Download or read book History and Philosophy of Constructive Type Theory written by Giovanni Sommaruga and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive survey of Martin-Löf's constructive type theory, considerable parts of which have only been presented by Martin-Löf in lecture form or as part of conference talks. Sommaruga surveys the prehistory of type theory and its highly complex development through eight different stages from 1970 to 1995. He also provides a systematic presentation of the latest version of the theory, as offered by Martin-Löf at Leiden University in Fall 1993. This presentation gives a fuller and updated account of the system. Earlier, brief presentations took no account of the issues related to the type-theoretical approach to logic and the foundations of mathematics, while here they are accorded an entire part of the book. Readership: Comprehensive accounts of the history and philosophy of constructive type theory and a considerable amount of related material. Readers need a solid background in standard logic and a first, basic acquaintance with type theory.
Download or read book Treatise on Intuitionistic Type Theory written by Johan Georg Granström and published by Springer Science & Business Media. This book was released on 2011-06-02 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.
Download or read book Twenty Five Years of Constructive Type Theory written by Giovanni Sambin and published by Clarendon Press. This book was released on 1998-10-15 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.
Download or read book Intuitionistic Type Theory written by Per Martin-Löf and published by . This book was released on 1984 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modal Homotopy Type Theory written by David Corfield and published by Oxford University Press. This book was released on 2020-02-06 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The old logic put thought in fetters, while the new logic gives it wings." For the past century, philosophers working in the tradition of Bertrand Russell - who promised to revolutionise philosophy by introducing the 'new logic' of Frege and Peano - have employed predicate logic as their formal language of choice. In this book, Dr David Corfield presents a comparable revolution with a newly emerging logic - modal homotopy type theory. Homotopy type theory has recently been developed as a new foundational language for mathematics, with a strong philosophical pedigree. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy offers an introduction to this new language and its modal extension, illustrated through innovative applications of the calculus to language, metaphysics, and mathematics. The chapters build up to the full language in stages, right up to the application of modal homotopy type theory to current geometry. From a discussion of the distinction between objects and events, the intrinsic treatment of structure, the conception of modality as a form of general variation to the representation of constructions in modern geometry, we see how varied the applications of this powerful new language can be.
Download or read book Philosophical Dimensions of Logic and Science written by Artur Rojszczak and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of outstanding contributed papers presented at the 11th International Congress of Logic, Methodology, and Philosophy of Science (Kraków, 1999). The articles address current issues in logic, metamathematics, philosophy of language, philosophy of science, and cognitive science, as well as philosophical problems of biology, chemistry and physics. The volume will be of interest to philosophers, logicians and scientists interested in foundational problems.
Download or read book Philosophical Lectures on Probability written by Bruno de Finetti and published by Springer Science & Business Media. This book was released on 2008-05-01 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bruno de Finetti (1906–1985) is the founder of the subjective interpretation of probability, together with the British philosopher Frank Plumpton Ramsey. His related notion of “exchangeability” revolutionized the statistical methodology. This book (based on a course held in 1979) explains in a language accessible also to non-mathematicians the fundamental tenets and implications of subjectivism, according to which the probability of any well specified fact F refers to the degree of belief actually held by someone, on the ground of her whole knowledge, on the truth of the assertion that F obtains.
Download or read book A Collection of Polish Works on Philosophical Problems of Time and Spacetime written by Helena Eilstein and published by Springer Science & Business Media. This book was released on 2002-06-30 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: These works concern fundamental philosophical problems of time and spacetime, such as the implications of the absolute and relations concepts of motion for the disputes about the character of spacetime, the role of relativity, quantum mechanics, quantum gravity and noncommutative geometry with respect to the controversy concerning the objectivity of the flow of time, the existence of the future, the concept of branching spacetime. One paper presents the views on time of an outstanding representative of phenomenology, Roman Ingarden, thus enriching the book with some questions of philosophical anthropology and ethics. The collection is mainly addressed to research workers and graduate students.
Download or read book Theoretical Knowledge written by Vi︠a︡cheslav Semenovich Stepin and published by Springer Science & Business Media. This book was released on 2005-07-12 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: He shows direct and inverse links between foundations of science and new theories and empirical facts evolved from those, how among many potentially possible histories of science a culture selects just those directions which become a real history of science. The author analyses mechanisms of the generation of scientific theories and shows that those are changed in the process of historical development of science. He displays three historical types of scientific rationality (classical, non-classical and post-non-classical, which appears in modern science) and shows features of their coexistence and interplay. It is shown that along with the emerging of post-non-classical rationality science increases the sphere of its worldview applications. Science begins to correlate not only with the basic values of technogenic civilization but also with some values and patterns of traditional cultures.
Download or read book Linking Game Theoretical Approaches with Constructive Type Theory written by Nicolas Clerbout and published by Springer. This book was released on 2015-07-08 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title links two of the most dominant research streams in philosophy of logic, namely game theory and proof theory. As the work’s subtitle expresses, the authors will build this link by means of the dialogical approach to logic. One important aspect of the present study is that the authors restrict themselves to the logically valid fragment of Constructive Type Theory (CTT). The reason is that, once that fragment is achieved the result can be extended to cover the whole CTT system. The first chapters in the brief offer overviews on the two frameworks discussed in the book with an emphasis on the dialogical framework. The third chapter demonstrates the left-to-right direction of the equivalence result. This is followed by a chapter that demonstrates the use of the algorithm in showing how to transform a specific winning strategy into a CCT-demonstration of the axiom of choice. The fifth chapter develops the algorithm from CTT-demonstrations to dialogical strategies. This brief concludes by introducing elements of discussion which are to be developed in subsequent work.
Download or read book Blameworthy Belief written by Nikolaj Nottelmann and published by Springer Science & Business Media. This book was released on 2007-07-18 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Believing the wrong thing can have drastic consequences. The question of when a person is not only ill-guided, but genuinely at fault for holding a particular belief goes to the root of our understanding of such notions as criminal negligence and moral responsibility. This book explores the conditions under which someone may be deemed blameworthy for holding a particular belief, drawing on contemporary epistemology, ethics and legal scholarship.
Download or read book Trading Ontology for Ideology written by L. Decock and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Willard VanOrman Quine has probably been the most influential th American philosopher of the 20 century. His work spans over seven decades, and covers many domains in philosophy. He has made major contributions to the fields of logic and set theory, philosophy of logic and mathematics, philosophy of language, philosophy of science, epistemology and metaphysics. Quine's first work in philosophy was in the field of logic. His major contributions are the two set-theoretic systems NF (1936) and ML (1940). 1 These systems were alternatives to the type theory of Principia Mathematica or Zermelo's set theory, and are still being studied by 2 mathematicians. An indirect contribution to the field of logic is his strong resistance to moda110gic. Quine's objectIons to the notions of necessity and analyticity have influenced the development of moda110gic? Quine has had an enormous influence on philosophy of mathematics. When Quine entered philosophy there was a discussion on the foundations of mathematics between the schools of intuitionism, formalism, and conventionalism. Quine soon took issue with Carnap's conventionalism in "Truth by convention,,4 (1936). Quine has never joined one of the other schools, but has added new elements that are the basic ones of the 5 contemporary schools of nominalism, platonism, and structuralism. Quine has long been in the shadow of Benacerraf and Putnam in this field. At the moment there seems to be a renewed interest in Quine's work, and most philosophers explicitly refer to Quine's work.
Download or read book The Limits of Logical Empiricism written by Arthur Pap and published by Springer Science & Business Media. This book was released on 2006-03-02 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Withdrawal of Rights written by O. Ezra and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like most discussions within the tradition of rights-talk, this study is motivated by the desire to promote the idea that rights are moral assets that people should acquire in the course of their membership within social and political frameworks. However, while most participants in rights-talk concentrate on the safety and protection constraints required for a successful exercising of rights, the present study inquires into the circumstances under which people's rights lose their validity. The author believes that if we want to prevent the erosion of the role of rights within society and to encourage their obligatory status, we should prevent their misuse, or their unjustified or excessive use. Those who have interests in rights, and are concerned about their withdrawal or denial, will find a unique and inventive way of dealing both with the use, as well as the abuse of rights.
Download or read book Formal Ontology and Conceptual Realism written by Nino B. Cocchiarella and published by Springer Science & Business Media. This book was released on 2007-09-05 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Visualization Explanation and Reasoning Styles in Mathematics written by P. Mancosu and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 20th century philosophy of mathematics has to a great extent been dominated by views developed during the so-called foundational crisis in the beginning of that century. These views have primarily focused on questions pertaining to the logical structure of mathematics and questions regarding the justi?cation and consistency of mathematics. Paradigmatic in this - spect is Hilbert’s program which inherits from Frege and Russell the project to formalize all areas of ordinary mathematics and then adds the requi- ment of a proof, by epistemically privileged means (?nitistic reasoning), of the consistency of such formalized theories. While interest in modi?ed v- sions of the original foundational programs is still thriving, in the second part of the twentieth century several philosophers and historians of mat- matics have questioned whether such foundational programs could exhaust the realm of important philosophical problems to be raised about the nature of mathematics. Some have done so in open confrontation (and hostility) to the logically based analysis of mathematics which characterized the cl- sical foundational programs, while others (and many of the contributors to this book belong to this tradition) have only called for an extension of the range of questions and problems that should be raised in connection with an understanding of mathematics. The focus has turned thus to a consideration of what mathematicians are actually doing when they produce mathematics. Questions concerning concept-formation, understanding, heuristics, changes instyle of reasoning, the role of analogies and diagrams etc.
Download or read book Dynamic Epistemic Logic written by Hans van Ditmarsch and published by Springer Science & Business Media. This book was released on 2007-05-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic Epistemic Logic is the logic of knowledge change. This book provides various logics to support such formal specifications, including proof systems. Concrete examples and epistemic puzzles enliven the exposition. The book also offers exercises with answers. It is suitable for graduate courses in logic. Many examples, exercises, and thorough completeness proofs and expressivity results are included. A companion web page offers slides for lecturers and exams for further practice.
