The laws of thought

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Instead of writing an original review I decided to quote excerpts from a review by Prof. James Van Evra, a noted authority on Boole and on the history of logic since 1800. The entire review can be found in the journal PHILOSOPHY IN REVIEW; Volume 24 (2004) pages 167-169. The words below are all by Prof. Van Evra.

The body of this book is a replica of the 1854 edition of George Boole’s great work in logic.  While it has been widely available in this form for over a century, what sets this edition apart is the inclusion of 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 conveniently bound with Boole’s major work.

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 (W. V. O. Quine’s review of Desmond MacHale’s biography of Boole (“In the Logical Vestibule”) is an excellent example of this approach).  There is some justification for doing this—Boole, after all, tended to be forward looking and had little positive to say about the tradition which preceded him.  The effect of such an approach, however, is a tendency to stress what is lacking in Boole, rather than his positive contribution.  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’ (xiii).  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.

            At the same time, 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 of Corcoran’s introduction is the inclusion of 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.

            This year is the sesquicentennial anniversary of the publication of Laws of Thought.  So much of what has happened in the meantime bears the mark of Boole’s influence that it is appropriate to mark the occasion with a fresh look at the work.  Corcoran’s excellent introduction does this with clarity and rigor.