> That "intuition" is what brought us Special and General Relativity Yes. Intuition is a good thing. It just shouldn't be relied on for proofs. To compare, Mat

> That "intuition" is what brought us Special and General Relativity Yes. Intuition is a good thing. It just shouldn't be relied on for proofs. To compare, Mathematicians followed their intuitions to bring us all kinds of results (eg. ). It's a good thing. It just shouldn't be used to prone to making mistakes when but shouldn't be relied on for (Mathematical) proof. > You can't expect to get Newton's second law and make it work with any kind of mathematical object. That's not rigour, that's generality. For an example of rigour, compare the treatment of (infinitesimal) calculus in Physics and in pure Mathematics (eg. see http://en.wikipedia.org/wiki/Calculus#Foundations http://en.wikipedia.org/wiki/Calculus#Foundations ). >> In Physics, there's just "=" > Scalar equality? Vector equality? Magnitude equality? I would say the first two are "instances" of the same principle (in the same way that, for example, intensional equality can be "instantiated" for integers, arrays, matrices, etc.). Magnitude equality composes the absolute value operation with "the" equality operation, so I would call it a shorthand rather than a distinct equality principle. > Also leptons are 'equal' following the Pauli exclusion principle? What an excellent example of a non-rigorous statement ;) (ie. what is your model of leptons?) For reference, some of the examples I mentioned are described at http://ncatlab.org/nlab/show/equality http://ncatlab.org/nlab/show/equality