David Bostock
- Published in print:
- 2006
- Published Online:
- May 2006
- ISBN:
- 9780199286867
- eISBN:
- 9780191603532
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199286868.001.0001
- Subject:
- Philosophy, Ancient Philosophy
The book features a collection of ten essays on themes from Aristotle’s Physics. Six of these have been previously published, and four are newly written for this volume. The first five essays are ...
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The book features a collection of ten essays on themes from Aristotle’s Physics. Six of these have been previously published, and four are newly written for this volume. The first five essays are based on single theme, namely Aristotle’s conception of substance as it appears in his physical works. The basic texts here are Physics I-II, but the essays also range quite widely over Aristotle’s other physical works, where these are relevant to his understanding of the notions of substance, matter, and form. The general view of these five essays is that Aristotle’s idea of matter was a winner, but his idea of form certainly was not. The remaining five essays are on various topics from Physics III-VI, with each confined to the text of the Physics itself. The topics covered fall broadly under the headings: space, time, and infinity.Less
The book features a collection of ten essays on themes from Aristotle’s Physics. Six of these have been previously published, and four are newly written for this volume. The first five essays are based on single theme, namely Aristotle’s conception of substance as it appears in his physical works. The basic texts here are Physics I-II, but the essays also range quite widely over Aristotle’s other physical works, where these are relevant to his understanding of the notions of substance, matter, and form. The general view of these five essays is that Aristotle’s idea of matter was a winner, but his idea of form certainly was not. The remaining five essays are on various topics from Physics III-VI, with each confined to the text of the Physics itself. The topics covered fall broadly under the headings: space, time, and infinity.
Louis A. Girifalco
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199228966
- eISBN:
- 9780191711183
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199228966.003.0019
- Subject:
- Physics, History of Physics
Gravity is responsible not only for the existence of stars and planets; it also creates the weirdest objects imaginable. A body with mass greater than 1.4 solar masses cannot remain a white dwarf and ...
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Gravity is responsible not only for the existence of stars and planets; it also creates the weirdest objects imaginable. A body with mass greater than 1.4 solar masses cannot remain a white dwarf and will collapse into a neutron star. But if the mass is greater than about two and a half solar masses, the collapse will continue until it becomes a black hole. This is the strangest object in the universe. Its gravity is so strong that even light cannot get out of it. Anything near it is sucked in, crushed to a point, and approaches infinite density. The laws of physics as now known do not apply at the centre of a black hole and the very meaning of its existence is in doubt.Less
Gravity is responsible not only for the existence of stars and planets; it also creates the weirdest objects imaginable. A body with mass greater than 1.4 solar masses cannot remain a white dwarf and will collapse into a neutron star. But if the mass is greater than about two and a half solar masses, the collapse will continue until it becomes a black hole. This is the strangest object in the universe. Its gravity is so strong that even light cannot get out of it. Anything near it is sucked in, crushed to a point, and approaches infinite density. The laws of physics as now known do not apply at the centre of a black hole and the very meaning of its existence is in doubt.
Jacob Rosen and Marko Malink
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199644384
- eISBN:
- 9780191743344
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199644384.003.0006
- Subject:
- Philosophy, Ancient Philosophy
In Prior Analytics 1. 15, Aristotle states the following rule of modal logic, which we may call the possibility rule: given the premiss that A is possible, and given a derivation of B from A, it can ...
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In Prior Analytics 1. 15, Aristotle states the following rule of modal logic, which we may call the possibility rule: given the premiss that A is possible, and given a derivation of B from A, it can be inferred that B is possible. Aristotle is the first philosopher known to state this rule, and it stands among his most significant contributions to philosophical thought about modality. He applies the possibility rule in arguments that are central to his physical and metaphysical views, in works such as the Physics, De caelo, De generationeetcorruptione, and the Metaphysics. These arguments have proved difficult to understand, largely because the exact nature of the possibility rule and its role in each argument is often unclear. The chapter offers a comprehensive treatment of the arguments throughout Aristotle's works, resulting in a better understanding both of the possibility rule and of the individual arguments in which it appears.Less
In Prior Analytics 1. 15, Aristotle states the following rule of modal logic, which we may call the possibility rule: given the premiss that A is possible, and given a derivation of B from A, it can be inferred that B is possible. Aristotle is the first philosopher known to state this rule, and it stands among his most significant contributions to philosophical thought about modality. He applies the possibility rule in arguments that are central to his physical and metaphysical views, in works such as the Physics, De caelo, De generationeetcorruptione, and the Metaphysics. These arguments have proved difficult to understand, largely because the exact nature of the possibility rule and its role in each argument is often unclear. The chapter offers a comprehensive treatment of the arguments throughout Aristotle's works, resulting in a better understanding both of the possibility rule and of the individual arguments in which it appears.
David Bostock
- Published in print:
- 2006
- Published Online:
- May 2006
- ISBN:
- 9780199286867
- eISBN:
- 9780191603532
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199286868.003.0007
- Subject:
- Philosophy, Ancient Philosophy
This essay argues that Aristotle misdescribes his own position when he sums it up as the claim that infinity can only be potential and never actual. He readily accepts that there are processes which ...
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This essay argues that Aristotle misdescribes his own position when he sums it up as the claim that infinity can only be potential and never actual. He readily accepts that there are processes which are actually infinite, that is, never-ending. But he denies that there can ever be a time when an infinite process has been completed. This means that he has to find some fault with Zeno’s well-known argument of Achilles and the tortoise, which he does by introducing the idea that points do not exist until they are ‘actualized’. It is argued that this idea, though ingenious and certainly appropriate to the problem, does not work out in the end.Less
This essay argues that Aristotle misdescribes his own position when he sums it up as the claim that infinity can only be potential and never actual. He readily accepts that there are processes which are actually infinite, that is, never-ending. But he denies that there can ever be a time when an infinite process has been completed. This means that he has to find some fault with Zeno’s well-known argument of Achilles and the tortoise, which he does by introducing the idea that points do not exist until they are ‘actualized’. It is argued that this idea, though ingenious and certainly appropriate to the problem, does not work out in the end.
Peter Adamson
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780195181425
- eISBN:
- 9780199785087
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195181425.003.0004
- Subject:
- Religion, Philosophy of Religion
This chapter surveys the Greek background in Plato’s Timaeus, Aristotle’s Physics and De Caelo, and the dispute between late Greek thinkers, especially Proclus and Philoponus. Against this ...
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This chapter surveys the Greek background in Plato’s Timaeus, Aristotle’s Physics and De Caelo, and the dispute between late Greek thinkers, especially Proclus and Philoponus. Against this background, al-Kindī’s arguments that only God can be eternal and that creation must be finite in time as well as space are explored. It is suggested that al-Kindī’s interest in this topic can be explained in terms of the contemporary ’Abbāsid dogma that the Koran is not eternal, but created.Less
This chapter surveys the Greek background in Plato’s Timaeus, Aristotle’s Physics and De Caelo, and the dispute between late Greek thinkers, especially Proclus and Philoponus. Against this background, al-Kindī’s arguments that only God can be eternal and that creation must be finite in time as well as space are explored. It is suggested that al-Kindī’s interest in this topic can be explained in terms of the contemporary ’Abbāsid dogma that the Koran is not eternal, but created.
José Ferreirós
- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691167510
- eISBN:
- 9781400874002
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691167510.003.0008
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter considers two crucial shifts in mathematical knowledge: the natural numbers ℕ and the real number system ℝ. ℝ has proved to serve together with the natural numbers ℕ as one of the two ...
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This chapter considers two crucial shifts in mathematical knowledge: the natural numbers ℕ and the real number system ℝ. ℝ has proved to serve together with the natural numbers ℕ as one of the two core structures of mathematics; together they are what Solomon Feferman described as “the sine qua non of our subject, both pure and applied.” Indeed, nobody can claim to have a basic grasp of mathematics without mastery of the central elements in the theory of both number systems. The chapter examines related theories and conceptions about real numbers, with particular emphasis on the work of J. H. Lambert and Sir Isaac Newton. It also discusses various conceptions of the number continuum, assumptions about simple infinity and arbitrary infinity, and the development of mathematics in relation to the real numbers. Finally, it reflects on the link between mathematical hypotheses and scientific practices.Less
This chapter considers two crucial shifts in mathematical knowledge: the natural numbers ℕ and the real number system ℝ. ℝ has proved to serve together with the natural numbers ℕ as one of the two core structures of mathematics; together they are what Solomon Feferman described as “the sine qua non of our subject, both pure and applied.” Indeed, nobody can claim to have a basic grasp of mathematics without mastery of the central elements in the theory of both number systems. The chapter examines related theories and conceptions about real numbers, with particular emphasis on the work of J. H. Lambert and Sir Isaac Newton. It also discusses various conceptions of the number continuum, assumptions about simple infinity and arbitrary infinity, and the development of mathematics in relation to the real numbers. Finally, it reflects on the link between mathematical hypotheses and scientific practices.
Andrew Moutu
- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780197264454
- eISBN:
- 9780191760501
- Item type:
- chapter
- Publisher:
- British Academy
- DOI:
- 10.5871/bacad/9780197264454.003.0006
- Subject:
- Anthropology, Asian Cultural Anthropology
This chapter examines some aspects of totemic names and the connection to kinship and marriage practices. It attempts to conceptualise relationships in ontological terms by identifying and employing ...
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This chapter examines some aspects of totemic names and the connection to kinship and marriage practices. It attempts to conceptualise relationships in ontological terms by identifying and employing four Western philosophical concepts — immanence and transcendence, necessity and contingency — and concretizes the nature of this conceptual approach by introducing further ethnographic material from neighbouring societies. The chapter opens with a discussion of Iqwaye and Iatmul, showing how the ontological issues of immanence and transcendence are located in social relations. It then considers the issues of necessity and contingency as they appear in the context of kinship and clan organization amongst the Iatmul and the Manambu. A theoretical dimension of this discussion concerns the manner in which time and relationships function in affecting and coordinating the behaviour of ownership. Since Iatmul names are generally considered as abundant in stock, and since they serve as vectors of integral relationships, another theoretical interest of the chapter relates to the question of the connection between relationships and infinity.Less
This chapter examines some aspects of totemic names and the connection to kinship and marriage practices. It attempts to conceptualise relationships in ontological terms by identifying and employing four Western philosophical concepts — immanence and transcendence, necessity and contingency — and concretizes the nature of this conceptual approach by introducing further ethnographic material from neighbouring societies. The chapter opens with a discussion of Iqwaye and Iatmul, showing how the ontological issues of immanence and transcendence are located in social relations. It then considers the issues of necessity and contingency as they appear in the context of kinship and clan organization amongst the Iatmul and the Manambu. A theoretical dimension of this discussion concerns the manner in which time and relationships function in affecting and coordinating the behaviour of ownership. Since Iatmul names are generally considered as abundant in stock, and since they serve as vectors of integral relationships, another theoretical interest of the chapter relates to the question of the connection between relationships and infinity.
Jon McGinnis
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780195331479
- eISBN:
- 9780199868032
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195331479.003.0007
- Subject:
- Religion, Islam
After a quick survey of the positions prior to Avicenna concerning the age of the universe, the chapter focuses on Avicenna’s unique arguments for the eternity of the world. To this end, it presents ...
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After a quick survey of the positions prior to Avicenna concerning the age of the universe, the chapter focuses on Avicenna’s unique arguments for the eternity of the world. To this end, it presents his conception of possibility as well as considering how Avicenna envisions the most basic modes of possible existence, namely, substances and accidents, with a particular emphasis on forms and matter. There is then a general discussion of Avicenna’s notion of metaphysical causality. Upon completing the investigation of possible existence, one will be in a position to appreciate Avicenna’s new modal arguments for the world’s eternity and his response to earlier criticisms against that thesis. The chapter, then, concludes with a section on the Necessary Existent’s relation to possible existence as exemplified in Avicenna’s unique twist on the Neoplatonic theory of emanation.Less
After a quick survey of the positions prior to Avicenna concerning the age of the universe, the chapter focuses on Avicenna’s unique arguments for the eternity of the world. To this end, it presents his conception of possibility as well as considering how Avicenna envisions the most basic modes of possible existence, namely, substances and accidents, with a particular emphasis on forms and matter. There is then a general discussion of Avicenna’s notion of metaphysical causality. Upon completing the investigation of possible existence, one will be in a position to appreciate Avicenna’s new modal arguments for the world’s eternity and his response to earlier criticisms against that thesis. The chapter, then, concludes with a section on the Necessary Existent’s relation to possible existence as exemplified in Avicenna’s unique twist on the Neoplatonic theory of emanation.
Michael Potter
- Published in print:
- 2002
- Published Online:
- May 2007
- ISBN:
- 9780199252619
- eISBN:
- 9780191712647
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199252619.003.0007
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Ludwig Wittgenstein studied with Russell in Cambridge from 1911 to 1913, and wrote the Tractatus while on active service in the Austrian army during the First World War. Large parts of the book are ...
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Ludwig Wittgenstein studied with Russell in Cambridge from 1911 to 1913, and wrote the Tractatus while on active service in the Austrian army during the First World War. Large parts of the book are devoted to explaining and correcting errors in the conception of logic to be found in Principia. Wittgenstein did not, as is sometimes suggested, reject the idea of a hierarchy of types, but he did reject the notion that mathematics (and in particular arithmetic) could be based, as in Principia, on classes. For this reason although the account of arithmetic given in the Tractatus is in a sense logicist, it is very different from Russell's.Less
Ludwig Wittgenstein studied with Russell in Cambridge from 1911 to 1913, and wrote the Tractatus while on active service in the Austrian army during the First World War. Large parts of the book are devoted to explaining and correcting errors in the conception of logic to be found in Principia. Wittgenstein did not, as is sometimes suggested, reject the idea of a hierarchy of types, but he did reject the notion that mathematics (and in particular arithmetic) could be based, as in Principia, on classes. For this reason although the account of arithmetic given in the Tractatus is in a sense logicist, it is very different from Russell's.
Michael Potter
- Published in print:
- 2002
- Published Online:
- May 2007
- ISBN:
- 9780199252619
- eISBN:
- 9780191712647
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199252619.003.0009
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Frank Ramsey was involved in preparing the English translation of the Tractatus as an undergraduate at Cambridge. He developed an account of the theory of types which avoided the difficulties ...
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Frank Ramsey was involved in preparing the English translation of the Tractatus as an undergraduate at Cambridge. He developed an account of the theory of types which avoided the difficulties associated with the axiom of reducibility by following what he took to be Wittgensteinian principles. In December 1924, he wrote an essay which was eventually published under the title ‘The foundations of mathematics’. The material in the essay that is relevant here falls into three distinct parts: in the first Ramsey showed how to develop a theory of types on Wittgensteinian principles that had no need of the problematic axiom of reducibility; in the second he dealt with the derivation of the theory of classes from the theory of types; and in the third he addressed the problematic dependence of the theory on the axiom of infinity.Less
Frank Ramsey was involved in preparing the English translation of the Tractatus as an undergraduate at Cambridge. He developed an account of the theory of types which avoided the difficulties associated with the axiom of reducibility by following what he took to be Wittgensteinian principles. In December 1924, he wrote an essay which was eventually published under the title ‘The foundations of mathematics’. The material in the essay that is relevant here falls into three distinct parts: in the first Ramsey showed how to develop a theory of types on Wittgensteinian principles that had no need of the problematic axiom of reducibility; in the second he dealt with the derivation of the theory of classes from the theory of types; and in the third he addressed the problematic dependence of the theory on the axiom of infinity.
Paul Crowther
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199579976
- eISBN:
- 9780191722615
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199579976.003.0008
- Subject:
- Philosophy, Aesthetics, History of Philosophy
This chapter rectifies shortcomings in the author's previous sustained treatment of this subject in his book The Kantian Sublime: From Morality to Art. The structure of Kant's account of the ...
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This chapter rectifies shortcomings in the author's previous sustained treatment of this subject in his book The Kantian Sublime: From Morality to Art. The structure of Kant's account of the mathematical sublime is analyzed, suggesting that the role played by infinity should be regarded as contingent rather than necessary, and that an austere reconstruction of his theory is to be preferred over Kant's own rather baroque account. A similar exposition is performed in relation to Kant's account of the dynamical sublime. In revising Kant's theory, special attention is paid to the hitherto neglected question of the specific perceptual cues that trigger experiences of both varieties of the sublime. The theory is also extended to cover artworks, including some of an avant-garde nature.Less
This chapter rectifies shortcomings in the author's previous sustained treatment of this subject in his book The Kantian Sublime: From Morality to Art. The structure of Kant's account of the mathematical sublime is analyzed, suggesting that the role played by infinity should be regarded as contingent rather than necessary, and that an austere reconstruction of his theory is to be preferred over Kant's own rather baroque account. A similar exposition is performed in relation to Kant's account of the dynamical sublime. In revising Kant's theory, special attention is paid to the hitherto neglected question of the specific perceptual cues that trigger experiences of both varieties of the sublime. The theory is also extended to cover artworks, including some of an avant-garde nature.
Hsueh-Man Shen
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780197265277
- eISBN:
- 9780191754203
- Item type:
- chapter
- Publisher:
- British Academy
- DOI:
- 10.5871/bacad/9780197265277.003.0008
- Subject:
- History, Cultural History
Modern art history practice often treats Buddhist icons or ritual objects as unique objects, focusing on their originality and uniqueness. This text investigates how the paradoxical Buddhist doctrine ...
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Modern art history practice often treats Buddhist icons or ritual objects as unique objects, focusing on their originality and uniqueness. This text investigates how the paradoxical Buddhist doctrine of ‘the one and the many’ was translated into visual language through manipulation of the relationship between copies and the original. It analyses the different tactics and strategies formulated around given socio-historical frameworks to visualise the notion of infinity, and ultimately the structure of the universe, and suggests that multiple copies of a single design were more potent a vehicle than single objects in expressing ideas related to the Buddhist metaphysics.Less
Modern art history practice often treats Buddhist icons or ritual objects as unique objects, focusing on their originality and uniqueness. This text investigates how the paradoxical Buddhist doctrine of ‘the one and the many’ was translated into visual language through manipulation of the relationship between copies and the original. It analyses the different tactics and strategies formulated around given socio-historical frameworks to visualise the notion of infinity, and ultimately the structure of the universe, and suggests that multiple copies of a single design were more potent a vehicle than single objects in expressing ideas related to the Buddhist metaphysics.
David Sedley
- Published in print:
- 2008
- Published Online:
- March 2012
- ISBN:
- 9780520253643
- eISBN:
- 9780520934368
- Item type:
- book
- Publisher:
- University of California Press
- DOI:
- 10.1525/california/9780520253643.001.0001
- Subject:
- Classical Studies, Ancient Greek, Roman, and Early Christian Philosophy
The world is configured in ways that seem systematically hospitable to life forms, especially the human race. Is this the outcome of divine planning or simply of the laws of physics? Ancient Greeks ...
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The world is configured in ways that seem systematically hospitable to life forms, especially the human race. Is this the outcome of divine planning or simply of the laws of physics? Ancient Greeks and Romans famously disagreed on whether the cosmos was the product of design or accident. This book examines this question and illuminates new historical perspectives on the pantheon of thinkers who laid the foundations of Western philosophy and science. Versions of what we call the “creationist” option were widely favored by the major thinkers of classical antiquity, including Plato, whose ideas on the subject prepared the ground for Aristotle's celebrated teleology. But Aristotle aligned himself with the anti-creationist lobby, whose most militant members—the atomists—sought to show how a world just like ours would form inevitably by sheer accident, given only the infinity of space and matter. This study explores seven major thinkers and philosophical movements enmeshed in the debate: Anaxagoras, Empedocles, Socrates, Plato, the atomists, Aristotle, and the Stoics.Less
The world is configured in ways that seem systematically hospitable to life forms, especially the human race. Is this the outcome of divine planning or simply of the laws of physics? Ancient Greeks and Romans famously disagreed on whether the cosmos was the product of design or accident. This book examines this question and illuminates new historical perspectives on the pantheon of thinkers who laid the foundations of Western philosophy and science. Versions of what we call the “creationist” option were widely favored by the major thinkers of classical antiquity, including Plato, whose ideas on the subject prepared the ground for Aristotle's celebrated teleology. But Aristotle aligned himself with the anti-creationist lobby, whose most militant members—the atomists—sought to show how a world just like ours would form inevitably by sheer accident, given only the infinity of space and matter. This study explores seven major thinkers and philosophical movements enmeshed in the debate: Anaxagoras, Empedocles, Socrates, Plato, the atomists, Aristotle, and the Stoics.
John Panteleimon Manoussakis
- Published in print:
- 2006
- Published Online:
- March 2011
- ISBN:
- 9780823225316
- eISBN:
- 9780823236893
- Item type:
- book
- Publisher:
- Fordham University Press
- DOI:
- 10.5422/fso/9780823225316.001.0001
- Subject:
- Religion, Theology
Who or what comes after God? In the wake of God, as the last fifty years of philosophy has shown, God comes back again, otherwise: Heidegger's last God, Levinas's God of Infinity, ...
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Who or what comes after God? In the wake of God, as the last fifty years of philosophy has shown, God comes back again, otherwise: Heidegger's last God, Levinas's God of Infinity, Derrida's and Caputo's tout autre, Marion's God without Being, and Kearney's God who may be. This book attempts to represent some of the most considered responses to Richard Kearney's recent writings on the philosophy of religion, in particular The God Who May Be: A Hermeneutics of Religion and Strangers, Gods, and Monsters: Interpreting Otherness. It brings together seventeen essays that share the common problematic of the otherness of the Other — seventeen different variations on the same theme: philosophy about God after God — that is to say, a way of thinking God otherwise than ontologically.Less
Who or what comes after God? In the wake of God, as the last fifty years of philosophy has shown, God comes back again, otherwise: Heidegger's last God, Levinas's God of Infinity, Derrida's and Caputo's tout autre, Marion's God without Being, and Kearney's God who may be. This book attempts to represent some of the most considered responses to Richard Kearney's recent writings on the philosophy of religion, in particular The God Who May Be: A Hermeneutics of Religion and Strangers, Gods, and Monsters: Interpreting Otherness. It brings together seventeen essays that share the common problematic of the otherness of the Other — seventeen different variations on the same theme: philosophy about God after God — that is to say, a way of thinking God otherwise than ontologically.
Peter C. Hodgson
- Published in print:
- 2005
- Published Online:
- April 2005
- ISBN:
- 9780199273614
- eISBN:
- 9780191602443
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199273618.003.0011
- Subject:
- Religion, Philosophy of Religion
The thesis of this chapter is that Hegel’s philosophy of religion provides fruitful resources for theological reflection today. The first task is to consider those who question this assumption. ...
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The thesis of this chapter is that Hegel’s philosophy of religion provides fruitful resources for theological reflection today. The first task is to consider those who question this assumption. Indeed, a strand of interpretation going back to Hegel’s own time claims that his philosophical reconstruction of religion is really a destruction (Kierkegaard), that the outcome of his thought is atheism (or humanism) rather than theism (Feuerbach). Along similar lines, William Desmond has recently argued that the God of Hegel’s system is a counterfeit rather than the true God of Christian faith. The chapter then turns to six sets of distinctions or contested sites in postmodernity and their Hegelian resolution: heterodoxy and ontotheology, totality and infinity, language and logic, tragedy and redemption, self and other, unity and diversity. The mediating categories of spirit, wholeness, narrative, Christ, community, and pluralism contribute to the project of theological reconstruction at the beginning of the twenty-first century.Less
The thesis of this chapter is that Hegel’s philosophy of religion provides fruitful resources for theological reflection today. The first task is to consider those who question this assumption. Indeed, a strand of interpretation going back to Hegel’s own time claims that his philosophical reconstruction of religion is really a destruction (Kierkegaard), that the outcome of his thought is atheism (or humanism) rather than theism (Feuerbach). Along similar lines, William Desmond has recently argued that the God of Hegel’s system is a counterfeit rather than the true God of Christian faith. The chapter then turns to six sets of distinctions or contested sites in postmodernity and their Hegelian resolution: heterodoxy and ontotheology, totality and infinity, language and logic, tragedy and redemption, self and other, unity and diversity. The mediating categories of spirit, wholeness, narrative, Christ, community, and pluralism contribute to the project of theological reconstruction at the beginning of the twenty-first century.
John Heil
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199596201
- eISBN:
- 9780191741876
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199596201.003.0003
- Subject:
- Philosophy, Metaphysics/Epistemology, General
Chapter 2 includes an argument aimed at showing that substances as I think property bearers must be simple. This chapter offers a second consideration favoring the simplicity of substances based on a ...
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Chapter 2 includes an argument aimed at showing that substances as I think property bearers must be simple. This chapter offers a second consideration favoring the simplicity of substances based on a traditional characterization of substances as non-dependent entities. An entity made up of substances depends on the substances that make it up, so would not, on such a view, count as a substance. Substantial parts of objects are distinguished from properties, on the one hand, and, on the other hand, from spatial and temporal parts. The chapter includes a discussion of the possibility of substantial complexity ‘all the way down’, and the question whether the universe could contain an infinite number of substances — an infinite number of electrons, for instance. The implications of particle entanglement in quantum physics are discussed in light of the possibility that entanglement yields new simple emergent substances in which constituent particles ‘lose their identity’ as substances.Less
Chapter 2 includes an argument aimed at showing that substances as I think property bearers must be simple. This chapter offers a second consideration favoring the simplicity of substances based on a traditional characterization of substances as non-dependent entities. An entity made up of substances depends on the substances that make it up, so would not, on such a view, count as a substance. Substantial parts of objects are distinguished from properties, on the one hand, and, on the other hand, from spatial and temporal parts. The chapter includes a discussion of the possibility of substantial complexity ‘all the way down’, and the question whether the universe could contain an infinite number of substances — an infinite number of electrons, for instance. The implications of particle entanglement in quantum physics are discussed in light of the possibility that entanglement yields new simple emergent substances in which constituent particles ‘lose their identity’ as substances.
David Bostock
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199651443
- eISBN:
- 9780191741197
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199651443.003.0006
- Subject:
- Philosophy, History of Philosophy, Metaphysics/Epistemology
Russell’s attempt to obey the Vicious Circle Principle must lead to the conclusion that there are only countably many propositional functions, but this conflicts with his axiom of reducibility. So we ...
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Russell’s attempt to obey the Vicious Circle Principle must lead to the conclusion that there are only countably many propositional functions, but this conflicts with his axiom of reducibility. So we do better to reject the ramified type theory, and thereby dispense with both. The simple type theory still has problems in deducing mathematics, e.g. over the axiom of infinity, and problems too over what this chapter calls ‘type-neutral’ predicates. A remedy for both of these points may be available, but it would take us into uncharted waters. One may observe that the axiom of choice (which Russell calls the ‘multiplicative’ axiom) is needed for the classical theory of infinite sets.Less
Russell’s attempt to obey the Vicious Circle Principle must lead to the conclusion that there are only countably many propositional functions, but this conflicts with his axiom of reducibility. So we do better to reject the ramified type theory, and thereby dispense with both. The simple type theory still has problems in deducing mathematics, e.g. over the axiom of infinity, and problems too over what this chapter calls ‘type-neutral’ predicates. A remedy for both of these points may be available, but it would take us into uncharted waters. One may observe that the axiom of choice (which Russell calls the ‘multiplicative’ axiom) is needed for the classical theory of infinite sets.
David Bostock
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199651443
- eISBN:
- 9780191741197
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199651443.003.0013
- Subject:
- Philosophy, History of Philosophy, Metaphysics/Epistemology
Russell argued in 1912 that particulars exist, as well as universals. In fact he recanted this argument much later, in 1940, and the recantation shows how weak that argument actually is. He always ...
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Russell argued in 1912 that particulars exist, as well as universals. In fact he recanted this argument much later, in 1940, and the recantation shows how weak that argument actually is. He always believed in universals (for what seem to be quite inadequate reasons), but there is a question over how this relates to his acceptance of propositional functions. The best solution seems to be that simple propositional functions correspond to universals, but others are merely arrangements of symbols, as also are the propositions that they are abstracted from. (But one may well ask whether this provides enough propositional functions, for the reduction of mathematics to logic apparently requires an uncountable infinity of them.)Less
Russell argued in 1912 that particulars exist, as well as universals. In fact he recanted this argument much later, in 1940, and the recantation shows how weak that argument actually is. He always believed in universals (for what seem to be quite inadequate reasons), but there is a question over how this relates to his acceptance of propositional functions. The best solution seems to be that simple propositional functions correspond to universals, but others are merely arrangements of symbols, as also are the propositions that they are abstracted from. (But one may well ask whether this provides enough propositional functions, for the reduction of mathematics to logic apparently requires an uncountable infinity of them.)
Thomas Holden
- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780199263264
- eISBN:
- 9780191601743
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199263264.003.0003
- Subject:
- Philosophy, History of Philosophy
According to the actual parts doctrine, all the parts into which a material body can be divided exist as so many independent beings. Various early modern philosophers argued that this entails that ...
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According to the actual parts doctrine, all the parts into which a material body can be divided exist as so many independent beings. Various early modern philosophers argued that this entails that bodies have a determinate number of parts, and thus that infinite divisibility entails a completely given ‘actual infinity’ of parts rather than an ever‐increasable ‘potential infinity’. Some further argued that, since all the parts are given, ultimate parts or atoms must be given. Assesses these arguments and compares them with other early modern arguments for a determinate number of parts and for atomism.Less
According to the actual parts doctrine, all the parts into which a material body can be divided exist as so many independent beings. Various early modern philosophers argued that this entails that bodies have a determinate number of parts, and thus that infinite divisibility entails a completely given ‘actual infinity’ of parts rather than an ever‐increasable ‘potential infinity’. Some further argued that, since all the parts are given, ultimate parts or atoms must be given. Assesses these arguments and compares them with other early modern arguments for a determinate number of parts and for atomism.
Penelope Maddy
- Published in print:
- 2007
- Published Online:
- January 2009
- ISBN:
- 9780199273669
- eISBN:
- 9780191706264
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199273669.003.0024
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Turning now to the role of mathematics in natural science, this chapter takes up a number of themes. First, the Quine/Putnam idea that the indispensability of mathematics for much of science confirms ...
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Turning now to the role of mathematics in natural science, this chapter takes up a number of themes. First, the Quine/Putnam idea that the indispensability of mathematics for much of science confirms the existence of mathematical objects: from a second-philosophical point of view, this argument ignores the fine-structure of scientific justifications (in favor of superficial holism) and the idealizations and simplifications involved in the use of mathematics. If indispensability arguments are rejected, then what does the evidence tell us about the mathematical structure of the world? The KF-structure already detected is enough to support elementary arithmetic, but based on a return to the developmental studies prominent in §III.5, the Second Philosopher argues that as soon as we reach the infinitary ‘and so on’ of number theory, we've entered the realm of idealized, abstract theorizing. The chapter concludes by applying the lessons of Diaconis's statistical work on coincidence to argue that Wigner's ‘miracle’ of applied mathematics is less miraculous than it might seem.Less
Turning now to the role of mathematics in natural science, this chapter takes up a number of themes. First, the Quine/Putnam idea that the indispensability of mathematics for much of science confirms the existence of mathematical objects: from a second-philosophical point of view, this argument ignores the fine-structure of scientific justifications (in favor of superficial holism) and the idealizations and simplifications involved in the use of mathematics. If indispensability arguments are rejected, then what does the evidence tell us about the mathematical structure of the world? The KF-structure already detected is enough to support elementary arithmetic, but based on a return to the developmental studies prominent in §III.5, the Second Philosopher argues that as soon as we reach the infinitary ‘and so on’ of number theory, we've entered the realm of idealized, abstract theorizing. The chapter concludes by applying the lessons of Diaconis's statistical work on coincidence to argue that Wigner's ‘miracle’ of applied mathematics is less miraculous than it might seem.
