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

by xeno6696 , Sonoran Desert, Sunday, March 07, 2010, 00:08 (5157 days ago) @ dhw

dhw,-The existence of numbers is actually still something of debate among mathematical philosophers, so I won't claim to have an answer. But we both represent different sides of the argument. For sake of clarity I will define how I'm going to talk about this. 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. -Mathematical language is how humans reason about mathematical objects. -Mathematical language requires the ability to observe numbers.-I would be a little more willing to agree that the concept of "twoness" requires language if it weren't for the fact that we know that several kinds of other animals can also observe this same fact--without evidence of any kind of mathematical or other language that approximates human language. For example, Crows on average can count up to 4. I view this as significant because if the numbers 1, 2, 3, 4 were products of language only, than it shouldn't be possible for animals that do not have language to observe the property of "twoness." -{.}
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{.....}- My position is that the existence of numbers (I have not yet addressed mathematics!) is no less a physical reality than the existence of any of the other objects we are discussing. We need language to talk to each other about numbers, but we don't need language to observe them. -Maybe a better way would be to ask you, how could "twoness" NOT exist? If the symbols "two" and "2" represent something that doesn't exist outside of language, then how would we prove this? -We'll give this one more shot, but if we still disagree, lets just agree to disagree and start discussing the rest of what you have to say?

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\"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.\"