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Author: Gottlob Frege
Publisher: John Wiley & Sons
ISBN: 0631126945
Category : Mathematics
Languages : en
Pages : 146
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Book Description
A philosophical discussion of the concept of number In the book, The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, Gottlob Frege explains the central notions of his philosophy and analyzes the perspectives of predecessors and contemporaries. The book is the first philosophically relevant discussion of the concept of number in Western civilization. The work went on to significantly influence philosophy and mathematics. Frege was a German mathematician and philosopher who published the text in 1884, which seeks to define the concept of a number. It was later translated into English. This is the revised second edition.
Author: Gottlob Frege
Publisher: John Wiley & Sons
ISBN: 0631126945
Category : Mathematics
Languages : en
Pages : 146
Get Book Here
Book Description
A philosophical discussion of the concept of number In the book, The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number, Gottlob Frege explains the central notions of his philosophy and analyzes the perspectives of predecessors and contemporaries. The book is the first philosophically relevant discussion of the concept of number in Western civilization. The work went on to significantly influence philosophy and mathematics. Frege was a German mathematician and philosopher who published the text in 1884, which seeks to define the concept of a number. It was later translated into English. This is the revised second edition.
Author: Gottlob Frege
Publisher: Univ of California Press
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 208
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Book Description
Author: Alexandru Buium
Publisher: American Mathematical Soc.
ISBN: 147043623X
Category : Mathematics
Languages : en
Pages : 357
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Book Description
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
Author: Donald Gillies
Publisher: Routledge
ISBN: 113672107X
Category : Mathematics
Languages : en
Pages : 115
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Book Description
First published in 1982, this reissue contains a critical exposition of the views of Frege, Dedekind and Peano on the foundations of arithmetic. The last quarter of the 19th century witnessed a remarkable growth of interest in the foundations of arithmetic. This work analyses both the reasons for this growth of interest within both mathematics and philosophy and the ways in which this study of the foundations of arithmetic led to new insights in philosophy and striking advances in logic. This historical-critical study provides an excellent introduction to the problems of the philosophy of mathematics - problems which have wide implications for philosophy as a whole. This reissue will appeal to students of both mathematics and philosophy who wish to improve their knowledge of logic.
Author: Michael Dummett
Publisher: Harvard University Press
ISBN: 9780674319356
Category : Mathematics
Languages : en
Pages : 364
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Book Description
No one has figured more prominently in the study of the German philosopher Gottlob Frege than Michael Dummett. His magisterial Frege: Philosophy of Language is a sustained, systematic analysis of Frege's thought, omitting only the issues in philosophy of mathematics. In this work Dummett discusses, section by section, Frege's masterpiece The Foundations of Arithmetic and Frege's treatment of real numbers in the second volume of Basic Laws of Arithmetic, establishing what parts of the philosopher's views can be salvaged and employed in new theorizing, and what must be abandoned, either as incorrectly argued or as untenable in the light of technical developments. Gottlob Frege (1848-1925) was a logician, mathematician, and philosopher whose work had enormous impact on Bertrand Russell and later on the young Ludwig Wittgenstein, making Frege one of the central influences on twentieth-century Anglo-American philosophy; he is considered the founder of analytic philosophy. His philosophy of mathematics contains deep insights and remains a useful and necessary point of departure for anyone seriously studying or working in the field.
Author: Rose Griffiths
Publisher:
ISBN: 9780198375616
Category :
Languages : en
Pages : 112
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Book Description
Making Numbers shares exemplars of good practice drawing on the latest research on using manipulatives to develop understanding of arithmetic. Focusing initially on the teaching of numbers from 1-12, Making Numbers progresses to 200 and beyond, including ideas for teaching partitioning, arrays, and times tables.
Author:
Publisher: Elsevier
ISBN: 008052687X
Category : Computers
Languages : en
Pages : 525
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Book Description
Agenda Relevance is the first volume in the authors' omnibus investigation ofthe logic of practical reasoning, under the collective title, A Practical Logicof Cognitive Systems. In this highly original approach, practical reasoning isidentified as reasoning performed with comparatively few cognitive assets,including resources such as information, time and computational capacity. Unlikewhat is proposed in optimization models of human cognition, a practical reasonerlacks perfect information, boundless time and unconstrained access tocomputational complexity. The practical reasoner is therefore obliged to be acognitive economizer and to achieve his cognitive ends with considerableefficiency. Accordingly, the practical reasoner avails himself of variousscarce-resource compensation strategies. He also possesses neurocognitivetraits that abet him in his reasoning tasks. Prominent among these is thepractical agent's striking (though not perfect) adeptness at evading irrelevantinformation and staying on task. On the approach taken here, irrelevancies areimpediments to the attainment of cognitive ends. Thus, in its most basic sense,relevant information is cognitively helpful information. Information can then besaid to be relevant for a practical reasoner to the extent that it advances orcloses some cognitive agenda of his. The book explores this idea with aconceptual detail and nuance not seen the standard semantic, probabilistic andpragmatic approaches to relevance; but wherever possible, the authors seek tointegrate alternative conceptions rather than reject them outright. A furtherattraction of the agenda-relevance approach is the extent to which its principalconceptual findings lend themselves to technically sophisticated re-expressionin formal models that marshal the resources of time and action logics andlabel led deductive systems. Agenda Relevance is necessary reading for researchers in logic, beliefdynamics, computer science, AI, psychology and neuroscience, linguistics,argumentation theory, and legal reasoning and forensic science, and will repaystudy by graduate students and senior undergraduates in these same fields.Key features:• relevance • action and agendas • practical reasoning • belief dynamics • non-classical logics • labelled deductive systems
Author: Alfred North Whitehead
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 688
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Book Description
Author: Tom Ricketts
Publisher: Cambridge University Press
ISBN: 113982578X
Category : Philosophy
Languages : en
Pages :
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Book Description
Gottlob Frege (1848–1925) was unquestionably one of the most important philosophers of all time. He trained as a mathematician, and his work in philosophy started as an attempt to provide an explanation of the truths of arithmetic, but in the course of this attempt he not only founded modern logic but also had to address fundamental questions in the philosophy of language and philosophical logic. Frege is generally seen (along with Russell and Wittgenstein) as one of the fathers of the analytic method, which dominated philosophy in English-speaking countries for most of the twentieth century. His work is studied today not just for its historical importance but also because many of his ideas are still seen as relevant to current debates in the philosophies of logic, language, mathematics and the mind. The Cambridge Companion to Frege provides a route into this lively area of research.
Author: Richard Johnsonbaugh
Publisher: Courier Corporation
ISBN: 0486134776
Category : Mathematics
Languages : en
Pages : 450
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Book Description
Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.
