Recent content by Omega1

> it appears nobody is a thorough-going formalist anymore Not since 1932 ;) Hilbert's thorough-going Formalism was a philosophy of mathematics together with a program to validate it -- namely, proving that purely formal, "finitary" methods suffice both to derive all mathematical truths as well...

Hurkyl's got it basically right. Maybe waxing technical will help eliminate confusion, so... permit me :) A theory is just a set of sentences of first-order logic (FOL) in some language. Examples include: the set of all sentences (which has no models), the theory of Abelian groups, ordered...