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Diagrammatic Immanence: Category Theory and Philosophy

Rocco "Gangle

Published in print:
2015
Published Online:
September 2016
ISBN:
9781474404174
eISBN:
9781474418645
Item type:
book
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9781474404174.001.0001
Subject:
Philosophy, Metaphysics/Epistemology

This book integrates insights from Spinoza’s metaphysics, Peirce’s semiotic theory and Deleuze’s philosophy of difference in conjunction with the formal operations of category theory. Spinoza, Peirce ... More


A Category Theory Explanation for Systematicity: Universal Constructions

Steven Phillips and William H. Wilson

in The Architecture of Cognition: Rethinking Fodor and Pylyshyn's Systematicity Challenge

Published in print:
2014
Published Online:
September 2014
ISBN:
9780262027236
eISBN:
9780262322461
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262027236.003.0009
Subject:
Philosophy, Philosophy of Mind

A theory of cognitive architecture should explain why systematicity is a necessary, not just possible consequence of the theory's core principles and base assumptions, without relying on arbitrary ... More


Diagrams of Difference: Adjunctions and Topoi

Rocco Gangle

in Diagrammatic Immanence: Category Theory and Philosophy

Published in print:
2015
Published Online:
September 2016
ISBN:
9781474404174
eISBN:
9781474418645
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9781474404174.003.0007
Subject:
Philosophy, Metaphysics/Epistemology

This chapter examines two advanced constructions in category theory: adjoint functors and topoi. Pairs of adjoint functors, or adjunctions, are formally defined and then illustrated with several ... More


Diagrams of Structure: Categories and Functors

Rocco Gangle

in Diagrammatic Immanence: Category Theory and Philosophy

Published in print:
2015
Published Online:
September 2016
ISBN:
9781474404174
eISBN:
9781474418645
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9781474404174.003.0003
Subject:
Philosophy, Metaphysics/Epistemology

This chapter introduces the elementary concepts and operations of category theory. It introduces the notion of category by generalizing from partial orders and systems of functions and then ... More


Diagrams of Variation: Functor Categories and Presheaves

Rocco Gangle

in Diagrammatic Immanence: Category Theory and Philosophy

Published in print:
2015
Published Online:
September 2016
ISBN:
9781474404174
eISBN:
9781474418645
Item type:
chapter
Publisher:
Edinburgh University Press
DOI:
10.3366/edinburgh/9781474404174.003.0005
Subject:
Philosophy, Metaphysics/Epistemology

This chapter begins by posing the question of linguistic meaning within the context of the mathematics of category theory. It then explains the notions of functor categories, natural transformations ... More


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