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UNIVERSES IN TOPOSES

Thomas Streicher

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0005
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses a notion of universe in toposes, which from a logical point of view gives rise to an extension of Higher Order Intuitionistic Arithmetic (HAH). In this way, one can construct ... More


SOME CONSTRUCTIVE ROADS TO TYCHONOFF

Steven Vickers

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0014
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter discusses the Tychonoff Theorem with respect to point-free topology from the point of view of both topos-valid and predicative mathematics. A new proof of the infinitary Tychonoff ... More


TOWARD A MINIMALIST FOUNDATION FOR CONSTRUCTIVE MATHEMATICS

Maria Emilia Maietti and Giovanni Sambin

in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566519
eISBN:
9780191713927
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566519.003.0006
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

The two main views in modern constructive mathematics usually associated with constructive type theory and topos theory are compatible with the classical view, but they are incompatible with each ... More


Unbuilding the Acropolis in Greek Literature

Vassilis Lambropoulos

in Classics and National Cultures

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199212989
eISBN:
9780191594205
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199212989.003.0010
Subject:
Classical Studies, Prose and Writers: Classical, Early, and Medieval

Despite its eminence as a physical location and imaginary topos, the Acropolis appears very rarely in modern Greek poetry and fiction. When it does, local writers instead of glorifying it, like their ... More


The Devil in the Detail

Mary Orr

in Flaubert's Tentation: Remapping Nineteenth-Century French Histories of Religion and Science

Published in print:
2008
Published Online:
January 2009
ISBN:
9780199258581
eISBN:
9780191718083
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199258581.003.0007
Subject:
Literature, World Literature, 19th-century and Victorian Literature

Devil's rides into space are a well‐worked topos in literature, but this chapter points out for the first time their literal realities in the Montgolfier balloons and Garnarin's parachute that ... More


Lyrics

A. C. Spearing

in Textual Subjectivity: The Encoding of Subjectivity in Medieval Narratives and Lyrics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198187240
eISBN:
9780191719035
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198187240.003.0006
Subject:
Literature, Early and Medieval Literature

This chapter turns from narrative to lyric, traditionally seen as expressing its writer’s own feelings. The ‘sincerity-topos’ is studied in the troubadour Bernart de Ventadorn and as embodied in ... More


Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic 'bridges'

Olivia Caramello

Published in print:
2017
Published Online:
March 2018
ISBN:
9780198758914
eISBN:
9780191818752
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198758914.001.0001
Subject:
Mathematics, Geometry / Topology, Pure Mathematics

This book is devoted to a general study of geometric theories from a topos-theoretic perspective. After recalling the necessary topos-theoretic preliminaries, it presents the main methodology it uses ... More


Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy

David Corfield

Published in print:
2020
Published Online:
March 2020
ISBN:
9780198853404
eISBN:
9780191888069
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853404.001.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

In[KF1] 1914, in an essay entitled ‘Logic as the Essence of Philosophy’, Bertrand Russell promised to revolutionize philosophy by introducing there the ‘new logic’ of Frege and Peano: “The old logic ... More


The p-adic Simpson Correspondence (AM-193)

Ahmed Abbes, Michel Gros, and Takeshi Tsuji

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170282
eISBN:
9781400881239
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170282.001.0001
Subject:
Mathematics, Algebra

The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms ... More


Covanishing topos and generalizations

Ahmed Abbes, Michel Gros, and Takeshi Tsuji

in The p-adic Simpson Correspondence (AM-193)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170282
eISBN:
9781400881239
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170282.003.0006
Subject:
Mathematics, Algebra

This chapter focuses on the Faltings topos, the general framework for Faltings' approach in p-adic Hodge theory. It presents a new approach to the Faltings topos based on a generalization of ... More


James I of Scotland and The Kingis Quair

JOANNA SUMMERS

in Late-Medieval Prison Writing and the Politics of Autobiography

Published in print:
2004
Published Online:
January 2010
ISBN:
9780199271290
eISBN:
9780191709586
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199271290.003.0003
Subject:
Literature, Early and Medieval Literature

This chapter examines the captivity of James I of Scotland, and discusses how the ‘I’ voice of The Kingis Quair may be read as James I's autobiographical identity. It examines how the identity James ... More


Patience and Passion in Shakespeare and Milton

Judith H. Anderson

in Reading the Allegorical Intertext: Chaucer, Spenser, Shakespeare, Milton

Published in print:
2008
Published Online:
September 2011
ISBN:
9780823228478
eISBN:
9780823241125
Item type:
chapter
Publisher:
Fordham University Press
DOI:
10.5422/fordham/9780823228478.003.0018
Subject:
Literature, Criticism/Theory

Milton's poetry recalls the centrality and complexity of Shakespeare's engagement with patience but goes beyond it to render the traditional significance of this virtue dynamic and revisionary. King ... More


The Other Side

Rachel Havrelock

in River Jordan: The Mythology of a Dividing Line

Published in print:
2011
Published Online:
September 2013
ISBN:
9780226319575
eISBN:
9780226319599
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226319599.003.0006
Subject:
Religion, Biblical Studies

This chapter shifts the focus from the Jordan, and the ramifications of crossing or not crossing it, to the other side referred to here as Transjordan. Considering how location also carries the ... More


Flat functors and classifying toposes

Olivia Caramello

in Theories, Sites, Toposes: Relating and studying mathematical theories through topos-theoretic 'bridges'

Published in print:
2017
Published Online:
March 2018
ISBN:
9780198758914
eISBN:
9780191818752
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198758914.003.0007
Subject:
Mathematics, Geometry / Topology, Pure Mathematics

This chapter develops a general theory of extensions of flat functors along geometric morphisms of toposes; the attention is focused in particular on geometric morphisms between presheaf toposes ... More


A Path to a New Logic

David Corfield

in Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy

Published in print:
2020
Published Online:
March 2020
ISBN:
9780198853404
eISBN:
9780191888069
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853404.003.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter explains how modal homotopy type theory combines ideas from two currents of thought: type theory and category theory. Despite what might appear to be rather different philosophical ... More


Spatial Types

David Corfield

in Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy

Published in print:
2020
Published Online:
March 2020
ISBN:
9780198853404
eISBN:
9780191888069
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198853404.003.0005
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

While modalities relate directly to the philosophical concerns of metaphysicians, it has been recognized recently by mathematicians that operators behaving similarly can be deployed to capture ... More


Scientific Methods at the Edge of Biomedicine

Colleen Derkatch

in Bounding Biomedicine: Evidence and Rhetoric in the New Science of Alternative Medicine

Published in print:
2016
Published Online:
September 2016
ISBN:
9780226345840
eISBN:
9780226345987
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226345987.003.0004
Subject:
History, History of Science, Technology, and Medicine

This chapter focuses on scientific method as the key rhetorical topos, or topic, within evidence-based medicine that furnishes lines of argument that researchers adopt to align complementary and ... More


The Rebirth of Poetics

Andrew Hui

in The Poetics of Ruins in Renaissance Literature

Published in print:
2017
Published Online:
September 2017
ISBN:
9780823273355
eISBN:
9780823273393
Item type:
chapter
Publisher:
Fordham University Press
DOI:
10.5422/fordham/9780823273355.003.0002
Subject:
Literature, 16th-century and Renaissance Literature

This chapter traces the genealogy of the immortality of poetry topos from antiquity to the sixteenth century. It argues that the Renaissance poetics of ruins’s yearning for timelessness is ... More


Heidegger and the Thinking of Place: Explorations in the Topology of Being

Jeff Malpas

Published in print:
2012
Published Online:
August 2013
ISBN:
9780262016841
eISBN:
9780262304139
Item type:
book
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262016841.001.0001
Subject:
Philosophy, General

The idea of place—of topos—runs through Martin Heidegger’s thinking almost from the very start. It can be seen not only in his attachment to the famous hut in Todtnauberg but in his constant ... More


The Physics of Sexual Difference in Aristotle and Irigaray

Emanuela Bianchi

in The Feminine Symptom: Aleatory Matter in the Aristotelian Cosmos

Published in print:
2014
Published Online:
May 2015
ISBN:
9780823262182
eISBN:
9780823266449
Item type:
chapter
Publisher:
Fordham University Press
DOI:
10.5422/fordham/9780823262182.003.0005
Subject:
Philosophy, Feminist Philosophy

Irigaray reads Aristotle on place in the Physics as giving a conception of sexual difference in which woman is resigned to a placeholder or container for man. This chapter deepens her analysis. ... More


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