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This groundbreaking work on logic by the brilliant 19th-century English mathematician George Boole remains influential to this day. Boole's major contribution was to demonstrate conclusively that the symbolic expressions of algebra could be adapted to convey the fundamental principles and operations of logic, which hitherto had been expressed only in words. Boole was thus the founder of today's science of symbolic logic. Summing up his innovative approach, Boole stated, "We ought no longer to associate Logic and ...
This groundbreaking work on logic by the brilliant 19th-century English mathematician George Boole remains influential to this day. Boole's major contribution was to demonstrate conclusively that the symbolic expressions of algebra could be adapted to convey the fundamental principles and operations of logic, which hitherto had been expressed only in words. Boole was thus the founder of today's science of symbolic logic. Summing up his innovative approach, Boole stated, "We ought no longer to associate Logic and Metaphysics, but Logic and Mathematics." As the great English logician Augustus De Morgan later put it, in praise of Boole, his genius consisted in showing that "the symbolic processes of algebra, invented as tools of numerical calculation, should be competent to express every act of thought, and to furnish the grammar and dictionary of an all-containing system of logic." The Laws of Thought lays out this new system in detail and also explores a "calculus of probability."
The story of Boole's life is as impressive as his work. Besides rudimentary lessons from his father and a few years at local schools, Boole was largely self-taught. Revealing his aptitude for many subjects at an early age, he began his career already at age 16 as a teacher at a village school. In his leisure time he tackled the daunting works of Newton, Laplace, and Lagrange on physics and mathematics. By the age of twenty-four he was submitting original papers to the Cambridge Mathematical Journal and at age twenty-nine he won a medal from the Royal Society for his contributions to mathematical analysis. He continued to so impress his contemporaries that five years later he was appointed professor of mathematics at Queens College even though he had no university degree.
At his untimely death of forty-nine, Boole could never have guessed that his new symbolic logic would become essential in the next century for telephone switching and the design of computers. For this practical reason, as well as the sheer intellectual importance of his accomplishment, The Laws of Thought merits our attention today.
|Ch. I||Nature and Design of this Work||1|
|Ch. II||Signs and their Laws||24|
|Ch. III||Derivation of the Laws||39|
|Ch. IV||Division of Propositions||52|
|Ch. V||Principles of Symbolical Reasoning||66|
|Ch. VI||Of Interpretation||80|
|Ch. VII||Of Elimination||99|
|Ch. VIII||Of Reduction||114|
|Ch. IX||Methods of Abbreviation||130|
|Ch. X||Conditions of a Perfect Method||150|
|Ch. XI||Of Secondary Propositions||159|
|Ch. XII||Methods in Secondary Propositions||177|
|Ch. XIII||Clarke and Spinoza||185|
|Ch. XIV||Example of Analysis||219|
|Ch. XV||Of the Aristotelian Logic||226|
|Ch. XVI||Of the Theory of Probabilities||243|
|Ch. XVII||General Method in Probabilities||253|
|Ch. XVIII||Elementary Illustrations||276|
|Ch. XIX||Of Statistical Conditions||295|
|Ch. XX||Problems on Causes||320|
|Ch. XXI||Probability of Judgments||376|
|Ch. XXII||Constitution of the Intellect||399|
Posted May 2, 2009
What sets this edition apart is John Corcoran's extensive and penetrating introduction both to the text and to Boole's logical thought more generally. The result is a valuable addition to Boole scholarship.
Boole is known for creating a formal analogy between logic and algebra by assigning logical interpretations to algebraic operations. The analogy was not perfect. That fact, however, is unimportant, for by creating even a partial analogy, Boole fundamentally changed the way logic is conceived.
Boole's work appeared during a revival of interest in logic after two centuries of unremitting criticism, due largely to misunderstandings about the nature of logic. Beginning in the early decades of the nineteenth century, defenders of logic began to argue that it should be treated as a science like any other, and drew simple analogies between it and mathematics and natural science.
The first of his two major works, Mathematical Analysis of Logic (1847), set out the ground for the formal analogy between mathematics and logic, and then illustrated his approach by recasting the syllogistic logic in algebraic terms.
Laws of Thought is even further removed from the traditional logic. It all but ignores the syllogism, and instead moves to even higher levels.
Corcoran's commentary is valuable to those already familiar with Boole's work, but is especially helpful to those approaching it for the first time. Many existing commentaries approach Boole from a present day perspective, i.e. as anticipating, however imperfectly, things to come. The effect of such an approach, however, is a tendency to stress what is lacking in Boole, rather than he added to logic. Corcoran, by contrast, uses Aristotle's theory of logic as a baseline for his analysis. Starting with simple sentences and immediate inference, Corcoran clearly and accurately shows how Boole's logic covers the same ground. As he puts it, 'Boole was one of the last logicians to take the subject-connector-predicate view of simple propositions seriously'. The result of Corcoran's approach is a view in which Boole's logic is seen to be simpler than Aristotle's in one respect (i.e. as a unified system), and more complicated in another (extending the range of propositions covered within it). By beginning with Aristotle, Corcoran's analysis provides an exceptionally clear account of Boole's positive contributions to logic.
Corcoran also describes things that Boole's system lacks. Thus he points out that Boole never recognized indirect inference, and he notes problems that arise when Boole attempts to use algebraic devices (such as solving equations) as a warrant for logical inference (not all algebraic operations result in logically valid inferences). By detailing both the strengths and weaknesses in Boole's theory, Corcoran provides a balanced and accurate account Boole's proper place in the modern development of logic.
Another welcome feature is the references, often to recent encyclopedia articles, at just those points at which readers with relatively little technical background encounter concepts that require some further explanation. Such an addition makes it easier for those with modest backgrounds in logic and algebra to work through Laws of Thought.
So much of what has happened since LT bears the mark of Boole's influence that it is appropriate to take a fresh look at the work. Corcoran's excellent introduction does this with clarity and rigor.
J. Van Evra
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