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Category Theory

Steve Awodey

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568612
eISBN:
9780191717567
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568612.001.0001
Subject:
Mathematics, Algebra

This book is a text and reference book on Category Theory, a branch of abstract algebra. The book contains clear definitions of the essential concepts, which are illuminated with numerous accessible ... More


Monad and Triad

Melchisedec TÖrÖnen

in Union and Distinction in the Thought of St Maximus the Confessor

Published in print:
2007
Published Online:
May 2007
ISBN:
9780199296118
eISBN:
9780191712258
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199296118.003.0005
Subject:
Religion, Early Christian Studies

An exposition of Maximus' understanding of the Trinity. The Trinity is a Triad in Monad and a Monad in Triad. The Triad-in-Monad is at once both united and distinguished and there is no confusion or ... More


s e v e n The Physical Monadology and theElements of Nature

Martin Schöneld

in The Philosophy of the Young Kant: The Precritical Project

Published in print:
2000
Published Online:
May 2006
ISBN:
9780195132182
eISBN:
9780199786336
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195132181.003.0008
Subject:
Philosophy, History of Philosophy

This chapter explores Kant’s professorial thesis, The Joint Use of Metaphysics and Geometry in Natural Philosophy, the First Example of Which Contains the Physical Monadology (1756). Section 1 ... More


The World is the Mirror of the Self

Jacqueline Mariña

in Transformation of the Self in the thought of Schleiermacher

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199206377
eISBN:
9780191709753
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199206377.003.0005
Subject:
Religion, Philosophy of Religion

This chapter examines Schleiermacher's Monologen in the context of his 1797-8 study of Leibniz's philosophy. It provides an analysis of his understanding of the self in its relation to God and of the ... More


MONADS AND ALGEBRAS

Steve Awodey

in Category Theory

Published in print:
2006
Published Online:
September 2007
ISBN:
9780198568612
eISBN:
9780191717567
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568612.003.0010
Subject:
Mathematics, Algebra

This chapter presents a third characterization of adjunctions. This one has the virtue of being entirely equational. Topics discussed include the triangle identities, monads and adjoints, algebras ... More


Some Rival Systems

Catherine Wilson

in Epicureanism at the Origins of Modernity

Published in print:
2008
Published Online:
September 2008
ISBN:
9780199238811
eISBN:
9780191716492
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199238811.003.0007
Subject:
Philosophy, History of Philosophy

While some 17th-century critics of Epicureanism, including Margaret Cavendish, focused on the impossibility of a structured and orderly world emerging from the purposeless collision of atoms, other ... More


The Number of Infinity

Svetla Slaveva-Griffin

in Plotinus on Number

Published in print:
2009
Published Online:
May 2009
ISBN:
9780195377194
eISBN:
9780199869572
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195377194.003.0004
Subject:
Classical Studies, Ancient Greek, Roman, and Early Christian Philosophy

This chapter analyzes Plotinus’ refutation of the Aristotle’s criticism of Plato’s view of number in the Parmenides. By rejecting any quantitative value of number in the intelligible realm, Plotinus ... More


Number and the Universe

Svetla Slaveva-Griffin

in Plotinus on Number

Published in print:
2009
Published Online:
May 2009
ISBN:
9780195377194
eISBN:
9780199869572
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195377194.003.0006
Subject:
Classical Studies, Ancient Greek, Roman, and Early Christian Philosophy

This chapter examines the relationship of Substantial Number and all intelligible entities: Absolute Being as “unified number;” Intellect as “number moving in itself”; beings as “unfolded number;” ... More


Metaphysics, Mathematics, and Metaphor

Kurt Smith

in Matter Matters: Metaphysics and Methodology in the Early Modern Period

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199583652
eISBN:
9780191723155
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199583652.003.0011
Subject:
Philosophy, History of Philosophy, Metaphysics/Epistemology

This chapter looks specifically at Leibniz's conception of mathematical structure—an ideal structure underlying the very possibility of the actual world. Both his early and late views are considered. ... More


Enchanting the World: “After Many Corrections and Forward Steps in my Thinking . . . ”

Daniel Garber

in Leibniz: Body, Substance, Monad

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199566648
eISBN:
9780191722035
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566648.003.0008
Subject:
Philosophy, General

This chapter begins with a discussion of real unities, entities without parts, and simple substances, the latter terms which seem to have entered Leibniz's vocabulary in 1695 or so. It then turns to ... More


Monads, Bodies, and Corporeal Substances: The Endgame

Daniel Garber

in Leibniz: Body, Substance, Monad

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199566648
eISBN:
9780191722035
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199566648.003.0009
Subject:
Philosophy, General

This chapter examines Leibniz's treatment of body in the context of a world grounded in monads. It examines a variety of ways in which Leibniz tries to integrate bodies into the world of monads, and ... More


Nature in Proclus:: From irrational immanent principle to goddess ⋆

Alain Lernould

in Neoplatonism and the Philosophy of Nature

Published in print:
2012
Published Online:
May 2012
ISBN:
9780199693719
eISBN:
9780191739019
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199693719.003.0005
Subject:
Philosophy, Ancient Philosophy, History of Philosophy

In the prologue of his commentary on Plato’s Timaeus Proclus defines Nature as the last of the productive causes of the corporeal, as an incorporeal essence inseparable from bodies. Nature is both an ... More


Leibniz: Determinist, Theist, Idealist

Robert Merrihew Adams

Published in print:
1999
Published Online:
November 2003
ISBN:
9780195126495
eISBN:
9780199870974
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0195126491.001.0001
Subject:
Philosophy, History of Philosophy

Explores the contributions of Gottfried Wilhelm Leibniz (1646–1716) to three areas of metaphysics. Part One (Chs. 1–3) is concerned with his determinism, chronicling his efforts to retain a place in ... More


Leibniz on Final Causation

Marleen Rozemond

in Metaphysics and the Good: Themes from the Philosophy of Robert Merrihew Adams

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199542680
eISBN:
9780191715396
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199542680.003.0008
Subject:
Philosophy, General

On a number of occasions Leibniz claims that the physical world is the realm of efficient causation, and that monads are the realm of final causation. Recent scholars have asked what Leibniz has in ... More


The System in Outline

Benson Mates

in The Philosophy of Leibniz: Metaphysics and Language

Published in print:
1989
Published Online:
November 2003
ISBN:
9780195059465
eISBN:
9780199833429
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195059468.003.0003
Subject:
Philosophy, History of Philosophy

This chapter presents the bare essentials of Leibniz's metaphysical system, usually called “the monadology.” Preliminary explications are given of some of the associated special terminology.


Xenocrates and the Systematization of Platonism

John Dillon

in The Heirs of Plato: A Study of the Old Academy (347-274 BC)

Published in print:
2003
Published Online:
November 2003
ISBN:
9780198237662
eISBN:
9780191597336
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198237669.003.0003
Subject:
Philosophy, Ancient Philosophy

Xenocrates, who had accompanied Plato on one of his visits to Sicily, became head of the Academy in 339 B.C. Xenocrates stays close to what he takes to be the cosmological doctrine of Plato's ... More


Corporeal Substance

Robert Merrihew Adams

in Leibniz: Determinist, Theist, Idealist

Published in print:
1999
Published Online:
November 2003
ISBN:
9780195126495
eISBN:
9780199870974
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195126491.003.0011
Subject:
Philosophy, History of Philosophy

Leibniz often speaks of “corporeal substances.” According to many texts a monad and its organic body are both constituents of a single corporeal substance. This chapter explores the relations among ... More


Primitive and Derivative Forces

Robert Merrihew Adams

in Leibniz: Determinist, Theist, Idealist

Published in print:
1999
Published Online:
November 2003
ISBN:
9780195126495
eISBN:
9780199870974
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195126491.003.0014
Subject:
Philosophy, History of Philosophy

The relation between primitive and derivative forces may be the hardest problem about the relation between Leibniz's physics and his metaphysics. He holds that derivative forces are modifications of ... More


Leibnizian Substances

Benson Mates

in The Philosophy of Leibniz: Metaphysics and Language

Published in print:
1989
Published Online:
November 2003
ISBN:
9780195059465
eISBN:
9780199833429
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0195059468.003.0012
Subject:
Philosophy, History of Philosophy

This chapter discusses a miscellany of problems connected with Leibniz's notions of Substance, Accident, Perception, Body, Phenomena, and other fundamentals of his metaphysics.


Substance and Phenomenal Substance

Rae Langton

in Kantian Humility: Our Ignorance of Things in Themselves

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199243174
eISBN:
9780191597909
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199243174.003.0004
Subject:
Philosophy, History of Philosophy

In considering phenomenal substance, an empiricist notion of ‘phenomenon’ as the manifest is to be distinguished from a rationalist notion of phenomenon as the non‐fundamental. And the pure concept ... More


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