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Das Überraschende: Wittgenstein on the Surprising in Mathematics

Juliet Floyd

in Wittgenstein and the Philosophy of Mind

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199737666
eISBN:
9780199933372
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199737666.003.0010
Subject:
Philosophy, Philosophy of Mind, General

This chapter explores the epistemic role that surprise and other psychological reactions play in mathematics. The chapter pursues the issue for its own sake, but also for its usefulness in ... More


Mathematics and Its Philosophy

Stewart Shapiro

in Philosophy of Mathematics: Structure and Ontology

Published in print:
2000
Published Online:
November 2003
ISBN:
9780195139303
eISBN:
9780199833658
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195139305.003.0002
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter deals with the relationship between the practice of mathematics and the philosophy of mathematics. The philosopher of mathematics is, or should be, concerned with mathematics as it is ... More


Philosophy of Mathematics: Structure and Ontology

Stewart Shapiro

Published in print:
2000
Published Online:
November 2003
ISBN:
9780195139303
eISBN:
9780199833658
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0195139305.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

The philosophy of mathematics articulated and defended in this book goes by the name of “structuralism”, and its slogan is that mathematics is the science of structure. The subject matter of ... More


The Metaphysical Unity of Natural Philosophy

Stephen Gaukroger

in The Collapse of Mechanism and the Rise of Sensibility: Science and the Shaping of Modernity, 1680-1760

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199594931
eISBN:
9780191595745
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199594931.003.0004
Subject:
Philosophy, Philosophy of Science, General

The chapter explores the collapse of mechanism and the competition between Newton's and Leibniz's non‐mechanistic models of physical explanation; the relation between Leibniz's metaphysics and his ... More


The Nature of Mathematical Knowledge

Philip Kitcher

Published in print:
1985
Published Online:
November 2003
ISBN:
9780195035414
eISBN:
9780199833368
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0195035410.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

The Nature of Mathematical Knowledge develops and defends an empiricist approach to mathematical knowledge. After offering an account of a priori knowledge, it argues that none of the ... More


Realism in Mathematics

Penelope Maddy

Published in print:
1992
Published Online:
November 2003
ISBN:
9780198240358
eISBN:
9780191597978
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/019824035X.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Many mathematicians understand their work as an effort to describe the denizens and features of an abstract mathematical world or worlds. Most philosophers of mathematics consider views of this sort ... More


Mathematics as a Science of Patterns

Michael D. Resnik

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198250142
eISBN:
9780191598296
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198250142.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Mathematics is regarded as our most developed science, and yet philosophical troubles surface as soon as we inquire about its subject matter partly because mathematics itself says nothing about the ... More


Mathematics without Numbers: Towards a Modal-Structural Interpretation

Geoffrey Hellman

Published in print:
1993
Published Online:
November 2003
ISBN:
9780198240341
eISBN:
9780191597664
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198240341.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Develops a structuralist understanding of mathematics, as an alternative to set‐ or type‐theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to ... More


Finding a problem

Michael Potter

in Wittgenstein's Notes on Logic

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199215836
eISBN:
9780191721243
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199215836.003.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter addresses the question of what led Wittgenstein to study philosophy with Russell in Cambridge. Since the narrative of Wittgenstein's life before 1911 is well summarized in available ... More


The Indispensability of Mathematics

Mark Colyvan

Published in print:
2001
Published Online:
November 2003
ISBN:
9780195137545
eISBN:
9780199833139
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/019513754X.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Looks at the Quine–Putnam indispensability argument in the philosophy of mathematics. This argument urges us to place mathematical entities on the same ontological footing as other theoretical ... More


Constructibility and Mathematical Existence

Charles S. Chihara

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239758
eISBN:
9780191597190
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198239750.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

A continuation of the study of mathematical existence begun in Ontology and the Vicious‐Circle Principle (published in 1973); in the present work, Quine's indispensability argument is rebutted by the ... More


Number

George Bealer

in Quality and Concept

Published in print:
1982
Published Online:
October 2011
ISBN:
9780198244288
eISBN:
9780191680762
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198244288.003.0007
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Mind

Since the theory of properties, relations, and propositions (PRPs) is a full-fledged part of natural logic, it can support a well justified logicist philosophy of mathematics. This chapter argues ... More


Leibniz's Constructivism and Infinitely Folded Matter

Samuel Levey

in New Essays on the Rationalists

Published in print:
2003
Published Online:
November 2003
ISBN:
9780195165418
eISBN:
9780199868285
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195165411.003.0006
Subject:
Philosophy, History of Philosophy

“Leibniz's Constructivism and Infinitely Folded Matter” This essay examines Leibniz's account of the structure of matter and its relation to his views of the infinite. Leibniz interprets the actually ... More


Second Philosophy: A Naturalistic Method

Penelope Maddy

Published in print:
2007
Published Online:
January 2009
ISBN:
9780199273669
eISBN:
9780191706264
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199273669.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. This book describes and practices a particularly austere form of ... More


A Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics

John P. Burgess and Gideon Rosen

Published in print:
1999
Published Online:
November 2003
ISBN:
9780198250128
eISBN:
9780191597138
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198250126.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

Numbers and other mathematical objects are exceptional in having no locations in space and time and no causes or effects in the physical world. This makes it difficult to account for the possibility ... More


Truth and the Absence of Fact

Hartry Field

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199242894
eISBN:
9780191597381
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0199242895.001.0001
Subject:
Philosophy, General

This is a collection of papers, written over many years, with substantial postscripts tying them together and giving an updated perspective on them. The first five are on the notions of truth and ... More


Naturalism in Mathematics

Penelope Maddy

Published in print:
2000
Published Online:
November 2003
ISBN:
9780198250753
eISBN:
9780191597961
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198250754.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

It is well known that certain natural statements of set theory, like Cantor's continuum hypothesis (CH), cannot be proved or disproved on the basis of the standard axioms (Zermelo–Fraenkel with ... More


Frege and Other Philosophers

Michael Dummett

Published in print:
1996
Published Online:
November 2003
ISBN:
9780198236283
eISBN:
9780191597343
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/019823628X.001.0001
Subject:
Philosophy, History of Philosophy

This book deals with Frege's philosophy by comparing and contrasting his views with those of other philosophers, mostly contemporary with him.


A Constraints-Based Philosophy of Mathematical Practice

Roi Wagner

in Making and Breaking Mathematical Sense: Histories and Philosophies of Mathematical Practice

Published in print:
2017
Published Online:
January 2018
ISBN:
9780691171715
eISBN:
9781400883783
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691171715.003.0004
Subject:
Mathematics, History of Mathematics

This chapter describes a constraints-based philosophy of mathematical practice and shows that mathematics can be so many different things, even if we look at a particular branch of mathematics in a ... More


Conclusion

Dominic J. O'Meara

in Pythagoras Revived: Mathematics and Philosophy in Late Antiquity

Published in print:
1990
Published Online:
April 2004
ISBN:
9780198239130
eISBN:
9780191600937
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198239130.003.0012
Subject:
Philosophy, Ancient Philosophy

The conclusion summarizes the main points established in the book concerning Iamblichus’ contribution to the development of Neoplatonism and to the emergence of a philosophy of mathematics and a ... More


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