The deductive system in Boole's Laws of Thought
(LT) involves both an algebra, which we call
proto-Boolean, and a "general method in Logic" making use
of that algebra. Our object is to elucidate these two components
of Boole's system, to prove his principal results, and to draw
some conclusions not explicit in LT. We also discuss some
examples of incoherence in LT; these mask the genius of
Boole's design and account for much of the puzzled and disparaging
commentary LT has received. Our evaluation of Boole's
logical system does not differ substantially from that advanced in
Hailperin's exhaustive study, Boole's Logic and
Probability. Unlike the latter work, however, we make direct
use of the polynomials native to LT rather than appealing
to formalisms such as multisets and rings.