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.
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.
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.
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.
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.
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.
