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The Philosophy of Alternative Logics

Andrew Aberdein and Stephen Read

in The Development of Modern Logic

Published in print:
2009
Published Online:
September 2009
ISBN:
9780195137316
eISBN:
9780199867912
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195137316.003.0041
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter focuses on alternative logics. It discusses a hierarchy of logical reform. It presents case studies that illustrate particular aspects of the logical revisionism discussed in the ... More


Paraconsistent Set Theory

Graham Priest

in In Contradiction

Published in print:
2006
Published Online:
May 2007
ISBN:
9780199263301
eISBN:
9780191718823
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199263301.003.0019
Subject:
Philosophy, Logic/Philosophy of Mathematics

The major topic of this chapter is set theory, and specifically the shape of an acceptable paraconsistent set theory. It reviews what is currently known about the matter and suggests some new ideas. ... More


Paraconsistent Fictions and Discontinuous Logic

John Ó Maoilearca

in All Thoughts Are Equal: Laruelle and Nonhuman Philosophy

Published in print:
2015
Published Online:
May 2016
ISBN:
9780816697342
eISBN:
9781452952291
Item type:
chapter
Publisher:
University of Minnesota Press
DOI:
10.5749/minnesota/9780816697342.003.0003
Subject:
Philosophy, General

This chapter examines the relationship between paraconsistent logic and Laruelle’s apparently anarchic approach to epistemology and thought, utilizing the idea of the rate of cuts (film edits) to ... More


Inconsistency in Science

Newton C. A. da Costa and Steven French

in Science and Partial Truth: A Unitary Approach to Models and Scientific Reasoning

Published in print:
2003
Published Online:
February 2006
ISBN:
9780195156515
eISBN:
9780199785896
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/019515651X.003.0006
Subject:
Philosophy, Philosophy of Science

This chapter presents a model-theoretic account in which regarding theories in terms of partial structures offers a straightforward and natural way of accommodating inconsistency. In particular, it ... More


Minimally Inconsistent LP

Graham Priest

in In Contradiction

Published in print:
2006
Published Online:
May 2007
ISBN:
9780199263301
eISBN:
9780191718823
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199263301.003.0017
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter shows how to construct a non-monotonic logic that implements the default assumption of consistency. In particular, the disjunctive syllogism is valid in consistent contexts, and when ... More


On the Formalization of the Law of Non-Contradiction *

Ross T. Brady

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/9780199265176.003.0003
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

This chapter examines three ways of formalizing the law of non-contradiction. The key feature of such a way is the enforcement of consistency of the formal system concerned. The first formalization ... More


FURTHER RESULTS AND DISCUSSION

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0017
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses further directions of research. A brief review of the results obtained on interpolation and definability, which were not included in this volume, is presented.


‘To Pee and not to Pee?’ Could That Be the Question? (Further Reflections of The Dog) *

Jay Garfield

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/9780199265176.003.0015
Subject:
Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics

Priest's LP is formulated with truth value gaps, but no gluts. The Dog argues on epistemological grounds that a paraconsistent logic with truth value gaps as well as gluts is better than one with ... More


Structure: An Eclectic Perspective

Stewart Shapiro

in Varieties of Logic

Published in print:
2014
Published Online:
September 2014
ISBN:
9780199696529
eISBN:
9780191784866
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199696529.003.0003
Subject:
Philosophy, Logic/Philosophy of Mathematics

This chapter begins with the Hilbertian theme concerning mathematics that emerged toward the end of the nineteenth century and continues to thrive today. The underlying idea is that consistency is ... More


The Problem of Bounded Rationality

Mark Jago

in The Impossible: An Essay on Hyperintensionality

Published in print:
2014
Published Online:
August 2014
ISBN:
9780198709008
eISBN:
9780191779596
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198709008.003.0007
Subject:
Philosophy, Metaphysics/Epistemology

This chapter clarifies and discusses the problem of bounded rationality. This is the problem of accounting for the normative connections between logically-related contents whilst avoiding logical ... More


Heidegger’s Grund: (Para-)Foundationalism

Filippo Casati

in Reality and its Structure: Essays in Fundamentality

Published in print:
2018
Published Online:
June 2018
ISBN:
9780198755630
eISBN:
9780191816772
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198755630.003.0016
Subject:
Philosophy, Metaphysics/Epistemology

Martin Heidegger holds the position according to which every entity is grounded in being and being is ungrounded. Some interpreters have recently shown that this metaphysical picture is untenable ... More


Inconsistency Theories

Nikk Effingham

in Time Travel: Probability and Impossibility

Published in print:
2020
Published Online:
April 2020
ISBN:
9780198842507
eISBN:
9780191878480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198842507.003.0010
Subject:
Philosophy, Metaphysics/Epistemology

Some believe dialetheism, i.e. that there can be true contradictions. If there can be true contradictions, then we might take the moral of the Grandfather Paradox to just be that, when time ... More


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