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

by dhw, Sunday, March 07, 2010, 22:43 (5373 days ago) @ xeno6696

MATT: I know I called "twoness" a concept, but I don't know how to describe a property sans language. I'm trying to say that "twoness" is a property that is observable, and exists outside of language.-That actually sums up the situation very neatly, and seems to me to coincide with my statement in my last post: "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." By articulate form, I mean the language of maths, which almost ties in with your statement that "we need language to talk to each other about numbers, but we don't need language to observe them." Almost. But I don't think it's just a matter of talking to each other about them. We give this meaningless "twoness" a substance that it doesn't have in itself. -You go on to ask how could "twoness" NOT exist? That is not what I'm arguing, as my earlier statement makes plain. The difference between us comes out most clearly through your wanting to put numbers on the same plane of reality as the sun. I like your reference to crows, though. Crows and chimps can count and use tools too. You're right, they can perform such simple intellectual, conceptual tasks without our language (usually when it involves obtaining food), so I can shift a bit further in your direction there. But even with crows and chimps (which are capable of thinking as well as observing), I still can't put numbers on a par with the independent, objective reality of the sun. Maybe what I'm about to say anticipates what you intend to move onto later. If we go from your simple "twoness" to, say, 0.75, or ½, or 2 x 1 = 2 we can certainly leave the crows and chimps behind. At this level, can we talk of numbers existing independently of human intellect and language, like the sun? I'd say this illustrates how the so-called "property" of your numbers depends on us for its substance etc. -We give names to everything we observe and everything we invent, and it may be that maths is a unique combination of the two: part observation, part invention. I say "unique" because I've been trying to think of a parallel, but can't. Earlier in this discussion, George suggested a link-up with legendary characters (part fact, part fiction), and it would certainly be more in line with our general theme if we could broaden the discussion in this way. However, with mathematical calculations one is able to test the accuracy of conclusions, which we generally can't do with history ... particularly ancient history. -Before we move on, I need to stress again that I'm not arguing from any fixed position. This is a subject about which I know nothing, and I've only entered the discussion because I felt certain statements should not go unchallenged. Ideally, you need a "mathematical philosopher" to take you on! I'm willing to learn, and I'll continue to challenge you, but on the understanding that my arguments are improvised and I have no idea where they're heading.