How on earth could you tell the difference? -Doing more digging it appears that Finitism is based on constructivism. -http://en.wikipedia.org/wiki/Mathematical_constructivism-So according to this, an induction proof proves nothing. Constructivists must not have many friends at all! Especially considering that the law of excluded middle is pretty much a cornerstone inside of Computer Science. Digging deeper I find that I'd like a bit more justification on why Finitism is "correct."

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\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"