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
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 and Deleuze are all, in different ways, philosophers of immanence. The methodological questions raised by a commitment to immanence in their respective philosophies are addressed by author Rocco Gangle in terms of diagrammatic practices understood in a highly general sense. The link between philosophical immanence and diagrammatic practice is established by demonstrating with the tools of category theory how diagrams may be used both as tools and as objects of philosophical inquiry via diagrammatic reasoning. Category theory reveals deep structural connections among logic, topology and diverse other areas of mathematics, and it provides constructive and rigorous concepts for investigating how diagrams work in a variety of contexts. Gangle offers a basic introduction to the relevant methods of category theory from a philosophical and diagrammatic perspective that allows philosophers with little or no mathematical training to come to grips with this important field. This coordination of immanent metaphysics, diagrammatic method and category theoretical mathematics opens a new horizon for contemporary thought.Less
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 and Deleuze are all, in different ways, philosophers of immanence. The methodological questions raised by a commitment to immanence in their respective philosophies are addressed by author Rocco Gangle in terms of diagrammatic practices understood in a highly general sense. The link between philosophical immanence and diagrammatic practice is established by demonstrating with the tools of category theory how diagrams may be used both as tools and as objects of philosophical inquiry via diagrammatic reasoning. Category theory reveals deep structural connections among logic, topology and diverse other areas of mathematics, and it provides constructive and rigorous concepts for investigating how diagrams work in a variety of contexts. Gangle offers a basic introduction to the relevant methods of category theory from a philosophical and diagrammatic perspective that allows philosophers with little or no mathematical training to come to grips with this important field. This coordination of immanent metaphysics, diagrammatic method and category theoretical mathematics opens a new horizon for contemporary thought.
Rocco Gangle
- Published in print:
- 2015
- Published Online:
- September 2016
- ISBN:
- 9781474404174
- eISBN:
- 9781474418645
- Item type:
- chapter
- Publisher:
- Edinburgh University Press
- DOI:
- 10.3366/edinburgh/9781474404174.003.0004
- Subject:
- Philosophy, Metaphysics/Epistemology
This chapter introduces Peirce’s theory of semiotics in terms of his distinction between dyadic and triadic modes of signification. The triadic concept of the sign is then constructively developed in ...
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This chapter introduces Peirce’s theory of semiotics in terms of his distinction between dyadic and triadic modes of signification. The triadic concept of the sign is then constructively developed in a three-stage theory of diagrammatic signification. The interpretation of semiotics via triadic relations is contrasted as a postmodern point of view with the dyadic and dualist modern approach of Cartesianism and Saussurean semiology.Less
This chapter introduces Peirce’s theory of semiotics in terms of his distinction between dyadic and triadic modes of signification. The triadic concept of the sign is then constructively developed in a three-stage theory of diagrammatic signification. The interpretation of semiotics via triadic relations is contrasted as a postmodern point of view with the dyadic and dualist modern approach of Cartesianism and Saussurean semiology.
Rocco Gangle
- 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
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 and presheaves. A formal theory of diagrammatic signs building on Peirce’s semiotic theory is presented as a triadic relation among functors, two of which are presheaves. This theory is illustrated by an example from Peirce’s Existential Graphs.Less
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 and presheaves. A formal theory of diagrammatic signs building on Peirce’s semiotic theory is presented as a triadic relation among functors, two of which are presheaves. This theory is illustrated by an example from Peirce’s Existential Graphs.
