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

by xeno6696 , Sonoran Desert, Monday, March 08, 2010, 00:07 (5156 days ago) @ dhw

dhw, -Alright, we'll move beyond the existence of numbers, though I think much of what I have to say might be automatically shot down just by virtue that I think numbers to be an observable physical property. -We'll start with the question you were most interested in:-"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?" -The difficult part of this deals with mathematics that outlines relationships. For example, it's largely accepted that if a tree falls in a forest, it does indeed make a sound. -I think that indeed, it *is* possible to say what you ask here. Things get incredibly muddied when you deal with creatures that intuitively make calculations... for example, when a flying squirrel leaps from one branch to another, it makes a series of difficult calculations. Namely, it calculates how much energy it needs, its trajectory, and it obviously adjusts for wind-speed and other factors as it makes its jump and glides to the next tree. -Isn't the squirrel doing physics? -Going back to one of your other points, I think its necessary for me to explain more of where I'm coming from.-"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."-There's something that troubles me here, and I'll try to name it. To me, language doesn't actually enter into mathematics until you need to start doing operations with the numbers. "2" by itself is a property; an observation. But 2 and 1 (2 + 1) is no longer an observation. Just like when we observe the sun, I submit that when we start describing the sun we begin building a structure of language around it. -2 + 1 by itself means nothing. What does it mean? Are we saying "Two, and then another," or "Another representation of the number 3," or are we meaning this to represent a relationship, such as "two apples and one orange?" -So, in my view, the generic concept of "twoness" is simply a natural property, only when it is taken into language to perform some kind of operation does it "become language." Or, maybe more succinctly, Two is a real object but the moment you reason about it, you are dealing with a man-made language. I don't see how to differentiate between "2" and the Sun. -
"I don't see maths as laws governing the natural processes of cause and effect, but as patterns extracted from those processes. Is it wrong to define maths as the study of numbers, quantities and shapes? If it's not, then I would suggest ... very tentatively! ... 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. Light travels at 299,792,458 metres per second, there are 2240 lb to the British ton, snowflakes are hexagonal, but these are all man-made formulae."-This is something you said earlier that I wanted to discuss. The first bolded statement, I would say that it is physics that does this, not maths. Physics uses mathematical language to describe the universe. But sometimes it is instead inspired by "pure" math. String Theory is a prime example of this. They took ideas from Riemannian and other differential geometries to explain the world. But all ideas in mathematics can trace their lineage back to the natural observation of "twoness." Perhaps numbers might just be axioms that exist only because we need them to--but I'm just not convinced of this.-[EDIT]-Also, when looking at what you discuss as "man-made formulae," lets dissect this a bit more. Metres per second is a language reference, but light travels at a fixed and constant velocity, whatever we call it. The British ton is more arbitrary, but snowflakes being hexagonal is yet another observable property. I'm not trying to say that "six" is a governing law behind snowflakes, but that snowflakes conform to a general semblance of a pattern. -[EDITED]

--
\"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.\"