Magazine article Times Higher Education

If A Then B: How the World Discovered Logic: Books

Magazine article Times Higher Education

If A Then B: How the World Discovered Logic: Books

Article excerpt

If A then B: How the World Discovered Logic. By Michael Shenefelt and Heidi White. Columbia University Press. 352pp, Pounds 62.00 and Pounds 20.50. ISBN 9780231161046 and 61053. Published 25 June 2013

Michael Shenefelt and Heidi White's new book is a risky undertaking and, I think, a valuable one. Their aim is to rescue logic from the mathematised corner of the classroom and put it squarely at the heart of philosophy - and indeed life. The risky part is the claim that reasoning, knowledge and rationality are first and foremost matters of logic, of applying that deceptively simple formula "if A then B" to the world. And, moreover, vice versa.

The authors argue, too, that the peculiar government structures of ancient Greece led to Aristotle's syllogisms, while the "new military-political system" of Philip II of Macedon and his son Alexander the Great entailed (so to speak) propositional logic. The Industrial Revolution, with its steam engines and railways, created the need for symbolic logic, and the rise of the middle classes in Europe brought in its wake inductive reasoning.

If the long battle between Catholics and Protestantism was about "whose version of Christianity was theologically correct", this social debate also encouraged renewed study of the problems of logic, the authors argue.

Martin Luther, by encouraging people to refer to the Bible themselves, emphasised both personal introspection and individual reasoning, rather than the blind acceptance of religious authorities. It was just unfortunate, then, that both sides started from different and opposed premises, "and so a great collision between Catholicism and Protestantism became inevitable".

Aristotle is the hero of the tale, but unusually, an effort is made to include less celebrated figures such as Chrysippus and George Boole. After all, as Shenefelt and White say, the basic notion of validity is not that deep. Aristotle's role was to find in geometry "the secret behind classification".

As to philosophy of language, why, no language is comprehen-sible unless it already "conforms to something like logical rules". Ludwig Wittgenstein's mistake came because he not only thought that logical necessities depend on language, but also held that most philosophical riddles were meaningless. In so saying, argue Shenefelt and White, he confused "two very different sorts of meaninglessness: ambiguity and unintelligibility".

Is it a problem that a valid argument in one system can be invalid in another? Does it make logic "relative"? In non-classical logics even our beloved modus ponens - the "valid inference" - is invalid! …

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