A clear, rigorous and thorough exposition of:
*The Propositional Calculus
*The Predicate Calculus
*Set Theory
*The different kinds of continuity and their respective natures
*The different kinds of number: cardinal, ordinal, rational, real, complex, hyper-complex, and transfinite
*The set-theoretic foundations of cardinal arithmetic and the various generalizations thereof
*The nature of formal languages
*Diagonalization and Incompleteness
*The nature of logic and of formal truth, and
*A proof of the incompleteness of any given system of deduction.