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PRESHEAF MODELS FOR CONSTRUCTIVE SET THEORIES

Nicola Gambino

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/9780198566519.003.0004
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter introduces new kinds of models for constructive set theories based on categories of presheaves. It concentrates on categories of classes rather than sets, following the lines of ... More


Logical Necessity

Ian Rumfitt

in The Boundary Stones of Thought: An Essay in the Philosophy of Logic

Published in print:
2015
Published Online:
June 2015
ISBN:
9780198733638
eISBN:
9780191798016
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198733638.003.0003
Subject:
Philosophy, Philosophy of Mind

Aristotle discerned a modal element in the notion of consequence: if a conclusion follows from some premisses, it is necessary that the conclusion is true whenever all the premisses are true. This ... More


Magnitudes

Christopher Peacocke

in The Primacy of Metaphysics

Published in print:
2019
Published Online:
July 2019
ISBN:
9780198835578
eISBN:
9780191873751
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198835578.003.0002
Subject:
Philosophy, Metaphysics/Epistemology

A new realistic account of an ontology of extensive magnitudes is developed, formulated in Seven Principles. The principles are defended by the role of magnitudes in scientific explanation and in ... More


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