By a logical theory I mean a formal system together with its semantics, meta-theory, and rules for translating ordinary language into its notation. Logical theories can be used descriptively (for example, to represent particular arguments or to depict the logical form of certain sentences). Here the logician uses the usual methods of empirical science to assess the correctness of his descriptions. However, the most important applications of logical theories are normative, and here, I argue, the epistemology is that of wide (...) reflective equilibrium. The result is that logic not only assesses our inferential practice but also changes it. I tie my discussion to Thagard's views concerning the relationship between psychology and logic, arguing against him that psychology has and should have only a peripheral role in normative (and most descriptive) applications of logic. (shrink)

Gilbert Harman, in Logic and Reasoning (Synthese 60 (1984), 107–127) describes an unsuccessful attempt ... to develop a theory which would give logic a special role in reasoning. Here reasoning is psychological, a procedure for revising one''s beliefs. In the present paper, I construe reasoning sociologically, as a process of linguistic interaction; and show how both reasoning in the psychologistic sense and logic are related to that process.

Some philosophers suspect that the functionalist account of mind supports a psychologistic account of logic. One who has argued for a connection of this kind is Remmel T. Nunn. If the connection holds, it might be a powerful support for the currently unfashionable position of psychologism; conversely, it might be a damaging objection to functionalism. In either case, to estabjish the connection would be an achievement of considerable philosophic interest.

Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre (...) Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations. (shrink)

Frege argued that though it is logically possible for an illogical community to exist, It is not possible that it should be right. Neither the assertion of false statements nor the acceptance of invalid arguments suffices to render a community illogical. The kinds of behavior which would suffice prove, On examination, To be very rare, But to justify frege's rather obscure remarks on illogicality and the universality of logical laws. The laws of logic are to be understood as constraints on (...) the kinds of rules governing linguistic exchanges needed if the language is to accommodate attempts to prove. (edited). (shrink)