I What is the ultimate foundation of mathematics and where does it all begin?

[Mr Davis 97]

This might be a naive question, but I were to ask you to briefly explain the ultimate foundation of mathematics in a formal manner to get to at least, say, the natural numbers, how would you do it? Where does it all begin? I would say that it begins with set theory, but in studying set theory it seems that a lot of mathematical logic presupposes it, such as model theory and first order logic.
Just a brief sketch of it all to wrap my head around would be nice.

 

[.Scott]

Check out Alfred North Whitehead's and Bertrand Russell's "Principia Mathematica".
They had the same question a century ago and wrote a book creating arithmetic from logic.

This links to a pdf - 582 pages:
https://docs.lib.noaa.gov/rescue/Rarebook_treasures/QA803A451846.PDF

 

[Mr Davis 97]

Check out Alfred North Whitehead's and Bertrand Russell's "Principia Mathematica".
They had the same question a century ago and wrote a book creating arithmetic from logic.

This links to a pdf - 582 pages:
https://docs.lib.noaa.gov/rescue/Rarebook_treasures/QA803A451846.PDF

That's the wrong "Principa Mathematica." The one you linked to was written by some guy called Newton.

 

[.Scott]

That's the wrong "Principa Mathematica." The one you linked to was written by some guy called Newton.

Sorry. Here's a good link: https://ia800602.us.archive.org/35/items/PrincipiaMathematicaVolumeI/WhiteheadRussell-PrincipiaMathematicaVolumeI.pdf

Things get exciting starting on page 362 (pdf page 406) where in section 54.43, we finally prove that 1+1=2.
There are 719 pdf pages all together.

It's a real page turner. Or maybe not. But you can find their book in any library.