Plato on the Self-Predication of Forms

Malcolm, John

doi:10.1093/acprof:oso/9780198239062.001.0001

Cited by 50 publications

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“…The notion of a concrete universal occurred in Plato's Theory of Forms [Malcolm 1991]. Plato's forms are often considered to be abstract or non-self-participating universals quite distinct and "above" the concrete instances.…”

Section: Concrete Universalsmentioning

confidence: 99%

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On Concrete Universals : A Modern Treatment Using Category Theory

Ellerman¹

2015

المخاطبات

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Today it would be considered "bad Platonic metaphysics" to think that among all the concrete instances of a property there could be a universal instance so that all instances had the property by virtue of participating in that concrete universal. Yet there is a mathematical theory, category theory, dating from the mid-20 th century that shows how to precisely model concrete universals within the "Platonic Heaven" of mathematics. This paper, written for the philosophical logician, develops this category-theoretic treatment of concrete universals along with a new concept to abstractly model the functions of a brain.

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Section: Concrete Universalsmentioning

confidence: 99%

“…Much of the modern Platonic literature on self-participation and self-predication [e.g., Malcolm 1991] stems from the work of Vlastos on the Third Man argument [1954,1981]. The name derives from Aristotle, but the argument occurs in the dialogues.…”

Section: The Third Man Argument In Platomentioning

confidence: 99%

On Concrete Universals : A Modern Treatment Using Category Theory

Ellerman¹

2015

المخاطبات

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“…And the adjective "concrete" in "concrete universal" is used in the technical sense to mean that the universal is "One among the many" instances of the property instead of "One over the many" (to borrow some of the language of the Third Man Argument considered later). Although "concrete universal" is a traditional philosophical (Hegel) and literary concept [Wimsatt 1947], we will mostly use the perhaps less-confusing adjective "self-predicative" [Malcolm 1991] or even "selfparticipating" interchangeably in case the adjective "concrete" is thought to refer to concrete entities like tables and chairs. 2 Quine's system ML [1955b] allows "VV" for the universal class V, but no standard model of ML has ever been found where "" is interpreted as set membership [Hatcher 1982, Chapter 7].…”

Section: Self-predicative or Concrete Universalsmentioning

confidence: 99%

“…The notion of a self-predicative universal goes back to Plato's Theory of Forms [Vlastos 1978[Vlastos , 1981[Vlastos ,1995Malcolm 1991]. Plato's forms are often considered to be abstract or non-selfpredicative universals quite distinct from and "above" the instances.…”

Section: Self-predicative or Concrete Universalsmentioning

confidence: 99%

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On Self-Predicative Universals in Category Theory

Ellerman

2015

SSRN Journal

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1. This paper shows how the universals of category theory in mathematics provide a model (in the Platonic Heaven of mathematics) for the self-predicative strand of Plato's Theory of Forms as well as for the idea of a "concrete universal" in Hegel and similar ideas of paradigmatic exemplars in ordinary thought.2. The paper also shows how the always-self-predicative universals of category theory provide the "opposite bookend" to the never-self-predicative universals of iterative set theory and thus that the paradoxes arose from having one theory (e.g., Frege's Paradise) where universals could be either self-predicative or non-self-predicative (instead of being always one or the other). 3. Moreover the paper considers one of the most important examples of self-predicative universals in pure mathematics, namely adjoint functors or adjunctions. It gives a parsing of adjunctions into two halves (left and right semi-adjunctions) using the heterodox notion of heteromorphisms, and then shows that the parts can be recombined in a new way to define the cognate-to-adjoints notion of a brain functor that provides an abstract conceptual model of a brain. 4. Finally the paper argues that at least one way category theory has foundational relevance is that it isolates the universal concepts and structures that are important throughout mathematics.

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P

Mittelstraß¹

2016

Enzyklopädie Philosophie Und Wissenschaftstheorie

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Plato on the Self-Predication of Forms

Cited by 50 publications

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On Concrete Universals : A Modern Treatment Using Category Theory

On Concrete Universals : A Modern Treatment Using Category Theory

On Self-Predicative Universals in Category Theory

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