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

by xeno6696 , Sonoran Desert, Wednesday, March 10, 2010, 17:28 (5370 days ago) @ dhw

Matt suggests that squirrels are intuitively doing physics when they leap from branch to branch. You might say that I'm also intuitively doing physics when I catch a ball (and I'm making a mess of physics when I drop it), or run across the road (hopefully before the bus can hit me). Even blinking can be broken down into scientific terminology, but it's only humans (or God, if he exists) that need and are able to do this. I can see that you're trying to draw a parallel here with numbers ... twoness exists just as squirrel-jumps exist just as the sun exists, and you've elaborated on this. You say: "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." I would say that "twoness" already requires an operation, but perhaps you can clarify this for me by dissecting an example, along the lines of your early man who put two rocks etc. next to each other. In my garden I observe a flower and another flower. With great pride I tell my wife that we have two snowdrops. I presume you would argue that the snowdrops have an objectively existing "twoness". However, as my wife knows all too well, I am an ignoramus. She points out that Flower A is a snowdrop, and Flower B is a snowflake. They are different. What, then, does the "twoness" relate to? Before there can be a twoness, doesn't there have to be a connection, an identity? How is that established? The flowers in themselves have no property of twoness. I must give it to them. Yes, there are two flowers. No, there are not two snowdrops. So is there an independent "twoness" or isn't there? It seems to me that if "2 + 1 means nothing", as you say, then "2" also means nothing until I have performed "an operation". 
> -You see, I look at this exactly the opposite way. Lets try this. Grab a pebble. Is it made of atoms? The knee-jerk response is "yes," but without sophisticated equipment, you're not going to be able to actually observe atoms. In my view, the "twoness" of your two flowers is just as much a property you can uncover as the fact that the pebble is made of atoms. The difference simply relies upon whether or not you observe the property. -Lets try perhaps a more difficult scenario. Helium is made of two and only two protons. What prevents us from stating that "twoness" isn't a real property in this instance? In my mind, since the atom is made of protons, and the defining characteristic of Helium is two protons, then the existence of "twoness" can be verified in this instance. Without the existence of "twoness," Helium wouldn't exist. If two protons are the necessary and sufficient conditions to make an atom of Helium, how can we assert that the "twoness" isn't a physical property? If its only one proton, it's hydrogen, and if its three, its Lithium. If there isn't some observable physical property of "twoness" then how can we base this upon fact?--> I'm in no position to judge the extent to which maths and physics overlap in extrapolating patterns from the natural processes of cause and effect. Nor do I know enough about the history of maths to comment on your statement that "all ideas in mathematics can trace their lineage back to the natural observation of "twoness"." You did say earlier that mathematical philosophers are still debating the existence of numbers, which suggests the issue is not so cut and dried. You also say numbers "might just be axioms that exist only because we need them to", but you're not convinced. I'm certainly not the person to convince you! As for the man-made formulae, they all provide terminology for existing objects or actions. I don't think we have any disagreement there, do we?
> -To be fair, *only* mathematical philosophers have that debate. By and large, most mathematicians (the prof I mentioned included) might not even have an opinion on the issue by the simple fact that well, since numbers work in the "real world," they obviously exist in some form, whether by necessity of language or by observable property. No real disagreement on how math is used in physics--they dialog and catalog real and existing relationships. -I think at this point, we can begin discussing how purely mathematical objects have found a foothold in our very real universe. (Not all objects are "numbers" per se, but I'll try to find a good way to keep that discussion at a "high level." (In computer-science, "low-level" means an increasing order of detail and mathematical description.) -> I should add that I greatly appreciate the trouble you're going to over this. I'm still unsure where it's heading, but then I'd say the same about life, evolution and the universe.-Though the existence of numbers is intriguing to me, a voice in the back of my head likes to remind me of the question "How is this question practical?" At least our other discussions--the three you mention above--all have real-world implications for everything we humans do!

--
\"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.\"