I've sworn off long, abstract internet arguments about philosophy with people I don't know, but here's my response:
1) yes, math is all tautologies. However, much of it is tautologies we wouldn't be able to work out without formalizing them. The fact that a sufficiently intelligent being could see all of math as trivial says nothing about its value to us. It's the same way that writing down a shopping list doesn't produce any information that wasn't in your head, but the shopping list helps supplement your limited memory and attention.
2) Yes, we need to do empirical experiments to determine the value of mathematical models. This does not affect the truth of the models, rather, it allows us to find out which model maps on to the relevant reality.
3) this does mean that the reality trumps the model. However, once the model is proven valid for representing the reality, we can use the model to do things we can't do with the reality. We know that 2+2=4 is a useful statement because when we put two things together with two other things, we have four things. But now that we know that, we can know what you get when you put two trillion things together with two trillion other things, without having to actually do it.
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Date: 2004-03-14 10:33 am (UTC)1) yes, math is all tautologies. However, much of it is tautologies we wouldn't be able to work out without formalizing them. The fact that a sufficiently intelligent being could see all of math as trivial says nothing about its value to us. It's the same way that writing down a shopping list doesn't produce any information that wasn't in your head, but the shopping list helps supplement your limited memory and attention.
2) Yes, we need to do empirical experiments to determine the value of mathematical models. This does not affect the truth of the models, rather, it allows us to find out which model maps on to the relevant reality.
3) this does mean that the reality trumps the model. However, once the model is proven valid for representing the reality, we can use the model to do things we can't do with the reality. We know that 2+2=4 is a useful statement because when we put two things together with two other things, we have four things. But now that we know that, we can know what you get when you put two trillion things together with two trillion other things, without having to actually do it.
great thred!
Date: 2004-03-16 12:17 am (UTC)