Chapter 1 - The Propositional Calculus
In the beginning there was simple intuitive logic. Then it got all axiomatic. This chapter starts by defining propositional calculus with truth tables, then winds through the building blocks for a syntactic theory based on axioms and methods for stepping through proofs.
Click here to view the exercises for chapter 1.
Section 1.1 - Propositional Connectives
Everything needs to start somewhere. Section 1.1 introduces the basic building blocks of propositional calculus. Much like all section 1.1's it starts out simple, thus lulling the reader into a sense that the whole book will be straight forward and easy.
Section 1.2 - Tautology
As you would imagine, this chapter covers tautologies. It, however, also covers contradictions, a slew of concepts preceded by "logical", parentheses, and a bunch of concepts only available to those who slog through the exercises.
With that, I was pleased to find many exercises that allowed me to use and develop algebraic tools. It wasn't a throw away section after all.
Section 1.3 - Adequate Sets of Connectives
The adequacy of connectives is novel, but I feel it distracts from the potential of variable truth functions. I suffered the section, but I with the exception of naming joint and alternative denial, I can't say I got much from it.
Section 1.4 - An Axiom System for the Propositional Calculus
Oh crap! Axiomatic theory is something. Here, the foundation of theory is syntactic, that is based entirely on the symbols and the arrangement of those symbols in an expression. It seemed okay at first, but they the axioms of propositional calculus hit, and smoke started coming out of my ears. I mean, do we really need to prove "if B then B"?