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Author: Juliette Kennedy Publisher: Cambridge University Press ISBN: 1107012570 Category : Mathematics Languages : en Pages : 201
Book Description
Introduces an original approach to foundations of mathematics, departing from Gödel and Tarski and spanning many different areas of logic.
Author: Juliette Kennedy Publisher: Cambridge University Press ISBN: 1107012570 Category : Mathematics Languages : en Pages : 201
Book Description
Introduces an original approach to foundations of mathematics, departing from Gödel and Tarski and spanning many different areas of logic.
Author: Juliette Kennedy Publisher: Cambridge University Press ISBN: 1009028235 Category : Science Languages : en Pages : 201
Book Description
Is mathematics 'entangled' with its various formalisations? Or are the central concepts of mathematics largely insensitive to formalisation, or 'formalism free'? What is the semantic point of view and how is it implemented in foundational practice? Does a given semantic framework always have an implicit syntax? Inspired by what she calls the 'natural language moves' of Gödel and Tarski, Juliette Kennedy considers what roles the concepts of 'entanglement' and 'formalism freeness' play in a range of logical settings, from computability and set theory to model theory and second order logic, to logicality, developing an entirely original philosophy of mathematics along the way. The treatment is historically, logically and set-theoretically rich, and topics such as naturalism and foundations receive their due, but now with a new twist.
Author: William D. Brewer Publisher: Springer Nature ISBN: 3031113098 Category : Mathematics Languages : en Pages : 502
Book Description
During his lifetime, Kurt Gödel was not well known outside the professional world of mathematicians, philosophers and theoretical physicists. Early in his career, for his doctoral thesis and then for his Habilitation (Dr.Sci.), he wrote earthshaking articles on the completeness and provability of mathematical-logical systems, upsetting the hypotheses of the most famous mathematicians/philosophers of the time. He later delved into theoretical physics, finding a unique solution to Einstein’s equations for gravity, the ‘Gödel Universe’, and made contributions to philosophy, the guiding theme of his life. This book includes more details about the context of Gödel’s life than are found in earlier biographies, while avoiding an elaborate treatment of his mathematical/scientific/philosophical works, which have been described in great detail in other books. In this way, it makes him and his times more accessible to general readers, and will allow them to appreciate the lasting effects of Gödel’s contributions (the latter in a more up-to-date context than in previous biographies, many of which were written 15–25 years ago). His work spans or is relevant to a wide spectrum of intellectual endeavor, and this is emphasized in the book, with recent examples. This biography also examines possible sources of his unusual personality, which combined mathematical genius with an almost childlike naiveté concerning everyday life, and striking scientific innovations with timidity and hesitancy in practical matters. How he nevertheless had a long and successful career, inspiring many younger scholars along the way, with the help of his loyal wife Adele and some of his friends, is a fascinating story in human nature.
Author: Juliette Kennedy Publisher: Cambridge University Press ISBN: 1107002664 Category : Literary Collections Languages : en Pages : 293
Book Description
In this groundbreaking volume, leading philosophers and mathematicians explore Kurt Gödel's work on the foundations and philosophy of mathematics.
Author: Johan van Benthem Publisher: MIT Press ISBN: 9780262720243 Category : Language Arts & Disciplines Languages : en Pages : 390
Book Description
Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities.
Author: Reinhard Siegmund-Schultze Publisher: Princeton University Press ISBN: 0691125937 Category : Biography & Autobiography Languages : en Pages : 501
Book Description
Based on archival sources that have never been examined before, the book discusses the preeminent emigrant mathematicians of the period, including Emmy Noether, John von Neumann, Hermann Weyl, and many others. The author explores the mechanisms of the expulsion of mathematicians from Germany, the emigrants' acculturation to their new host countries, and the fates of those mathematicians forced to stay behind. The book reveals the alienation and solidarity of the emigrants, and investigates the global development of mathematics as a consequence of their radical migration.
Author: Ravi P Agarwal Publisher: Springer ISBN: 3319108700 Category : Mathematics Languages : en Pages : 514
Book Description
The book records the essential discoveries of mathematical and computational scientists in chronological order, following the birth of ideas on the basis of prior ideas ad infinitum. The authors document the winding path of mathematical scholarship throughout history, and most importantly, the thought process of each individual that resulted in the mastery of their subject. The book implicitly addresses the nature and character of every scientist as one tries to understand their visible actions in both adverse and congenial environments. The authors hope that this will enable the reader to understand their mode of thinking, and perhaps even to emulate their virtues in life.
Author: Juliette Kennedy
Author: Juliette Kennedy
Author: Juliette Kennedy
Author: William D. Brewer
Author: Antonio Piccolomini d'Aragona
Author: Anita Burdman Feferman
Author: Juliette Kennedy
Author: Johan van Benthem
Author: John T. Baldwin
Author: Reinhard Siegmund-Schultze
Author: Ravi P Agarwal