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

by xeno6696 , Sonoran Desert, Wednesday, March 17, 2010, 00:27 (5148 days ago) @ dhw

We could probably go on indefinitely offering examples and counter-examples to show that "twoness" does or does not exist independently of human observation and language. I think my example of the snowdrop and snowflake (yes, two flowers, but no, not two snowdrops) shows pretty conclusively that "twoness" requires a human act of association, but your helium v. hydrogen v. lithium makes a good case for your version. I was inclined to leave it at that, but out of interest I googled "Do numbers exist?" and found an article by Lee Lady: www.math.hawaii.edu/~lee/exist.html. I'm afraid I haven't had time to read and digest it fully, but I noted down the following: 
> 
> "The prevailing opinion among mathematicians, at least as far as I know, is that mathematics has to do with a man-made universe, a mental universe, completely separate from the "real world," whatever that may be. But it takes a highly intellectually sophisticated mind to think that supernovas and electrons are real but that numbers such as 6 and 59 are not."
> 
> This suggests he's on your side (except that he thinks the opposition is more widespread than you do). However, it may not be so, as you will see later from another quote.
> -In truth, mathematicians admit there's no existence proof for numbers, but the prof I pseudo-quoted told me something like "At the end of the day, and behind closed doors, few mathematicians feel they are studying something that isn't real." Having been exposed to this debate however, all the discussion happens in mathematical philosophy journals, and isn't typically broached in any class I've ever taken. -> ... Much more important to me is whether mathematicians are in a position to explain the mechanisms of life and the universe, as David suggests. And do their formulae imply a conscious intelligence at work (David's view), or a natural, unconscious order of things (George's view). Here is another quote from Lee Lady (but other passages in the article suggest he is not religious):
> -I view that David is correct as well. Insomuch as mathematical structure can be observed.-> "I believe it was Kronecker who said, "The natural numbers were created by God; all the others are the invention of humans." I believe that most contemporary mathematicians would agree that Kronecker was wrong only in his statement about natural numbers; they too are the creation of human minds."-To complete what I'd originally set out to do (and using the basic-chemistry example I began previously) if you have *any* kind of countable things, you can begin to build and infer about them. I undoubtedly recognize that the vast swath of mathematics deals with language, but all mathematics are logically built upon axioms for their structure. Yes, in many cases these axioms are either tautologies or improvable statements.-
As for what to do about the greater part of your questions, this short article will do: -http://en.wikipedia.org/wiki/Perspectivism-Again, a Nietzschean concept, but one that very clearly shapes our debate. It may well be that it is absolutely impossible to divorce yourself from a perspective. (Even agnosticism is a perspective.) Only by analyzing all competing perspectives can we possibly reach a truth, if one even exists.

--
\"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.\"