Jump to ContentJump to Main Navigation

You are looking at 1-17 of 17 items

  • Keywords: mathematical proof x
Clear All Modify Search

View:

Tracking Reason: Proof, Consequence, and Truth

Jody Azzouni

Published in print:
2006
Published Online:
October 2011
ISBN:
9780195187137
eISBN:
9780199850570
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195187137.001.0001
Subject:
Philosophy, Logic/Philosophy of Mathematics

When ordinary people—mathematicians among them—take something to follow (deductively) from something else, they are exposing the backbone of our self-ascribed ability to reason. This book ... More


Understanding Proofs

Jeremy Avigad

in The Philosophy of Mathematical Practice

Published in print:
2008
Published Online:
February 2010
ISBN:
9780199296453
eISBN:
9780191711961
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296453.003.0013
Subject:
Philosophy, Logic/Philosophy of Mathematics

In informal speech, ascriptions of mathematical understanding are typically clarified by spelling out the kinds of abilities an agent is assumed to possess. This chapter argues that such an approach ... More


Introduction to Part II

Jody Azzouni

in Tracking Reason: Proof, Consequence, and Truth

Published in print:
2006
Published Online:
October 2011
ISBN:
9780195187137
eISBN:
9780199850570
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195187137.003.0009
Subject:
Philosophy, Logic/Philosophy of Mathematics

This part of the book provides information about the remainder of the book. The next two-thirds of the book take up, respectively, proof and consequence. The book now turns to the absolutely central ... More


Computer Proof, Apriori Knowledge, and Other Minds *

Tyler Burge

in Cognition Through Understanding: Self-Knowledge, Interlocution, Reasoning, Reflection: Philosophical Essays, Volume 3

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199672028
eISBN:
9780191751929
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199672028.003.0013
Subject:
Philosophy, Philosophy of Mind, Metaphysics/Epistemology

‘Computer Proof, Apriori Knowledge, and Other Minds’ (1998) discusses the question: Does the fact that a mathematical proof is carried out by a computer, and is too long for a mathematician to check, ... More


Artificial Extensions of Natural Language

Jody Azzouni

in Semantic Perception: How the Illusion of a Common Language Arises and Persists

Published in print:
2013
Published Online:
September 2013
ISBN:
9780199967407
eISBN:
9780199346066
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199967407.003.0013
Subject:
Philosophy, Philosophy of Language

The history of the emergence of artificial languages is sketched. It’s shown how our experience of natural language makes the invention of artificial languages possible. The emergence of artificial ... More


Wittgenstein on Necessity: Some Reflections

Michael Dummett

in The Seas of Language

Published in print:
1996
Published Online:
November 2003
ISBN:
9780198236214
eISBN:
9780191597350
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198236212.003.0019
Subject:
Philosophy, Philosophy of Language

Radical conventionalism treats every necessary truth as a linguistic convention, akin to the statement ’There are seven days in a week’. Wittgenstein's endorsement of this view was a result of his ... More


The Perfection of Pure Logic

Jan von Plato

in The Great Formal Machinery Works: Theories of Deduction and Computation at the Origins of the Digital Age

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691174174
eISBN:
9781400885039
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174174.003.0010
Subject:
History, History of Science, Technology, and Medicine

This chapter explains how Gerard Gentzen presented the general logical structure of mathematical proofs as a system of rules of proof by which a path is built from the assumptions of a theorem to its ... More


Two Flavours of Mathematical Explanation

Mark Colyvan, John Cusbert, and Kelvin McQueen

in Explanation Beyond Causation: Philosophical Perspectives on Non-Causal Explanations

Published in print:
2018
Published Online:
June 2018
ISBN:
9780198777946
eISBN:
9780191823404
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198777946.003.0012
Subject:
Philosophy, Philosophy of Science, Metaphysics/Epistemology

A proof of a mathematical theorem tells us that the theorem is true (or should be accepted), but some proofs go further and tell us why the theorem is true (or should be accepted). That is, some, but ... More


Provability, Mechanism, and the Diagonal Problem

Graham Leach-Krouse

in Gödel's Disjunction: The scope and limits of mathematical knowledge

Published in print:
2016
Published Online:
November 2016
ISBN:
9780198759591
eISBN:
9780191820373
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198759591.003.0009
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

The primary goal in this chapter is to understand and to make a start at evaluating Gödel and Post’s conceptions of absolute provability. The starting point will be Gödel’s famous assertion from the ... More


Logic, 1900–1940

John A. Goldsmith and Bernard Laks

in Battle in the Mind Fields

Published in print:
2019
Published Online:
September 2019
ISBN:
9780226550800
eISBN:
9780226550947
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226550947.003.0008
Subject:
History, History of Ideas

This chapter looks at the ways in which mathematicians and logicians rethought the nature of mathematical proof during the first four decades of the twentieth century. Three styles of thinking about ... More


Husserl on the Origins of Geometry

Ian Hacking

in Science and the Life-World: Essays on Husserl's Crisis of European Sciences

Published in print:
2009
Published Online:
June 2013
ISBN:
9780804756044
eISBN:
9780804772945
Item type:
chapter
Publisher:
Stanford University Press
DOI:
10.11126/stanford/9780804756044.003.0004
Subject:
Philosophy, Philosophy of Science

This chapter examines the foundations of mathematics, focusing on The Origin of Geometry, an appendix to the Crisis. It notes that Husserl is one of those philosophers who is awed by mathematics, ... More


The Deep Question: P vs. NP

Cristopher Moore and Stephan Mertens

in The Nature of Computation

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199233212
eISBN:
9780191775079
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199233212.003.0006
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter considers the consequences of the possibility that P is equal to NP. It examines why it is extremely difficult to prove that P is not equal to NP by focusing on a set of ‘metatheorems’ ... More


Absolute Provability and Safe Knowledge of Axioms

Timothy Williamson

in Gödel's Disjunction: The scope and limits of mathematical knowledge

Published in print:
2016
Published Online:
November 2016
ISBN:
9780198759591
eISBN:
9780191820373
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198759591.003.0010
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

Are there any in-principle (or absolutely) undecidable hypotheses? In order to make progress with this question, its terms must be first clarified. Against the background of a proposed clarification, ... More


Gödel's Disjunction: The scope and limits of mathematical knowledge

Leon Horsten and Philip Welch (eds)

Published in print:
2016
Published Online:
November 2016
ISBN:
9780198759591
eISBN:
9780191820373
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198759591.001.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

The logician Kurt Gödel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is equivalent to a Turing machine (i.e., a ... More


Do We Have Reason to Doubt the Importance of the Distinction between A Priori and A Posteriori Knowledge?: A Reply to Williamson1 Paul Boghossian

Paul Boghossian and Timothy Williamson

in Debating the A Priori

Published in print:
2020
Published Online:
October 2020
ISBN:
9780198851707
eISBN:
9780191886317
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198851707.003.0009
Subject:
Philosophy, General

This essay defends the a priori–a posteriori distinction against two skeptical challenges posed by Williamson in Chapter 8. Against the argument that no top-down characterization of the distinction ... More


Intellectual Gestalts

Elijah Chudnoff

in Phenomenal Intentionality

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199764297
eISBN:
9780199932191
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199764297.003.0010
Subject:
Philosophy, Philosophy of Mind

Phenomenal holism is the thesis that some phenomenal characters can only be instantiated by experiences that are parts of certain wholes. The first aim of this paper is to defend phenomenal holism. ... More


Williamson on the Distinction between the A Priori and the A Posteriori Once Again1: Paul Boghossian

Paul Boghossian and Timothy Williamson

in Debating the A Priori

Published in print:
2020
Published Online:
October 2020
ISBN:
9780198851707
eISBN:
9780191886317
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198851707.003.0011
Subject:
Philosophy, General

This essay responds to Williamson’s reformulated argument against the feasibility of a top-down characterization of the a priori–a posteriori distinction, arguing that Williamson fails to show that ... More


View: