Reddit reviews Principia Mathematica - Volume One

A three-volume set (one, two, three) appears to be available on Amazon.com for $25 per volume.

> Sure even our number system is a social construct, but the fact that one and one make two isn't.

I don't think you quite understand what the statement "1+1=2" is. Try reading Russell & Whitehead to see how they literally construct that statement from axioms - and before doing so, construct the concepts "1", "+", "=" and "2".

Edit: you need Vol. II for the construction of arithmetics.

It's the other way around: mathematics is logic, and has been described that way, again, ever since Frege's Basic Laws of Arithmetic, although the most famous work in attempting to put mathematics on a solid logical foundation remains the three volumes of Russell and Whitehead's Principia Mathematica. And now we come to our own history, because Alonzo Church came up with a simpler, more powerful logic than Russell and Whitehead's, but then his grad students Kleene and Rosser proved that it was inconsistent. So Church added a variant of Russell's theory of types to his logic, and here we are today.

Update: This isn't to say everyone who does math does so explicitly in terms of logic, of course. But when we say "you can't divide by zero," or "this series diverges," or we do "real" or "complex analysis," or when we use "set theory," we are explicitly making logical statements or employing the logical descriptions of the mathematics, possibly even going so far as to talk about the "real" numbers in terms of Cauchy completion or Dedekind cuts. Any good, modern text on mathematical foundations will define the natural numbers in terms of the Peano axioms, then the integers in terms of the natural numbers, then the rationals in terms of the integers, and finally the reals in terms of the rationals. And so on.

Well if you're going to start at the beginning, you might as well start at the beginning, I suggest you pick up this little number