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 ...
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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 examples. It provides full proofs of all the important propositions and theorems, and aims to make the basic ideas, theorems, and methods of Category Theory understandable. Although it assumes few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; and monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided.Less
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 examples. It provides full proofs of all the important propositions and theorems, and aims to make the basic ideas, theorems, and methods of Category Theory understandable. Although it assumes few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; and monads. An extra topic of cartesian closed categories and the lambda-calculus is also provided.
Melchisedec TÖrÖnen
- 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 ...
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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 separation in it. A balance between essence and hypostasis is at the heart of this doctrine.Less
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 separation in it. A balance between essence and hypostasis is at the heart of this doctrine.
Martin Schöneld
- 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 ...
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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 describes Euler’s problem that Kant sets out to solve — How can indivisible, unextended points make up divisible and extended bodies? Section 2 discusses Kant’s dynamic solution: his conception of “activity spheres” as ultimate and energetic constituents of matter. Section 3 examines Kant’s argument for combining qualitative-conceptual and quantitative-empirical perspectives, and its role in the pre-critical project.Less
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 describes Euler’s problem that Kant sets out to solve — How can indivisible, unextended points make up divisible and extended bodies? Section 2 discusses Kant’s dynamic solution: his conception of “activity spheres” as ultimate and energetic constituents of matter. Section 3 examines Kant’s argument for combining qualitative-conceptual and quantitative-empirical perspectives, and its role in the pre-critical project.
Jacqueline Mariña
- 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 ...
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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 self in its relation to the world. With Kant, and against Leibniz, Schleiermacher argues that individuals genuinely interact with one another; this is a qualified monadic individualism in which transcendental freedom also plays a role. In the Monologen, Schleiermacher presents his vision of the transcendentally free being who expresses himself or herself into the world. The self has no reflexive access to itself aside from the way that it unites its representations and constructs its world; in a play on Leibniz's idea of the self as the mirror of the world, Schleiermacher affirms that ‘the world is spirit's most beautiful work, its self-created mirror’. Here, Schleiermacher is well on his way to one of the fundamental ideas behind the Dialectic and The Christian Faith, namely, that the rule through which a person connects representations and thereby represents the world to himself or herself is seamlessly integrated with his or her desires, and hence with his or her actions. All are elements of the person's self-expression, itself the product of the transcendental activity of the self. The self knows itself through this expressive activity, which is received and reflected back to it through the activity of others.Less
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 self in its relation to the world. With Kant, and against Leibniz, Schleiermacher argues that individuals genuinely interact with one another; this is a qualified monadic individualism in which transcendental freedom also plays a role. In the Monologen, Schleiermacher presents his vision of the transcendentally free being who expresses himself or herself into the world. The self has no reflexive access to itself aside from the way that it unites its representations and constructs its world; in a play on Leibniz's idea of the self as the mirror of the world, Schleiermacher affirms that ‘the world is spirit's most beautiful work, its self-created mirror’. Here, Schleiermacher is well on his way to one of the fundamental ideas behind the Dialectic and The Christian Faith, namely, that the rule through which a person connects representations and thereby represents the world to himself or herself is seamlessly integrated with his or her desires, and hence with his or her actions. All are elements of the person's self-expression, itself the product of the transcendental activity of the self. The self knows itself through this expressive activity, which is received and reflected back to it through the activity of others.
Steve Awodey
- 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 ...
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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 for a monad, comonads and coalgebras, and algebras for endofunctors. Exercises are given in the last part of the chapter.Less
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 for a monad, comonads and coalgebras, and algebras for endofunctors. Exercises are given in the last part of the chapter.
Catherine Wilson
- 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 ...
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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 critics challenged the coherence of the notion of a material particle as a fundamental building block, hoping to extirpate atheism and materialism at their source. Leibniz evolved an unusual scheme of immaterial atoms, which he termed ‘monads’. Monads were mind-like entities, dimensionless, devoid of physical properties such as shape, impenetrability, and location in absolute space, and differentiated by their experiences. Berkeley went further in proclaiming matter an incoherent idea and insisting that only ideas, God, and the human will really existed, and that the ‘external’ world was in fact in the mind.Less
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 critics challenged the coherence of the notion of a material particle as a fundamental building block, hoping to extirpate atheism and materialism at their source. Leibniz evolved an unusual scheme of immaterial atoms, which he termed ‘monads’. Monads were mind-like entities, dimensionless, devoid of physical properties such as shape, impenetrability, and location in absolute space, and differentiated by their experiences. Berkeley went further in proclaiming matter an incoherent idea and insisting that only ideas, God, and the human will really existed, and that the ‘external’ world was in fact in the mind.
Svetla Slaveva-Griffin
- 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 ...
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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 specifically focuses on Aristotle’s inability to understand the Monad and the Indefinite Dyad as the principles of creation and order of the intelligible. The chapter shows that Plotinus not only follows the steps of his Platonic and Neopythagorean predecessors in defence of Plato’s position, but cleverly uses Aristotle’s own ideas in arguing that number in the intelligible is activity and a property of primary substance (ousia). The result is an original and ontologically elaborate theory of substantial number which offers a new and more successful defence of Plato’s “true numbers” against Aristotle’s criticism and explains the relationship between substantial non-quantitative number and monadic quantitative number as that between intelligible paradigm and its material copy.Less
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 specifically focuses on Aristotle’s inability to understand the Monad and the Indefinite Dyad as the principles of creation and order of the intelligible. The chapter shows that Plotinus not only follows the steps of his Platonic and Neopythagorean predecessors in defence of Plato’s position, but cleverly uses Aristotle’s own ideas in arguing that number in the intelligible is activity and a property of primary substance (ousia). The result is an original and ontologically elaborate theory of substantial number which offers a new and more successful defence of Plato’s “true numbers” against Aristotle’s criticism and explains the relationship between substantial non-quantitative number and monadic quantitative number as that between intelligible paradigm and its material copy.
Svetla Slaveva-Griffin
- 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;” ...
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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;” and the Complete Living Being as “encompassing number.” A closer examination reveals that the four aspects of substantial number correspond to Plato’s primary kinds of rest, movement, otherness, and sameness respectively. The chapter concludes that the properties of substantial number enact the above four primary kinds, while the fifth primary kind, that of being, is the common denominator which represents them all. This conclusion also elucidates the relationship of substantial number with the One and Soul, as Plotinus does not identify them with a particular property of number. Since the properties of substantial number order Intellect on the inside and since both the One and Soul stand on the outside of Intellect, they do not inherit a particular property of number. Substantial number is an ontological expression of the One “beyond Being,” which does not possess any particular characteristic. Soul, however, as an image of Intellect, possesses all the properties of substantial number.Less
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;” and the Complete Living Being as “encompassing number.” A closer examination reveals that the four aspects of substantial number correspond to Plato’s primary kinds of rest, movement, otherness, and sameness respectively. The chapter concludes that the properties of substantial number enact the above four primary kinds, while the fifth primary kind, that of being, is the common denominator which represents them all. This conclusion also elucidates the relationship of substantial number with the One and Soul, as Plotinus does not identify them with a particular property of number. Since the properties of substantial number order Intellect on the inside and since both the One and Soul stand on the outside of Intellect, they do not inherit a particular property of number. Substantial number is an ontological expression of the One “beyond Being,” which does not possess any particular characteristic. Soul, however, as an image of Intellect, possesses all the properties of substantial number.
Kurt Smith
- 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. ...
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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. The chapter shows how it is that Leibniz employed mathematics as a metaphor aimed at explicating his metaphysical views. The metaphysical concepts of unity and harmony, for example, are made clearer by looking at how Leibniz conceived them via the mathematical concepts of function and determinant.Less
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. The chapter shows how it is that Leibniz employed mathematics as a metaphor aimed at explicating his metaphysical views. The metaphysical concepts of unity and harmony, for example, are made clearer by looking at how Leibniz conceived them via the mathematical concepts of function and determinant.
Daniel Garber
- 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 ...
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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 Leibniz's discovery of monads. By 1700 or so, Leibniz had clearly committed himself to the new metaphysics of simple substances, substances without parts, what he had come to call monads. This chapter traces how the terms simple substance and monad are introduced, and how Leibniz moved from the metaphysics of corporeal substance in his middle years to the monadological metaphysics of his last years. Special attention is paid to the ‘Système nouveau’ of 1695 and the correspondence with Burcher de Volder.Less
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 Leibniz's discovery of monads. By 1700 or so, Leibniz had clearly committed himself to the new metaphysics of simple substances, substances without parts, what he had come to call monads. This chapter traces how the terms simple substance and monad are introduced, and how Leibniz moved from the metaphysics of corporeal substance in his middle years to the monadological metaphysics of his last years. Special attention is paid to the ‘Système nouveau’ of 1695 and the correspondence with Burcher de Volder.
Daniel Garber
- 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 ...
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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 a variety of ways in which he treats the notion of corporeal substance in the context of the monadological metaphysics. These views range all the way from views that seem to eliminate bodies altogether to views in which monads seem to be eliminated in favour of bodies and corporeal substances. In the end, it is proposed that Leibniz left behind many loose ends in his thought, questions he considered but did not resolve. In his later years, he was struggling with the problems and struggling toward a considered view on these issues. But he died before he got there.Less
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 a variety of ways in which he treats the notion of corporeal substance in the context of the monadological metaphysics. These views range all the way from views that seem to eliminate bodies altogether to views in which monads seem to be eliminated in favour of bodies and corporeal substances. In the end, it is proposed that Leibniz left behind many loose ends in his thought, questions he considered but did not resolve. In his later years, he was struggling with the problems and struggling toward a considered view on these issues. But he died before he got there.
Alain Lernould
- 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 ...
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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 immanent (following Aristotle) ontological principle and a transcendent one (following Plato). It is an intermediate hypostasis between soul and the corporeal, possessing the reason-principles of sensible bodies—an hypostasis which Proclus identifies with the Divisible Essence that becomes in bodies, mentioned at Timaeus 35a2f. Immanence and transcendence can here be reconciled by the distinction between Nature as monad and the many natures dependent from this monad. Another important point is the distinction between nature qua nature and nature qua soul, intellect, One. Nature is so defined as ‘divine art’ and ‘instrument of the gods’—an instrument which is not deprived of self-motion and is integrated in the divine order.Less
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 immanent (following Aristotle) ontological principle and a transcendent one (following Plato). It is an intermediate hypostasis between soul and the corporeal, possessing the reason-principles of sensible bodies—an hypostasis which Proclus identifies with the Divisible Essence that becomes in bodies, mentioned at Timaeus 35a2f. Immanence and transcendence can here be reconciled by the distinction between Nature as monad and the many natures dependent from this monad. Another important point is the distinction between nature qua nature and nature qua soul, intellect, One. Nature is so defined as ‘divine art’ and ‘instrument of the gods’—an instrument which is not deprived of self-motion and is integrated in the divine order.
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 ...
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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 his system for contingency, and arguing that his famous denial of alternative possibilities (or transworld identity) for individuals is not dictated solely by his logic, but is largely motivated by metaphysical considerations. Part Two (Chs. 4 –8) studies Leibniz's attempts to provide theistic answers to fundamental questions in ontology, and argues that these substantively metaphysical considerations are more promising as a basis for theistic argument than his proposals for more purely formal development of the ontological argument for theism. Part Three (Chs. 9–13) defends a broadly idealist interpretation of Leibniz's conception of bodies or physical objects, and their relation to simple substances or monads, and tries to show the plausibility and interest of some of its leading ideas.Less
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 his system for contingency, and arguing that his famous denial of alternative possibilities (or transworld identity) for individuals is not dictated solely by his logic, but is largely motivated by metaphysical considerations. Part Two (Chs. 4 –8) studies Leibniz's attempts to provide theistic answers to fundamental questions in ontology, and argues that these substantively metaphysical considerations are more promising as a basis for theistic argument than his proposals for more purely formal development of the ontological argument for theism. Part Three (Chs. 9–13) defends a broadly idealist interpretation of Leibniz's conception of bodies or physical objects, and their relation to simple substances or monads, and tries to show the plausibility and interest of some of its leading ideas.
Marleen Rozemond
- 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 ...
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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 mind when endorsing final causation, especially in light of the general rejection of final causation by other early moderns. This chapter illuminates his notion of final causation in the context of his use of the notion of substantial form, and what that notion means in his thought.Less
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 mind when endorsing final causation, especially in light of the general rejection of final causation by other early moderns. This chapter illuminates his notion of final causation in the context of his use of the notion of substantial form, and what that notion means in his thought.
John Dillon
- 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 ...
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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 Timaeus; indeed Xenocrates’ doctrine may be seen as something of a retreat from Speusippus’ radical position, perhaps in response to Aristotle's criticisms. Dillon reconstructs Xenocrates's cosmological or metaphysical scheme as comprising a pair of first principles, the Monad, or Nous, and the Dyad, or the ‘Everflowing’, to which the Pythagorean tetraktys corresponds as the active counterpart; and a World‐Soul, which receives the forms from the Supreme God's mind, and projects them upon the physical plane. In Logic, Xenocrates remained faithful to Platonic logic, rejecting the Aristotelian categories, although he did argue that the species was prior to the genus; in Ethics, while keen to formalize Plato's teachings, Xenocrates ends up with a position very similar to Aristotle's, in that he emphasizes the needs of the body as well as those of the soul. Xenocrates had a dominant effect on the development of Platonism, because he systematized what he took to be Plato's philosophical system, thus laying the foundation for the ‘Platonic’ system of philosophy; it is Xenocrates’ definition of Form, for instance, which became the standard definition of a Platonic Form.Less
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 Timaeus; indeed Xenocrates’ doctrine may be seen as something of a retreat from Speusippus’ radical position, perhaps in response to Aristotle's criticisms. Dillon reconstructs Xenocrates's cosmological or metaphysical scheme as comprising a pair of first principles, the Monad, or Nous, and the Dyad, or the ‘Everflowing’, to which the Pythagorean tetraktys corresponds as the active counterpart; and a World‐Soul, which receives the forms from the Supreme God's mind, and projects them upon the physical plane. In Logic, Xenocrates remained faithful to Platonic logic, rejecting the Aristotelian categories, although he did argue that the species was prior to the genus; in Ethics, while keen to formalize Plato's teachings, Xenocrates ends up with a position very similar to Aristotle's, in that he emphasizes the needs of the body as well as those of the soul. Xenocrates had a dominant effect on the development of Platonism, because he systematized what he took to be Plato's philosophical system, thus laying the foundation for the ‘Platonic’ system of philosophy; it is Xenocrates’ definition of Form, for instance, which became the standard definition of a Platonic Form.
Benson Mates
- 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.
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.
Robert Merrihew Adams
- 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 ...
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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 them, and argues for an interpretation of Leibniz's corporeal substances as exhaustively constituted by relations of harmony among simple substances, and thus as consistent with his idealism. It argues also that after 1706, when it came to seem doubtful to both Leibniz and his contemporaries that such an interpretation could provide adequately for the strong unity that all agreed a corporeal substance must have, he tended to back away from the notion of corporeal substance rather than abandon his view of the world as composed ultimately of monads.Less
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 them, and argues for an interpretation of Leibniz's corporeal substances as exhaustively constituted by relations of harmony among simple substances, and thus as consistent with his idealism. It argues also that after 1706, when it came to seem doubtful to both Leibniz and his contemporaries that such an interpretation could provide adequately for the strong unity that all agreed a corporeal substance must have, he tended to back away from the notion of corporeal substance rather than abandon his view of the world as composed ultimately of monads.
Robert Merrihew Adams
- 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 ...
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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 primitive forces, but also that physical forces, which he classifies as derivative forces, belong to bodies, which are aggregates, whereas primitive forces belong to unextended perceiving substances (monads) and constitute their essence. This chapter addresses this problem, arguing that a major part of it can be solved on the supposition that physical events are only phenomena, and hence ultimately determined by modifications of the primitive forces of perceiving substances (monads).Less
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 primitive forces, but also that physical forces, which he classifies as derivative forces, belong to bodies, which are aggregates, whereas primitive forces belong to unextended perceiving substances (monads) and constitute their essence. This chapter addresses this problem, arguing that a major part of it can be solved on the supposition that physical events are only phenomena, and hence ultimately determined by modifications of the primitive forces of perceiving substances (monads).
Benson Mates
- 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.
This chapter discusses a miscellany of problems connected with Leibniz's notions of Substance, Accident, Perception, Body, Phenomena, and other fundamentals of his metaphysics.
Rae Langton
- 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 ...
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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 of substance as subject is to be distinguished from the schematized concept of substance as enduring. The notion of phaenomenon substantiatum in Leibniz, Baumgarten, and early Kant is that of a non‐substance that is treated as a substance, e.g. a property treated as a subject of properties, whether in metaphor (‘love is blind’) or metaphysics. Body and matter were prime examples of such ‘merely comparative’ subjects, monads being the true fundamental substances. Phenomenal substance in later Kant is a species of phaenomenon substantiatum, constituted by relational properties of attraction and impenetrability; it is a non‐substance that serves as substance because it endures.Less
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 of substance as subject is to be distinguished from the schematized concept of substance as enduring. The notion of phaenomenon substantiatum in Leibniz, Baumgarten, and early Kant is that of a non‐substance that is treated as a substance, e.g. a property treated as a subject of properties, whether in metaphor (‘love is blind’) or metaphysics. Body and matter were prime examples of such ‘merely comparative’ subjects, monads being the true fundamental substances. Phenomenal substance in later Kant is a species of phaenomenon substantiatum, constituted by relational properties of attraction and impenetrability; it is a non‐substance that serves as substance because it endures.
