MARK BALAGUER, California State University, Los Angeles
Platonism and Anti-Platonism in Mathematics
In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He does this by establishing that both platonism and
anti-platonism are defensible views. Introducing a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, he proceeds to defend anti-platonism (in particular, mathematical fictionalism) against various attacks, most notably the Quine-Putnam indispensability attack. He concludes by arguing that it is not simply that we do not currently have any good argument for or against platonism, but that we could never have such an argument
and, indeed, that there is no fact of the matter as to whether platonism is correct.
paper
0195143981
March 2001
Due: 03/15/01
Bob Hale, Professor of Metaphysical Philosophy, University of Glasgow,
and Crispin Wright, Professor of Logic and Metaphysics,
and Wardlaw Professor, University of St AndrewsThe Reason's Proper Study
Essays towards a Neo-Fregean Philosophy of Mathematics
480 pages, 234mm x 156mm
Details
Hardback,
0-19-823639-5
Publication date:
February 2001
Description
Readership: Philosophers, logicians and mathematicians with interests in the foundations of mathematics.
Bob Hale and Crispin Wright draw together here the key writings in which they have worked out their distinctive approach to the fundamental questions: what is mathematics about, and how to we know it? The volume features much new material: introduction, postscript, bibliographies, and a new essay on a key problem. The Reason's Proper Study is the strongest presentation yet of the controversial neo-Fregean view that mathematical knowledge is essentially no different from logical knowledge. It will prove indispensable reading not just to philosophers of mathematics but to all who are interested in the fundamental metaphysical and epistemological issues which the programme raises.
Contents/contributors
Origins of the Essays
Introduction
I. Ontology and Abstraction Principles
1 Bob Hale: Singular Terms (1)
2 Bob Hale: Singular Terms (2)
3 Crispin Wright: Why Frege Does Not Deserve His Grain of Salt:
A Note on the Paradox of 'The Concept Horse' and the Ascription
of Bedeutungen to Predicates
4 Bob Hale: Grundlagen 64
5 Bob Hale and Crispin Wright: Implicit Definition and the A Priori
II. Responses to Critics
6 Crispin Wright: Field and Fregean Platonism
7 Bob Hale: Is Platonism Epistemologically Bankrupt?
8 Bob Hale: Dummett's Critique of Wright's Attempt to Resuscitate Frege
9 Critical Notice of Michael Dummett's Frege: Philosophy of
MathematicsCrispin Wright:
III. Hume's Principle
10 Crispin Wright: On the Harmless Impredicativity of Hume's Principle
11 Crispin Wright: Response to Dummett
12 Crispin Wright: On the Philosophical Significance of Frege's Theorem
13 Crispin Wright: Is Hume's Principle Analytic?
IV. On the Differentiation of Abstracta
14 Bob Hale and Crispin Wright: To Bury Caesar...
V. Beyond Number-theory
15 Bob Hale: Reals by Abstraction
Postscript: Seventeen Problems
Bibliography
Bibliography of further relevant writings
Index
More in the same subject area: Philosophy of mathematics;
Mathematical logic; Metaphysics & ontology; Epistemology, theory of
knowledge
John L. Casti and Werner DePauli
Godel
A Life of Logic
Hardcover
Availability Date: 09/14/00
Available
Perseus Publishing
ISBN: 0-7382-0274-6
Description
Kurt Godel was an intellectual giant. His Incompleteness Theorem turned not only mathematics but also the whole world of science and philosophy on its head. Equally legendary were Godel's eccentricities, his close friendship with Albert Einstein, and his paranoid fear of germs that eventually led to his death from self-starvation. Now, in the first popular biography of this strange
and brilliant thinker, John Casti and Werner DePauli bring the legend to life. After describing his childhood in the Moravian capital of Brno, the authors trace the arc of Godel's remarkable career, from the famed Vienna Circle, where philosophers and scientists debated notions of truth, to the Institute for Advanced Study in Princeton, New Jersey, where he lived and worked until his death in 1978. In the process, they shed light on Godel's contributions to mathematics, philosophy, computer science, artificial intelligence--even cosmology--in an entertaining and accessible way.
Biography
John L. Casti , a member of the faculty of both the Santa Fe Institute and the Technical University of Vienna, is one of the most esteemed science writers of our time. He has written numerous acclaimed popular science books, including Would-Be Worlds, Five Golden Rules, and The Cambridge Quintet. Werner Depauli is University Assistant and Oberrat at the Institute of Statistics and Computer Science of the University of Vienna. He is the author of several books in German about Godel and has produced a film on Godel for German television.
Number of pages: 224
Trim Size: 5-3/8X8-1/4
Season: FAL2000
M Morris Mano
Charles R KimeLogic and Computer Design Fundamentals, Updated Edition, 2/e
Copyright 2001, 672 pp.
Cloth Bound w/CD-ROM format
ISBN 0-13-031486-2
Summary
For introductory courses in Computer Engineering or Computer Hardware Design in departments of Electrical and Computer Engineering, Computer Science, Electrical Engineering, or Electrical Engineering Technology; also appropriate for a Digital Systems Design course.
Covers the fundamentals of hardware and computer design with exceptional breadth and in a very accessible style using abundant examples to build understanding and problem-solving skills. Reflects the current industry trend of designing with hardware description languages (HDLs)
instead of logic diagrams - provides optional introductory treatments of both VHDL and Verilog languages - with additional coverage available on the Companion Website for more substantial treatment. Gives the instructor maximum flexibility in HDL coverage. By covering
broadly-based fundamentals, provides an excellent foundation and perspective for more advanced courses in digital hardware design and computer architecture and organization preparation.
Grigori Mints /Stanford University, CA, USA
A Short Introduction to Intuitionistic Logic
Intuitionistic logic is presented here as part of familiar classical logic which allows mechanical extraction of programs from proofs. to make the material more accessible, basic tchniques are
presented first for propositional logic; Part II contains extensions to predicate logic. This material provides an introduction and a safe background for reading research literature in logic and
computer science as well as advanced monographs. Readers are assumed to be familiar with basic notions of first order logic. One device for making this book short was inventing new proofs of
several theorems. The presentation is based on natural deduction.
The topics include programming interpretation of intuitionistic logic by simply typed lambda-calculus (Curry-Howard isomorphism), negative translation of classical into intuitionistic
logic, normalization of natural deductions, applications to category theory, Kripke models, algebraic and topological semantics, proof-search methods, interpolation theorem. The text developed
from materal for several courses taught at Stanford University in 1992・999.
Contents
Introduction. I: Intuitionistic Propositional Logic. 1. Preliminaries. 2. Natural Deduction for Propositional Logic. 3. Negative Translation: Glivenko's Theorem. 4. Program Interpretation of Intuitionistic Logic. 5. Computations with Deductions. 6. Coherence Theorem. 7. Kripke Models. 8.
Gentzen-type Propositional System LJpm. 9. Topological Completeness. 10. Proof-Search. 11. System LJpm. 12. Interpolation Theorem. II: Intuitionistic Predicate Logic. 13. Natural Deduction System NJ. 14. Kripke Models for Predicate Logic. 15. Systems LJm, LJ. 16. Proof-Search in Predicate Logic. References. Index.
Kluwer Academic/Plenum Publishers
Hardbound, ISBN 0-306-46394-6
October 2000, 138 pp.