rinted them, in 1865, in a supplementary volume.

With the exception of Augustus de Morgan, Boole was probably the first
English mathematician since the time of John Wallis who had also written
upon logic. His novel views of logical method were due to the same
profound confidence in symbolic reasoning to which he had successfully
trusted in mathematical investigation. Speculations concerning a
calculus of reasoning had at different times occupied Boole's thoughts,
but it was not till the spring of 1847 that he put his ideas into the
pamphlet called _Mathematical Analysis of Logic_. Boole afterwards
regarded this as a hasty and imperfect exposition of his logical system,
and he desired that his much larger work, _An Investigation of the Laws
of Thought, on which are founded the Mathematical Theories of Logic and
Probabilities_ (1854), should alone be considered as containing a mature
statement of his views. Nevertheless, there is a charm of originality
about his earlier logical work which no competent reader can fail to
appreciate. He did not regard logic as a branch of mathematics, as the
title of his earlier pamphlet might be taken to imply, but he pointed
out such a deep analogy between the symbols of algebra and those which
can be made, in his opinion, to represent logical forms and syllogisms,
that we can hardly help saying that logic is mathematics restricted to
the two quantities, 0 and 1. By unity Boole denoted the universe of
thinkable objects; literal symbols, such as x, y, z, v, u, &c., were
used with the elective meaning attaching to common adjectives and
substantives. Thus, if x=horned and y=sheep, then the successive acts of
election represented by x and y, if performed on unity, give the whole
of the class _horned sheep_. Boole showed that elective symbols of this
kind obey the same primary laws of combination as algebraical symbols,
whence it followed that they could be added, subtracted, multiplied and
even divided, almost exactly in the same manner as numbers. Thus, 1 - x
would represent the operation of selecting all things in the world
except _horned things_, that is, _all not horned things_, and (1 - x)(1
- y) would give us _all things neither horned nor sheep_. By the use of
such symbols propositions could be reduced to the form of equations, and
the syllogistic conclusion from two premises was obtained by eliminating
the middle term according to ordinary algebraic rules.

Still more original and re