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Let p denote a prime. In this article we provide the first published lower bounds for the greatest prime factor of p − 1 exceeding (p − 1) 1 2 in which the constants are effectively computable. As a result we prove that it is possible to calculate a value x 0 such that for every x > x 0 there is a p < x with the greatest prime factor of p − 1 exceeding x 3… (More)

The Problem The problem of induction is sometimes motivated via a comparison between rules of induction and rules of deduction. Valid deductive rules are necessarily truth preserving, while inductive rules are not. So, for example, one valid deductive rule might be this: (D) From premises of the form "All F are G" and "a is F," the corresponding conclusion… (More)

In this article, we provide a tutorial overview of some aspects of statistical learning theory, which also goes by other names such as statistical pattern recognition, nonparametric classification and estimation, and supervised learning. We focus on the problem of two-class pattern classification for various reasons. This problem is rich enough to capture… (More)

- Neil Francis Delaney, Thomas Flint, Paul Benacerraf, Mark Johnston, Gilbert Harman, Tom Cavanaugh +2 others
- 2006

Philosophers from Hart to Lewis, Johnston and Bennett have expressed various degrees of reservation concerning the doctrine of double effect. A common concern is that, with regard to many activities that double effect is traditionally thought to prohibit, what might at first look to be a directly intended bad effect is really, on closer examination, a… (More)

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