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Math and science use exactly the same method of reducing their claims to their basic claims and backing those with a failed search for counterexamples. Conseque

Math and science use exactly the same method of reducing their claims to their basic claims and backing those with a failed search for counterexamples. Consequently, all untruth is invariably always the result of the untruth hidden in the basic claims. The untruth in the basic claims obviously exists but it is sheer impossible to pinpoint precisely where exactly it is.

lutusp 14y ago
> Math and science use exactly the same method of reducing their claims to their basic claims and backing those with a failed search for counterexamples. This is false. You're overlooking a very important difference between math and science. Science is empirical, which means any scientific theory can be overthrown by new evidence arising in nature. This is not true for mathematics -- once a conjecture becomes a theorem, it's irrevocable. Your viewpoint is a philosophical one that fails to account for the key difference between math and science.
- eriksank 14y ago
  Probably worse than that. I simply refuse to make any such key difference between math and science. In my opinion, both math and science are empirical.
  - gizmo686 14y ago
    In what way is math empirical? If one wants to prove that 1+1=2, one does not take one apple, add another apple, and observe that one now has two apples. One defines: x + 0 = x x + successor(y) = successor(x) + y 1=successor(0) 2=successor(1) One then takes the true true statement 1+1=1+1 | Identity And finds: 1+successor(0)=1+1 | Definition of 1 successor(1) + 0 = 1+1 | Definition of + 2 + 0 = 1+1 | Definition of 2 2=1+1 | Definition of + I made no observation to prove 1+1=2. What I do observe is that if we map the counting numbers to the count of how many apples I have, and we map the addition operation to combing to groups of apples, then the mathematical result is consistent with reality. However, if we empirically discover that the mathematical result is not constitent with reality, than that does not mean that the math is wrong, it simply means that the reality does not behave in a way that corresponds to the math.
    - eriksank 14y ago
      > it simply means that the reality does not behave in a way that corresponds to the math. In that case, we should watch out to use that kind of math in engineering or for example calculate expected airplane behaviour with it.

lutusp 14y ago

> Math and science use exactly the same method of reducing their claims to their basic claims and backing those with a failed search for counterexamples. This is false. You're overlooking a very important difference between math and science. Science is empirical, which means any scientific theory can be overthrown by new evidence arising in nature. This is not true for mathematics -- once a conjecture becomes a theorem, it's irrevocable. Your viewpoint is a philosophical one that fails to account for the key difference between math and science.

eriksank 14y ago
Probably worse than that. I simply refuse to make any such key difference between math and science. In my opinion, both math and science are empirical.
- gizmo686 14y ago
  In what way is math empirical? If one wants to prove that 1+1=2, one does not take one apple, add another apple, and observe that one now has two apples. One defines: x + 0 = x x + successor(y) = successor(x) + y 1=successor(0) 2=successor(1) One then takes the true true statement 1+1=1+1 | Identity And finds: 1+successor(0)=1+1 | Definition of 1 successor(1) + 0 = 1+1 | Definition of + 2 + 0 = 1+1 | Definition of 2 2=1+1 | Definition of + I made no observation to prove 1+1=2. What I do observe is that if we map the counting numbers to the count of how many apples I have, and we map the addition operation to combing to groups of apples, then the mathematical result is consistent with reality. However, if we empirically discover that the mathematical result is not constitent with reality, than that does not mean that the math is wrong, it simply means that the reality does not behave in a way that corresponds to the math.
  - eriksank 14y ago
    > it simply means that the reality does not behave in a way that corresponds to the math. In that case, we should watch out to use that kind of math in engineering or for example calculate expected airplane behaviour with it.