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Author: J.R. Lucas
Publisher: Routledge
ISBN: 1134622279
Category : Philosophy
Languages : en
Pages : 471
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Book Description
The Conceptual Roots of Mathematics is a comprehensive study of the foundation of mathematics. J.R. Lucas, one of the most distinguished Oxford scholars, covers a vast amount of ground in the philosophy of mathematics, showing us that it is actually at the heart of the study of epistemology and metaphysics.
Author: J.R. Lucas
Publisher: Routledge
ISBN: 1134622279
Category : Philosophy
Languages : en
Pages : 471
Get Book Here
Book Description
The Conceptual Roots of Mathematics is a comprehensive study of the foundation of mathematics. J.R. Lucas, one of the most distinguished Oxford scholars, covers a vast amount of ground in the philosophy of mathematics, showing us that it is actually at the heart of the study of epistemology and metaphysics.
Author: J. R. Lucas
Publisher:
ISBN:
Category :
Languages : en
Pages : 452
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Book Description
Author: J.R. Lucas
Publisher: Routledge
ISBN: 1134622260
Category : Philosophy
Languages : en
Pages : 469
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Book Description
The Conceptual Roots of Mathematics is a comprehensive study of the foundation of mathematics. J.R. Lucas, one of the most distinguished Oxford scholars, covers a vast amount of ground in the philosophy of mathematics, showing us that it is actually at the heart of the study of epistemology and metaphysics.
Author: Carl Posy
Publisher: Cambridge University Press
ISBN: 1108669530
Category : Philosophy
Languages : en
Pages : 333
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Book Description
The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context of his Critical philosophy, and also show sensitivity to its historical background. The volume will be important for readers seeking a comprehensive picture of the current scholarship about the development of Kant's philosophy of mathematics, its place in his overall philosophy, and the Kantian themes that influenced mathematics and its philosophy after Kant.
Author: Danielle Macbeth
Publisher: OUP Oxford
ISBN: 0191009954
Category : Philosophy
Languages : en
Pages : 507
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Book Description
Realizing Reason pursues three interrelated themes. First, it traces the essential moments in the historical unfolding—from the ancient Greeks, through Descartes, Kant, and developments in the nineteenth century, to the present—that culminates in the realization of pure reason as a power of knowing. Second, it provides a cogent account of mathematical practice as a mode of inquiry into objective truth. And finally, it develops and defends a new conception of our being in the world, one that builds on and transforms the now standard conception according to which our experience of reality arises out of brain activity due, in part, to merely causal impacts on our sense organs. Danielle Macbeth shows that to achieve an adequate understanding of the striving for truth in the exact sciences we must overcome this standard conception and that the way to do that is through a more adequate understanding of the nature of mathematical practice and the profound transformations it has undergone over the course of its history, the history through which reason is first realized as a power of knowing. Because we can understand mathematical practice only if we attend to the systems of written signs within which to do mathematics, Macbeth provides an account of the nature and role of written notations, specifically, of the principal systems that have been developed within which to reason in mathematics: Euclidean diagrams, the symbolic language of arithmetic and algebra, and Frege's concept-script, Begriffsschrift.
Author: Bob Hale
Publisher:
ISBN: 0198854293
Category : Mathematics
Languages : en
Pages : 318
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Book Description
Essays on Existence and Essence presents a series of writings--including several previously unpublished--by Bob Hale on the topics of ontology and modality. The essays develop and elucidate Hale's work on essence, truthmakers, and several other topics. Also included are an introduction by Kit Fine and a bibliography of Hale's work.
Author: Carlos R. Bovell
Publisher: Wipf and Stock Publishers
ISBN: 1498276717
Category : Religion
Languages : en
Pages : 181
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Book Description
By Good and Necessary Consequence presents a critical examination of the reasoning behind the "good and necessary consequence" clause in the Westminster Confession of Faith and makes five observations regarding its suitability for contemporary Reformed and evangelical adherents. 1) In the seventeenth century, religious leaders in every quarter were expected to respond to a thoroughgoing, cultural skepticism. 2) In response to the onslaught of cultural and epistemological skepticism, many looked to mimic as far as possible the deductive methods of mathematicians. 3) The use to which biblicist foundationalism was put by the Westminster divines is at variance with the classical invention, subsequent appropriation, and contemporary estimation of axiomatic and deductive methodology. 4) Although such methodological developments in theology might have seemed natural during the seventeenth century, their epistemological advantage is not evident today. 5) When a believer's faith is epistemologically ordered in a biblicist foundationalist way, once the foundation--the axiomatic use of a veracious scripture--is called into question, the entire faith is in serious danger of crashing down. In a nutshell, Bovell argues that it is not wise to structure the Christian faith in this biblicist foundationalist way, and that it is high time alternate approaches be sought.
Author: Michele Friend
Publisher: Routledge
ISBN: 1317493796
Category : Philosophy
Languages : en
Pages : 217
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Book Description
What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.
Author: Bertrand Russell
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 224
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Book Description
Author: Stanisław Krajewski
Publisher: IOS Press
ISBN: 9781586038144
Category : Mathematics
Languages : en
Pages : 380
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Book Description
This volume honors Professor Andrzej Grzegorczyk, the nestor of Polish logicians, on his 85th anniversary. The editors would like to express the respect and sympathy they have for him. His textbook The Outline of Mathematical Logic has been published in many editions and translated into several languages. It was this textbook that introduced many of us into the world of mathematical logic. Professor Grzegorczyk has made fundamental contributions to logic and to philosophy. His results, mainly on hierarchy of primitive recursive functions, known as the Grzegorczyk hierarchy, are of fundamental importance to theoretical computer science. In particular, they were precursory for the computational complexity theory. The editors would like to stress that this special publication celebrates a scientist who is still actively pursuing genuinely innovative directions of research. Quite recently, Andrzej Grzegorczyk gave a new proof of undecidability of the first order functional calculus. His proof does not use the arithmetization of Kurt Gödel. In recognition of his merits, the University of Clermont-Ferrand conferred to Professor Andrzej Grzegorczyk the Doctorat Honoris Causa. The work and life of Professor Andrzej Grzegorczyk is presented in the article by Professors Stanislaw Krajewski and Jan Wolenski. The papers in this collection have been submitted on invitational basis.
