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

by xeno6696 , Sonoran Desert, Wednesday, March 03, 2010, 15:35 (5377 days ago) @ dhw

MATT, quoting a UNO mathematician: One thing that you might bring up is the fact that while mathematical objects are a consequence of their axiomatic basis (language and the rules of language), they are not time-dependent. Nor are they culturally dependent (relativism). So I wouldn't consider them to be purely imaginary.
> 
> Since the peak of my mathematical career was a pass at O-Level, I'm going to limit myself to what seems to me a link to our more general discussions. Under "Back to Irreducible Complexity (Part Two)" on 21 February at 20.49, you wrote: "all things we view as causes and effects are as such because we build them to appear that way." I pointed out that this negated about 90% of science, to which you responded: "Yes, I especially mean that for science. Everything we know, we know by language. Everything we know by science as well." I would say the laws of science were no more "time-dependent" or "culturally dependent" than the laws of maths, and if you're going to argue that causes and effects are the result of our own constructions, this seems to me far more apparent in maths than in the natural sciences. -I think it would be fair to file a disclaimer that I also recall saying "I'm willing to entertain the notion" or something of that nature, as that particular discussion was in my experience with the Buddhist perspective on life. You're actually dangerously close to what I consider to be my basis for what I believe are "objective truths," namely, constructs that exist independent of an observer. -"At least we can say that thanks to the law of gravity, when I fall off a ladder here on Earth, I go downwards and not upwards, regardless of the language in which we describe the process. I suppose you can argue that taking three bricks away from five would leave two even if we didn't have words to describe the change, but in terms of cause and effect, I'd have thought there was rather more solid "reality" behind my fall than there is behind the mathematical concept. If we're going to talk in terms of reality v. imagination, I wonder whether it might be a fair test to ask whether something would continue to exist in the absence of human beings. I suspect that the laws of physics would manage to carry on pretty well without us. How about maths?-
And now we're not "dangerously close," we're on the head. I rate all "truths" by exactly that criteria: Would it exist independent of human existence? From what I know of that prof, he would say "In maths, especially." (I'm not so sure.) For the very structure of our universe as we have unraveled it, we have done so via mathematical objects. An atom is an atom, whether or not we humans exist. Obviously, the only maths we can be sure of, are those maths where we've observed them in nature--the fact that our universe isn't one of a (purely) Euclidean nature is what allowed us to dig into deeper geometries, and it is these geometries that String Theory bases some of its claims upon. (n-dimensional spaces is a fancy word for "Building a bigger cube around another cube." -Things such as the Fibonacci relation occur naturally and this gives credence to number theory as something that studies "real objects," even though the concept of a number itself is something that tends to be quite abstract.

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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.\"