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Author: Giovanni Sommaruga
Publisher: Springer Science & Business Media
ISBN: 9401593930
Category : Philosophy
Languages : en
Pages : 377
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Book Description
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.
Author: Giovanni Sommaruga
Publisher: Springer Science & Business Media
ISBN: 9401593930
Category : Philosophy
Languages : en
Pages : 377
Get Book Here
Book Description
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.
Author: David Corfield
Publisher: Oxford University Press
ISBN: 0192595032
Category : Philosophy
Languages : en
Pages : 208
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Book Description
"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.
Author: Per Martin-Löf
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 116
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Book Description
Author: Shahid Rahman
Publisher: Springer Science & Business Media
ISBN: 1402028083
Category : Philosophy
Languages : en
Pages : 618
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Book Description
The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.
Author: Johan Georg Granström
Publisher: Springer Science & Business Media
ISBN: 9400717369
Category : Philosophy
Languages : en
Pages : 198
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Book Description
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.
Author: Elaine M. Landry
Publisher: Oxford University Press
ISBN: 019874899X
Category : Mathematics
Languages : en
Pages : 486
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Book Description
This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, in an accessible waythat builds on the concepts that are already familiar to philosophers working in these areas.
Author: Bruno de Finetti
Publisher: Springer Science & Business Media
ISBN: 1402082010
Category : Science
Languages : en
Pages : 239
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Book Description
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.
Author: Helena Eilstein
Publisher: Springer Science & Business Media
ISBN: 9781402006708
Category : Juvenile Nonfiction
Languages : en
Pages : 176
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Book Description
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.
Author: Vi︠a︡cheslav Semenovich Stepin
Publisher: Springer Science & Business Media
ISBN: 9781402030451
Category : Philosophy
Languages : en
Pages : 440
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Book Description
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.
Author: Nicolas Clerbout
Publisher: Springer
ISBN: 3319190636
Category : Philosophy
Languages : en
Pages : 118
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Book Description
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.
