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I am excerpting Alasdair Urquhart's BSL review.
This volume is a collection of fourteen papers presented at the Colloquium on Logic and Analytic Philosophy at Santiago de Compostela between 2001 and 2005. In the first part, seven papers (not reviewed here) are devoted to topics in analytic philosophy.
The second part consists of seven papers presented at “The Corcoran Symposium,” a two-day conference held in connection with the conferral of the degree Doctor Honoris Causa on Professor John Corcoran in October 2003.
Corcoran’s article is a conspectus of the history of logic, with Aristotle, Boole and Tarski as representative of the earliest, transitional and most recent periods. Aristotle’s contribution is described as consisting of the systematization of methods of proving validity in a limited domain of propositions expressed in canonical notation, as well as the method of countermodels for establishing invalidity. Boole presented the first system of mathematical
logic, and was the founder of logic as formal ontology by including the study of tautologies and metalogical laws such as excluded middle. Tarski in his fundamental papers of the 1930s on truth, consequence and definability identified and addressed the need for systematic metatheory of logical theories.
Ignacio Jane is concerned with the “common concept of consequence” discussed by Tarski in his well known paper of 1936 on the concept of logical consequence (JSL II 83). Jane provided detailed arguments in an earlier article (BSL XII 1–42) showing that the “common concept” that Tarski had in mind was the conception current in the development of mathematical axiomatics. In the present article, he addresses the question of whether Tarski’s definition is adequate in more general settings, outside formal axiomatics. The overall upshot
is negative, due to the fact that a given informal argument can be held to be logically valid or invalid, depending on the formalization chosen.
The article by Martınez-Vidal discusses five papers by Corcoran that have been
translated into Spanish, and their influence on logical work at the U.S.C. These include articles on the interpretation of Aristotle’s logic and argumentation theory. She concludes with a survey of Corcoran’s general views on logic: mathematical logic as a technique of modelling mathematical discourse, and the contrast between the atemporal, objective notion of logical consequence and the timebound, personal activity of producing concrete proofs.
Nepomuceno's contribution takes up the information theoretic approach
to logic developed by Corcoran in three papers published in the 1990s. Nepomuceno proposes an information-based approach to defining relevant consequence.
Stephen Read’s article is a vigorous defence of the law of indiscernability of identicals, and of the view that there are no opaque contexts. Saguillo touches on several of the themes in Corcoran’s work mentioned above, as well as others, such as his advocacy of second-order logic, his influential work on Aristotle’s syllogistic as a natural deduction system, and and his views on logicalparadoxes.
Finally, Stewart Shapiro’s contribution surveys Corcoran’s more technical contributions to logic, including natural deduction formulations of modal logic, work on variable binding term operators, string theory and investigations of categoricity in second order languages.
The editors have succeeded in assembling an interesting collection of diverse papers reflecting the work of a philosopher-logician who has been influential both through his writing and teaching.
Department of Computer Science, University of Toronto, Toronto, Ontario
Juan José Acero
Agustín Arrieta Urtizberea
Antonio Blanco Salgueiro
Ernest Lepore Ludwig Kirk
Genoveva Martí José Martínez Fernández
Javier Vilanova Árias
Part ii Segunda Parte