Re: an important set theory post

On Jul 28, 10:27 am, Mike Kelly <mikekell...@xxxxxxxxxxxxxx> wrote:
...
I don't know how much this helps. The important points: formal
mathematical definitions are abbreviations; in a formal treatment some
terms must go undefined; we may have intuitive ideas about what the
undefined terms "really mean" but this has no bearing on the
mathematics.

I understand all this, and it's not the first time
I've heard it. But I'm not in the least interested
in using logic for its own sake, proving theorems,
and building complicated structures, just for the
abstract beauty and purity of it all. I want to 'see'
in my mind's eye what we are talking about. So points,
lines, and planes have to be seen for what I think
they are, or else I will have no use for geometry.
Similarly for all the rest of mathematics.

Take real numbers, for example. If I can't have the
real line, then no thanks; or for complex numbers,
the complex plane is a necessity. You can have your
x + iy. I want to see (x,y).

I'm aware that sometimes we can't visualize things. In
college we were forever proving things for n dimensions.
But at least we could visualize them for n = 2 and n = 3.
.

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