Tractatus Logico-Philosophicus by Ludwig Wittgenstein: three parallel tree-structured editions. (1) Tree-structured arrangement of the German text, edited by David G. Stern, Joachim Schulte and Katia Saporiti. (2) Tree-structured arrangement of the English translation by Ogden and Ramsey, edited by David G. Stern. (3) Tree-structured arrangement of the English translation by Pears and McGuinness, edited by David G. Stern.

Recent developments in the semantics of natural language seem to lead to a genuine synthesis of ideas from linguistics and logic, producing novel concepts and questions of interest to both parent disciplines. This book is a collection of essays on such new topics, which have arisen over the past few years. Taking a broad view, developments in formal semantics over the past decade can be seen as follows. At the beginning stands Montague's pioneering work, showing how a rigorous semantics can (...) be given for complete fragments of natural language by creating a suitable fit between syntactic categories and semantic types. This very enterprise already dispelled entrenched prejudices concerning the separation of linguistics and logic. Having seen the light, however, there is no reason at all to stick to the letter of Montague's proposals, which are often debatable. Subsequently, then, many improvements have been made upon virtually every aspect of the enterprise. More sophisticated grammars have been inserted (lately, lexical-functional grammar and generalized phrase structure grammar), more sensitive model structures have been developed (lately, 'partial' rather than 'total' in their com position), and even the mechanism of interpretation itself may be fine-tuned more delicately, using various forms of 'representations' mediating between linguistic items and semantic reality. In addition to all these refinements of the semantic format, descriptive coverage has extended considerably. (shrink)

In this manuscript, published here for the first time, Tarski explores the concept of logical notion. He draws on Klein's Erlanger Programm to locate the logical notions of ordinary geometry as those invariant under all transformations of space. Generalizing, he explicates the concept of logical notion of an arbitrary discipline.

In this paper I develop a new conception of Tarskian logic based on Tarski’s intuitive characterization of logical consequence as formal and necessary in his 1936 paper. Special emphasis is placed on the role of logic in our system of knowledge, the origins of semantics, the semantic definition of logical consequence, and the role of logical and non-logical terms in a logical system. The paper offers a new definition of logical terms based on the question: what division of terms into (...) logical and extra-logical would yield a logical system that satisfies Tarski’s intuitive characterization of logical consequence in complete generality? I discuss the consequences of the new conception for revision in logic, the logicist thesis, and the relation between logic and mathematics. I offer a proof-theoretic perspective on the semantic conception delineated in this paper. And I conclude with a postscript on Tarski’s lecture, “What are Logical Notions?”, which was published shortly after the present conception of logic was developed. (shrink)

Vann McGee; XIII*—Two Problems with Tarski's Theory of Consequence, Proceedings of the Aristotelian Society, Volume 92, Issue 1, 1 June 1992, Pages 273–292, htt.

Alternative readings of quantification are considered. The absence of an unequivocal translation into ordinary speech is noted. Some examples are cited which, in the opinion of the author, are a result of equivocal readings of quantification, or unnecessarily restrictive readings which obscure its primary function.

Wilfrid Hodges; VIII*—Truth in a Structure, Proceedings of the Aristotelian Society, Volume 86, Issue 1, 1 June 1986, Pages 135–152, https://doi.org/10.1093/ari.

A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional (...) coverage of introductory material such as sets. Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. Reduced mathematical rigour to fit the needs of undergraduate students. (shrink)