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

by dhw, Friday, March 05, 2010, 21:40 (5375 days ago) @ xeno6696

MATT (bold type mine): Prior to writing a symbol that represents the number "2," early man had a concept of "twoness," where you could put two rocks, two dogs, two people, and say two apples next to each other and were able to reason that all these different objects had a commonality--the aforementioned property of "twoness." So, for certain, mathematics had its birth in the very real world, by observation of a natural phenomenon--"twoness." So in that light, I would ask you if you think numbers are real--like the sun, or are they purely imaginary?-My (tentative) suggestion was "that numbers, quantities and shapes are part of the language we use to systematize our observation of nature, whereas the laws of physics, though we express them in words, operate actively and independently of our observation." I can't see any difference between us here, if you accept that the symbol "2", like the word "two", is part of language. -You wrote on 3 March at 15.35, "I rate all "truths" by exactly that criteria: Would it exist independent of human existence?" Your starting-point above is early man's concept of "twoness", which already depends on human existence. If there were no humans, there would be no concept of "twoness", but there would still be a sun. I'm not enamoured of the real v. imaginary dichotomy ... the word "football" represents something real, but if there were no humans, there would be no football. I wonder if a better alternative might be natural and man-made. I would (again tentatively!) suggest, in opposition to the title of this thread, that language is a man-made system used to represent all aspects of the world we live in, and mathematics is the form of language that represents numbers, shapes, quantities etc. If there were no humans, there would be no language, including maths, and no "concepts", but the natural objects and processes represented by language would still exist.
 
In view of the convoluted relationship between physics and maths, and to accommodate David's belief in design and related "math truths", I'd be interested in an answer to the question with which I ended my last post: "Could one perhaps say that mathematical calculations are needed to measure or predict the physical effects of physical causes, and that without humans such calculations are not needed and cannot be made, except by a possible God?" However, I don't want to drag you into a discussion that may not lead anywhere, and I only entered it myself out of curiosity about certain claims that were being made. So do feel free to end it if it seems unproductive.