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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


Logical Non-Apriorism and the ‘Law’ of Non-Contradiction

Otávio Bueno and Mark Colyvan

in The Law of Non-Contradiction

Published in print:
2004
Published Online:
May 2010
ISBN:
9780199265176
eISBN:
9780191713989
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199265176.003.0010
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

A common response to those who question the Law of Non-Contradiction (LNC) is that it is impossible to debate such a fundamental law of logic. The reasons for this response vary, but what seems to ... More


Conceptualism

Philip Kitcher

in The Nature of Mathematical Knowledge

Published in print:
1985
Published Online:
November 2003
ISBN:
9780195035414
eISBN:
9780199833368
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195035410.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

If we are to obtain a priori mathematical knowledge by following proofs, then we have to be able to have a priori knowledge of the axioms. This chapter continues Chapter 3's examination of the major ... More


Toward a Defensible Empiricism

Philip Kitcher

in The Nature of Mathematical Knowledge

Published in print:
1985
Published Online:
November 2003
ISBN:
9780195035414
eISBN:
9780199833368
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195035410.003.0006
Subject:
Philosophy, Logic/Philosophy of Mathematics

The next stage is to set up the main question for the rest of the book: How is empirical mathematical knowledge possible? The outline of an answer is given: relatively simple experiences provide ... More


Reality, Intellect, Realism

Gila Sher

in Epistemic Friction: An Essay on Knowledge, Truth, and Logic

Published in print:
2016
Published Online:
August 2016
ISBN:
9780198768685
eISBN:
9780191822032
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198768685.003.0005
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

The chapter develops an integrated view of realism, reality, and reason (intellect) for the new model. Its starting point is the “basic human epistemic situation”—a situation in which limited yet ... More


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