Foundations Of Axiomatic Linguistics

TRENDS IN LINGUISTICS is a series of books that open new perspectives in our understanding of language. The series publishes state-of-the-art work on core areas of linguistics across theoretical frameworks as well as studies that provide new insights by building bridges to neighbouring fields such as neuroscience and cognitive science. TRENDS IN LINGUISTICS considers itself a forum for cutting-edge research based on solid empirical data on language in its various manifestations, including sign languages. It regards linguistic variation in its synchronic and diachronic dimensions as well as in its social contexts as important sources of insight for a better understanding of the design of linguistic systems and the ecology and evolution of language. TRENDS IN LINGUISTICS publishes monographs and outstanding dissertations as well as edited volumes, which provide the opportunity to address controversial topics from different empirical and theoretical viewpoints. High quality standards are ensured through anonymous reviewing.

In 1962 a mimeographed sheet of paper fell into my possession. It had been prepared by Ernest Adams of the Philosophy Department at Berkeley as a handout for a colloquim. Headed 'SOME FALLACIES OF FORMAL LOGIC' it simply listed eleven little pieces of reasoning, all in ordinary English, and all absurd. I still have the sheet, and quote a couple of the arguments here to give the idea. • If you throw switch S and switch T, the motor will start. There fore, either if you throw switch S the motor will start, or, if you throw switch T the motor will start . • It is not the case that if John passes history he will graduate. Therefore, John will pass history. The disconcerting thing about these inferences is, of course, that under the customary truth-functional interpretation of and, or, not, and if-then, they are supposed to be valid. What, if anything, is wrong? At first I was not disturbed by the examples. Having at that time consider able personal commitment to rationality in general and formal logic in par ticular, I felt it my duty and found myself easily able (or so I thought) to explain away most of them. But on reflection I had to admit that my expla nations had an ad hoc character, varying suspiciously from example to example.

Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.

First published in 1967. The problems of theoretical phonology are among the most controversial in linguistics. This monograph is a step towards an adequate logical reconstruction of phonological theories and is mainly concerned with Z. S. Harris’ structuralist theory, one of the principal phonological theories of the present day. Topics covered in the work include almost all essential problems of theoretical phonology. The author establishes a set of basic concepts which define almost all other concepts of phonology, and gives an axiomatic characterisation of these concepts. The notion of a unit-length segment is analysed and defined, and a precise formulation of the principles of distribution is given. The author offers a formal analysis of the notion of a phoneme, and finally formulates and discusses fundamental hypotheses of phonology.

TRENDS IN LINGUISTICS is a series of books that open new perspectives in our understanding of language. The series publishes state-of-the-art work on core areas of linguistics across theoretical frameworks as well as studies that provide new insights by building bridges to neighbouring fields such as neuroscience and cognitive science. TRENDS IN LINGUISTICS considers itself a forum for cutting-edge research based on solid empirical data on language in its various manifestations, including sign languages. It regards linguistic variation in its synchronic and diachronic dimensions as well as in its social contexts as important sources of insight for a better understanding of the design of linguistic systems and the ecology and evolution of language. TRENDS IN LINGUISTICS publishes monographs and outstanding dissertations as well as edited volumes, which provide the opportunity to address controversial topics from different empirical and theoretical viewpoints. High quality standards are ensured through anonymous reviewing.

Programming Language Foundations is a concise text that covers a wide range of topics in the mathematical semantics of programming languages, for readers without prior advanced background in programming languages theory. The goal of the book is to provide rigorous but accessible coverage of essential topics in the theory of programming languages. Stump’s Programming Language Foundations is intended primarily for a graduate-level course in programming languages theory which is standard in graduate-level CS curricula. It may also be used in undergraduate programming theory courses but ONLY where students have a strong mathematical preparation.

This volume comprises a selection of papers that were contributed to the 7th International Congress of Logic, Methodology and Philosophy of Science, which was held in Salzburg from the 11th - 16th July, 1983. There were 14 sections in this congress: 1. proof theory and foundations of mathematics 2. model theory and its applica ti on 3. recursion theory and theory of computation 4. axiomatic set theory 5. philosophical logic 6. general methodology of science 7. foundations of probability and induction 8. foundations and philosophy of the physical sciences 9. foundati ons and phi 1 osophy of biology 10. foundations and philosophy of psychology foundations and philosophy 11. of the social sciences 12. foundati ons and philosophy of linguistics 13. history of logic, methodology and philosophy of science 14. fundamental principles of the ethics of science In each section, three or four invited addresses were given, which will be published in the Congress Proceedings (Ruth Barcan Marcus, Georg J. W. Dorn and Paul Weingartner, eds. : Logic, Metho dology and Philosophy of Science VII. Proceedings of the Seventh International Congress of Logic, Methodology and Philosophy of v PREFACE Science, Salzburg, 1983. - Amsterdam, New York, Oxford: North-Holland Publishing 'Company, 1985. ) Every section with the exception of section 14 also contained contributed papers.

Axiomatic functionalism is a highly distinctive and challenging approach in the European functionalist tradition, which has been developed over the last 50 years. It emphasises clarity and accuracy of theory and methods with philosophical awareness for the analysis of languages. Axiomatic Functionalism is even more relevant at a time when functionalism is widely adopted and speculative universalism is being refuted. This book gives a clear orientation in the Axiomatic Functionalist approach with a new introduction, recent previously unpublished work, the latest version of the theory, a reference bibliography, key previously published articles, and an assessment of the contribution of Axiomatic Functionalism. The book covers the key areas of theory, methods, grammar, phonology, and semantics. It provides clear perspectives on a wide range of fundamental and current issues in linguistics.