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

by dhw, Saturday, March 06, 2010, 22:07 (5374 days ago) @ xeno6696

MATT: The Sun would exist just the same without a human to name it "Sun". The same thing that goes for "twoness". [...] I feel that we need some kind of agreement that the concept of "two" is as independent a fact as the existence of the sun, atoms and molecules. You seem to be asserting that two is a concept that REQUIRES language. I disagree.-We're on very slippery ground here, and I'm not treading with any confidence. However, it's pleasing to hear that I'm saying some things "of merit", and I'm happy to blunder on if you think the discussion will be fruitful!-You are actually asking me to agree with you before you deal with my reasons for disagreeing with you, which I think is a little unfair, but on a certain level I can do so. Perhaps that's what it boils down to ... levels of existence.-As I see it, certain types of reality like the sun, the law of gravity, the mechanics of heredity are independent of human observation, and language merely represents them. Unlike the sun, "twoness" requires human intelligence to observe, identify and describe it. "Twoness", as you have said yourself, is a concept. In your example, you talked of early man establishing "a commonality" between pairs of rocks, dogs etc. It's this need for man's interpretation that in my view distinguishes the reality of "two" from that of the sun, which didn't require early man to establish anything. I accept that "twoness" exists in nature (this is the level on which I can agree with you), but it can only assume reality/meaning/ significance/substance as a concept because man has observed connections and given them articulate form. In other words, without the language of maths, the CONCEPT of "twoness" (as opposed, let's say, to the STATE of "twoness") would not exist, in the sense that we would not be able to experience it, discuss it, develop it. In fact, I'm not at all sure that it's possible for any concept to exist without language. -Even while I'm writing this, I'm aware of David looking disapprovingly over my shoulder, because I'm ignoring design, and therefore ignoring the "math truths" which he has discerned in the universe. If God designed the universe, I would have to say that mathematical concepts exist independently of man's observation and his language. This, however, is the same as saying that the concept of God depends on man unless God exists.-I'm also aware of George looking disapprovingly over my other shoulder, but that might be my imagination.