4 ms·
> The way that Mathematics and approaches this is, using the Axiomatic way. You can view this as a game: Let's make some assumtions / axioms, and see what we ca
by zajio1am 7y ago
> The way that Mathematics and approaches this is, using the Axiomatic way. You can view this as a game: Let's make some assumtions / axioms, and see what we can build with it.
It is often described in such way and you can see it like that in retrospect, but actually it is often intuitive grasp of mathematical structures first, axiomazation second.
For example, natural numbers was understood (including number theory) for thousand years, but Peano axioms are from the end of 19. century.
But that does not say there is 'absolute thruth', there are just infinite different graspable math structures and it is arbitrary (or pragmatic), which we consider interesting to develop.
- heinrichhartman 7y agoSure, that's the historic route that we ended up at the place we are in. However, this is not the logical foundations that are used for current teaching and research. There has been a lot of effort, in particular in the late 19the century by folks like Hilbert, Goedel, Frege, etc. to put Mathematics on solid foundations. This is what we ended up with.