Semantical Investigations In Heyting S Intuitionistic Logic
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Semantical Investigations In Heyting S Intuitionistic Logic
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Author : Dov M. Gabbay
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Semantical Investigations In Heyting S Intuitionistic Logic written by Dov M. Gabbay and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Philosophy categories.
From the point of view of non-classical logics, Heyting's implication is the smallest implication for which the deduction theorem holds. This book studies properties of logical systems having some of the classical connectives and implication in the neighbourhood of Heyt ing's implication. I have not included anything on entailment, al though it belongs to this neighbourhood, mainly because of the appearance of the Anderson-Belnap book on entailment. In the later chapters of this book, I have included material that might be of interest to the intuitionist mathematician. Originally, I intended to include more material in that spirit but I decided against it. There is no coherent body of material to include that builds naturally on the present book. There are some serious results on topological models, second order Beth and Kripke models, theories of types, etc., but it would require further research to be able to present a general theory, possibly using sheaves. That would have postponed pUblication for too long. I would like to dedicate this book to my colleagues, Professors G. Kreisel, M.O. Rabin and D. Scott. I have benefited greatly from Professor Kreisel's criticism and suggestions. Professor Rabin's fun damental results on decidability and undecidability provided the powerful tools used in obtaining the majority of the results reported in this book. Professor Scott's approach to non-classical logics and especially his analysis of the Scott consequence relation makes it possible to present Heyting's logic as a beautiful, integral part of non-classical logics.
Advances In Proof Theoretic Semantics
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Author : Thomas Piecha
language : en
Publisher: Springer
Release Date : 2015-10-24
Advances In Proof Theoretic Semantics written by Thomas Piecha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-24 with Philosophy categories.
This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.
David Makinson On Classical Methods For Non Classical Problems
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Author : Sven Ove Hansson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-20
David Makinson On Classical Methods For Non Classical Problems written by Sven Ove Hansson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-20 with Philosophy categories.
The volume analyses and develops David Makinson’s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson’s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources of classical logic. Among the contributions included in the volume, one chapter focuses on the “inferential preferential method”, i.e. the combined use of classical logic and mechanisms of preference and choice and provides examples from Makinson’s work in non-monotonic and defeasible reasoning and belief revision. One chapter offers a short autobiography by Makinson which details his discovery of modern logic, his travels across continents and reveals his intellectual encounters and inspirations. The chapter also contains an unusually explicit statement on his views on the (limited but important) role of logic in philosophy.
Formal Models And Semantics
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Author : Bozzano G Luisa
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Formal Models And Semantics written by Bozzano G Luisa and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
The second part of this Handbook presents a choice of material on the theory of automata and rewriting systems, the foundations of modern programming languages, logics for program specification and verification, and some chapters on the theoretic modelling of advanced information processing.
Philosophy And Logic In Search Of The Polish Tradition
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Author : Jaakko Hintikka
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Philosophy And Logic In Search Of The Polish Tradition written by Jaakko Hintikka and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Philosophy categories.
On the occasion of bis sixtieth birthday, we dedicate this volume to Jan Wo leriski-s-our teacher, our colleague, our friend. Both of us are particularly indebted to Jan not only with regards to profes sional matters, but some private ones as well. Hence, we hope that he forgives us an occasional lapse into fondness and affection. That said, may the list of bis personalmerits remain shrouded in mystery; rather than unveil them, we open here by appraising Jan's presence from a broader perspective. Tonote that Jan was not always a part of our lives would not evoke surprise. However, to imagine the Institute of Pbilosophy on Grodzka Street or Krakow pbilosophy without him in it would be a harder task-at least for us, Nonethe less, we do remember the days when he was commuting to Krakow as a guest lecturer. Is there anything about those days which particularly comes to mind? To shed light on the story which follows, one must begin by stating that the early 1980s when we were studying philosophy was not a bright period. The great masters of Krakow philosophy-Ingarden, Mehlberg, Zawirski, or Dambska-> were either dead or, for political reasons, kept silent. The years following Martial Law (1981-1983) were intellectually very blighted and barren. In the midst of all this we were attending Jan's course on general methodology.
The Limits Of Logical Empiricism
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Author : Arthur Pap
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-02
The Limits Of Logical Empiricism written by Arthur Pap and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-02 with Philosophy categories.
This volume collects some of the most significant papers of Arthur Pap. Pap’s work played an important role in the development of the analytic tradition. This goes beyond the merely historical fact of Pap’s influential views of dispositional and modal concepts. Pap's writings in philosophy of science, modality, and philosophy of mathematics provide insightful alternative perspectives on philosophical problems of current interest.
I Am You
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Author : Daniel Kolak
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-03
I Am You written by Daniel Kolak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-03 with Philosophy categories.
Borders enclose and separate us. We assign to them tremendous significance. Along them we draw supposedly uncrossable boundaries within which we believe our individual identities begin and end, erecting the metaphysical dividing walls that enclose each one of us into numerically identical, numerically distinct, entities: persons. Do the borders between us - physical, psychological, neurological, causal, spatial, temporal, etc. - merit the metaphysical significance ordinarily accorded them? The central thesis of I Am You is that our borders do not signify boundaries between persons. We are all the same person. Variations on this heretical theme have been voiced periodically throughout the ages (the Upanishads, Averroës, Giordano Bruno, Josiah Royce, Schrödinger, Fred Hoyle, Freeman Dyson). In presenting his arguments, the author relies on detailed analyses of recent formal work on personal identity, especially that of Derek Parfit, Sydney Shoemaker, Robert Nozick, David Wiggins, Daniel C. Dennett and Thomas Nagel, while incorporating the views of Descartes, Leibniz, Wittgenstein, Schopenhauer, Kant, Husserl and Brouwer. His development of the implied moral theory is inspired by, and draws on, Rawls, Sidgwick, Kant and again Parfit. The traditional, commonsense view that we are each a separate person numerically identical to ourselves over time, i.e., that personal identity is closed under known individuating and identifying borders - what the author calls Closed Individualism - is shown to be incoherent. The demonstration that personal identity is not closed but open points collectively in one of two new directions: either there are no continuously existing, self-identical persons over time in the sense ordinarily understood - the sort of view developed by philosophers as diverse as Buddha, Hume and most recently Derek Parfit, what the author calls Empty Individualism - or else you are everyone, i.e., personal identity is notclosed under known individuating and identifying borders, what the author calls Open Individualism. In making his case, the author: - offers a new explanation both of consciousness and of self-consciousness - constructs a new theory of Self - explains psychopathologies (e.g. multiple personality disorder, schizophrenia) - shows Open Individualism to be the best competing explanation of who we are - provides the metaphysical foundations for global ethics. The book is intended for philosophers and the philosophically inclined - physicists, mathematicians, psychiatrists, psychologists, linguists, computer scientists, economists, and communication theorists. It is accessible to graduate students and advanced undergraduates.
Attitudes And Changing Contexts
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Author : Robert van Rooij
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Attitudes And Changing Contexts written by Robert van Rooij and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Philosophy categories.
In this book, the author defends a unified externalists account of propositional attitudes and reference, and formalizes this view within possible world semantics. He establishes a link between philosophical analyses of intentionality and reference and formal semantic theories of discourse representation and context change. Stalnakerian diagonalization plays an important role here. Anaphora are treated as referential expressions, while presupposition is seen as a propositional attitude. The relation between belief change and the semantic analyses of conditional sentences and evidential (knowledge) and buletic (desire) propositional attitudes is discussed extensively.
Brouwer Meets Husserl
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Author : Mark van Atten
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-08
Brouwer Meets Husserl written by Mark van Atten and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-08 with Mathematics categories.
Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost? And are there objects of pure mathematics that can change through time? Mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is "yes''. To this end he introduced a new kind of object into mathematics, the choice sequence. But other mathematicians and philosophers have been voicing objections to choice sequences from the start. This book aims to provide a sound philosophical basis for Brouwer's choice sequences by subjecting them to a phenomenological critique in the style of the later Husserl.
Formal Ontology And Conceptual Realism
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Author : Nino B. Cocchiarella
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-05
Formal Ontology And Conceptual Realism written by Nino B. Cocchiarella and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-05 with Philosophy categories.
Theories about the ontological structure of the world have generally been described in informal, intuitive terms. This book offers an account of the general features and methodology of formal ontology. The book defends conceptual realism as the best system to adopt based on a logic of natural kinds. By formally reconstructing an intuitive, informal ontological scheme as a formal ontology we can better determine the consistency and adequacy of that scheme.