Publisher Summary This chapter discusses George Boole's book on algebra. In this book Boole's algebra of logic received its definitive form. Its influence was slow to develop, and then some changes in the algebra were made by others; but the theory became part of the fabric of logic, and also of computing in modern times. The book also contains a notable contribution to probability theory. In his book, Boole showed that he saw his algebraised logic as applied mathematics. The title of mathematical analysis of logic (MAL) shows it already; and in the main text of his article titled LT, he stated his aim as not only “to investigate the fundamental laws of those operations of the mind by which reasoning is performed,” but also “to give expression to them in the symbolic language of a Calculus.” A major difference from MAL was the status of syllogistic logic. Boole had realized in the meantime that he had advanced his algebra of logic far beyond the Aristotelian tradition. The proposed theory was normative; Boole did not try to treat the mysterious depths of actual thought. Now Babbage's work presaged the modern computer, which is the chief source of the ubiquity of Boole's name today.
[1]
Theodore Hailperin,et al.
Boole's logic and probability
,
1976
.
[2]
David Eugene Smith,et al.
History of Modern Mathematics
,
2007,
Nature.
[3]
Desmond MacHale,et al.
George Boole: His Life and Work
,
1985
.
[4]
I. Grattan-Guinness.
The correspondence between george boole and stanley jevons, 1863–1864
,
1991
.
[5]
George Boole,et al.
VIII. On a general method in analysis
,
1844,
Philosophical Transactions of the Royal Society of London.
[6]
John Corcoran,et al.
Boole's criteria for validity and invalidity
,
1980,
Notre Dame J. Formal Log..
[7]
Daniel D. Merrill.
Augustus De Morgan and the Logic of Relations
,
1990
.
[8]
Maria Panteki.
Relationships between algebra, differential equations and logic in England 1800-1860
,
1991
.
[9]
George Boole,et al.
The mathematical analysis of logic
,
1948
.