Boole's logic

This chapter presents the principles of Boole's algebraic logic that have unlimitedly many uses. Boole in his philosophical moments seems to have thought that the extension of his logic to probability theory and its use in what he refers to as the use of logic in the further investigation of the mind are its most important applications. The judgment of history is rather different, and not entirely in agreement with Boole's own assessment. Probability theory has since been established as an independent mathematical theory with only incidental connections to logic as Boole conceived of it. The use of logic as a tool for the systematic study of thought has equally failed to attract much of a following in the years since Boole's death. The idea that logic describes laws of thought and can be used in turn as a method of psychology has come to be regarded as an objectionable kind of psychologism, which Boolean algebra has managed to survive in spite of itself in the opinion of many contemporary logicians and mathematicians.