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This book provides a synthesis of four versions of program semantic—srelational semantics, predicate transformer semantics, information systems, and domain theory—showing, through an exhaustive case study analysis, that it is possible to do back-and-forth translation from any of these versions of program semantics into any of the others, and demonstrating that while there are many variations of each, in principle they may be thought of as intertranslatable.

During his long and continuing scholarly career, Patrick Suppes has contributed significantly both to the sciences and to scientific philosophies. In this volume, an international group of Suppes’s colleagues, collaborators, and students seeks to build upon Suppes’s insights. Each of their essays is accompanied by a response from Suppes himself, which together create a uniquely engaging dialogue. Suppes and his peers explore a diverse array of topics including the relationship between science and philosophy; the philosophy of physics; problems in the foundations of mathematics; theory of measurement, decision theory, and probability; the foundations of economics and political theory; psychology, language, and the philosophy of language; Suppes’s most recent research in neurobiology; and the alignment (or misalignment) of method and policy.

The application of logic to grammar is a fundamental issue in philosophy and has been investigated by such renowned philosophers as Leibniz, Bolzano, Frege, and Husserl. Language and Grammar examines categorial grammars and type-logical grammars, two linguistic theories that play a significant role in this area of study yet have been overshadowed until recently. The prominent scholars contributing to this volume also explore the impact of the Lambek program on linguistics and logical grammar, producing, ultimately, an exciting and important resource that demonstrates how type-logical grammars are promising future models of reasoning and computation.

With the rise of the internet and the proliferation of technology to gather and organize data, our era has been defined as "the information age." With the prominence of information as a research concept, there has arisen an increasing appreciation of the intertwined nature of fields such as logic, linguistics, and computer science that answer the questions about information and the ways it can be processed. The many research traditions do not agree about the exact nature of information. By bringing together ideas from diverse perspectives, this book presents the emerging consensus about what a conclusive theory of information should be. The book provides an introduction to the topic, work on the underlying ideas, and technical research that pins down the richer notions of information from a mathematical point of view.

The book contains contributions to a general theory of information, while also tackling specific problems from artificial intelligence, formal semantics, cognitive psychology, and the philosophy of mind. There is focus on the dynamics of information flow, and also a consideration of static approaches to information content; both quantitative and qualitative approaches are represented.

Mathematicians at every level use diagrams to prove theorems. Mathematical Reasoning with Diagrams investigates the possibilities of mechanizing this sort of diagrammatic reasoning in a formal computer proof system, even offering a semi-automatic formal proof system—called Diamond—which allows users to prove arithmetical theorems using diagrams.

Mathematical Structures in Languages introduces a number of mathematical concepts that are of interest to the working linguist. The areas covered include basic set theory and logic, formal languages and automata, trees, partial orders, lattices, Boolean structure,  generalized quantifier theory, and linguistic invariants, the last drawing on Edward L. Keenan and Edward Stabler’s Bare Grammar: A Study of Language Invariants, also published by CSLI Publications. Ideal for advanced undergraduate and graduate students of linguistics, this book contains numerous exercises and will be a valuable resource for courses on mathematical topics in linguistics. The product of many years of teaching, Mathematic Structures in Languages is very much a book to be read and learned from.

This considerably revised second edition of Wittgenstein's 1914-16 notebooks contains a new appendix with photographs of Wittgenstein's original work, a new preface by Elizabeth Anscombe, and a useful index by E.D. Klemke. Corrections have been made throughout the text, and notes have been added, making this the definitive edition of the notebooks. The writings intersperse Wittgenstein's technical logical notations with his thoughts on the meaning of life, happiness, and death.

"When the first edition of this collection of remarks appeared in 1961 we were provided with a glimpse of the workings of Wittgenstein's mind during the period when the seminal ideas of the Tractatus Logico-Philosophicus were being worked out. This second edition provided the occasion to be struck anew by the breadth, rigor, and above all the restlessness of that mind."—T. Michael McNulty, S. J., The Modern Schoolman

When in May 1930, the Council of Trinity College, Cambridge, had to decide whether to renew Wittgenstein's research grant, it turned to Bertrand Russell for an assessment of the work Wittgenstein had been doing over the past year. His verdict: "The theories contained in this new work . . . are novel, very original and indubitably important. Whether they are true, I do not know. As a logician who likes simplicity, I should like to think that they are not, but from what I have read of them I am quite sure that he ought to have an opportunity to work them out, since, when completed, they may easily prove to constitute a whole new philosophy."

"[Philosophical Remarks] contains the seeds of Wittgenstein's later philosophy of mind and of mathematics. Principally, he here discusses the role of indispensable in language, criticizing Russell's The Analysis of Mind. He modifies the Tractatus's picture theory of meaning by stressing that the connection between the proposition and reality is not found in the picture itself. He analyzes generality in and out of mathematics, and the notions of proof and experiment. He formulates a pain/private-language argument and discusses both behaviorism and the verifiability principle. The work is difficult but important, and it belongs in every philosophy collection."—Robert Hoffman, Philosophy

"Any serious student of Wittgenstein's work will want to study his Philosophical Remarks as a transitional book between his two great masterpieces. The Remarks is thus indispensible for anyone who seeks a complete understanding of Wittgenstein's philosophy."—Leonard Linsky, American Philosophical Association

The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. In this volume, after a general presentation of weak arithmetics, the following topics are studied: the properties of integers of a real closed field equipped with exponentiation; conservation results for the induction schema restricted to first-order formulas with a finite number of alternations of quantifiers; a survey on a class of tools called pebble games; the fact that the reals e and pi have approximations expressed by first-order formulas using bounded quantifiers; properties of infinite pictures depending on the universe of sets used; a language that simulates in a sufficiently nice manner all  algorithms of a certain restricted class; the logical complexity of the axiom of infinity in some variants of set theory without the axiom of  foundation; and the complexity to determine whether a trace is included in another one.

The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. New Studies in Weak Arithmetics is dedicated to late Australian mathematician Alan Robert Woods (1953-2011), whose seminal thesis is published here for the first time. This volume also contains the unpublished but significant thesis of Hamid Lesan (1951-2006) as well as other original papers on topics addressed in Woods’s thesis and life’s work that were first presented at the 31st Journées sur les Arithmétiques Faibles meeting held in Samos, Greece, in 2012.

The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. This third volume in the weak arithmetics collection contains nine substantive papers based on lectures delivered during the two last meetings of the conference series Journées sur les Arithmétiques, held in 2014 at the University of Gothenburg, Sweden, and in 2015 at the City University of New York Graduate Center.

Although Wittgenstein claimed that his first book, the Tractatus Logico-Philosophicus, was essentially an ethical work, it has been viewed insistently as a purely logical one. His later work, Philosophical Investigations, is generally seen as presenting totally different ideas from his earlier writings. In this book, Michael Hodges shows how Wittgenstein’s later work emerged from his earlier Tractatus, and he unifies the early philosophy, both its well-known logical aspects and the lesser known ethical dimensions, in terms of the notion of transcendence.

Hodges studies the Tractatus in light of Wittgenstein’s own claim that the Philosophical Investigations can only be understood when read against the background of the Tractatus. At the heart of an understanding of the earlier work is the idea of transcendence which structures both Wittgenstein’s logical and ethical insights. Seen in terms of this notion, the rigorous unity of Wittgenstein’s early thinking becomes apparent and the gestalt shift to the later philosophy comes clearly into focus.

Throughout the twentieth century, the classical logic of Frege and Russell dominated the field of formal logic. But, as Ross Brady argues, a new type of weak relevant logic may prove to be better equipped to present new solutions to persistent paradoxes. Universal Logic begins with an overview of classical and relevant logic and discusses the limitations of both in analyzing certain paradoxes. It is the first text to demonstrate how the main set-theoretic and semantic paradoxes can be solved in a systematic way and as such will be of great interest to both scholars and students of logic.