Saturday, August 11, 2007

Generalizations

Generalizations, it is said, are crucial to inferences about the workings of the world. But there is a deep mystery about how and why generalizations work (if they do work). Consider John Woods, Ralph Johnson, Dov Gabbay & Hans Ohlbach, "Logic and the Practical Turn," in HANDBOOK OF THE LOGIC OF ARGUMENT AND INFERENCE 1, 16 (2002) (vol. 1 in series STUDIES IN LOGIC AND PRACTICAL REASONING, eds., D. Gabbay, J. Siekmann, J. van Benthem & J. Woods):
How is it possible that there be a range of cases by which projections from samples are so nearly right while at the same time qualifying as travesties of what the logic of induction requires? The empirical record amply attests to a human being's capacity for pre-inductive generalization and projection.
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