There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.

An argument is self-defeating when it contains defeaters for some of its own defeasible lines. It is shown that the obvious rules for defeat among arguments do not handle self-defeating arguments correctly. It turns out that they constitute a pervasive phenomenon that threatens to cripple defeasible reasoning, leading to almost all defeasible reasoning being defeated by unexpected interactions with self-defeating arguments. This leads to some important changes in the general theory of defeasible reasoning.

By means of an example, shows the possibility of beliefs that are separately rational whilst together inconsistent.

Practical reasoning aims at deciding what actions to perform in light of the goals a rational agent possesses. This has been a topic of interest in both philosophy and artificial intelligence, but these two disciplines have produced very different models of practical reasoning. The purpose of this paper is to examine each model in light of the other and produce a unified model adequate for the purposes of both disciplines and superior to the standard models employed by either.The philosophical (decision-theoretic) (...) model directs activity by evaluating acts one at a time in terms of their expected utilities. It is argued that, except in certain special cases, this constitutes an inadequate theory of practical reasoning leading to intuitively incorrect action prescriptions. Acts must be viewed as parts of plans, and plans evaluated as coherent units rather than piecemenal in terms of the acts comprising them. Rationality dictates choosing acts by first choosing the plans prescribing them. Plans, in turn, are compared by looking at their expected values. However, because plans can be embedded in one another, we cannot select plans just by maximizing expected values. Instead, we must employ a more complex criterion here named coextendability. (shrink)

The system presented by the author in The Logical Foundations of Statistical Inference suffered from certain technical difficulties, and from a major practical difficulty; it was hard to be sure, in discussing examples and applications, when you had got hold of the right reference class. The present paper, concerned mainly with the characterization of randomness, resolves the technical difficulties and provides a well structured framework for the choice of a reference class. The definition of randomness that leads to this framework (...) is simplified and clarified in a number of respects. It resolves certain puzzles raised by S. Spielman and W. Harper in their contributions to Profiles: Henry E. Kyburg, Jr. and Isaac Levi 1982). (shrink)