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Putting Logic in Its Place: Formal Constraints on Rational Belief

4 out of 5 stars 1 customer review
ISBN-13: 978-0199204311
ISBN-10: 0199204314
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Editorial Reviews

Review

Putting Logic in its place is a well-written book, made accessible by its brevity and lack of technicality. It will admirably serve both the seasoned hand and the newcomer looking for a survey of the territory. Michael G. Titelbaum MIND

About the Author

David Christensen is in the Department of Philosophy, University of Vermont. --This text refers to the Hardcover edition.
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Product Details

  • Paperback: 200 pages
  • Publisher: Oxford University Press (April 12, 2007)
  • Language: English
  • ISBN-10: 0199204314
  • ISBN-13: 978-0199204311
  • Product Dimensions: 7.9 x 0.5 x 5.3 inches
  • Shipping Weight: 11.4 ounces (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #1,381,784 in Books (See Top 100 in Books)

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The Oxford series of which this slim volume is a member is a very exciting series of books designed to be introductions to major areas of intellectual life--sort of a "dummies" series for academia. I have read many of these slim volumes with great profit.

This contribution is introductory only in the sense that it does not presume that the reader has read the relevant literature. It is not introductory in that the issues dealt with are highly specialized, and the general field of "logic" is not covered at all. Indeed, the author assumes we are interested in a particular form of modal logic in which truth is replaced by something like warranted belief.

This is a very interesting idea, leading to a host of interesting problems that do not arise in standard logic. For instance, Modus Ponens says that p and (p implies q) implies q. Not for Cristensen. If you believe p and you believe p implies q, but you don't believe q, then you have a problem. Perhaps you you stop believing p, because you are pretty hooked on q being true. Or, perhaps p does not imply q.

A key problem addressed by Christensen is the following. Suppose p stands for "the ball in in the red urn" and q stands for "the ball is in the green urn." If I know the ball is in one of the urns, then I believe p or q, but if I don't know which one it is in, then I don't believe p and I don't believe q. Now in standard logic p or q is true implies p is true or q is true. But in this modal logic, I can believe p or q, but I don't have to believe p or believe q.

Christensen uses this and other techniques to argue that we need a graded, probabilistic notion of belief, not a zero-one notion. This of course is what Bayesian have maintained all the time. Indeed, I even find the idea of believing something with probability one to be questionable, since there is no way to update if you are wrong (without having implausible hierarchies of belief).
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