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

by dhw, Monday, March 08, 2010, 20:01 (5155 days ago) @ xeno6696

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". -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?-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.