Mark David Spence
- Published in print:
- 2000
- Published Online:
- October 2011
- ISBN:
- 9780195142433
- eISBN:
- 9780199848812
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195142433.001.0001
- Subject:
- History, American History: 20th Century
This book examines the ideal of wilderness preservation in the United States from the antebellum era to the first half of the twentieth century, showing how the early conception of the wilderness as ...
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This book examines the ideal of wilderness preservation in the United States from the antebellum era to the first half of the twentieth century, showing how the early conception of the wilderness as the place where Indians lived (or should live) gave way to the idealization of uninhabited wilderness. It focuses on specific policies of Indian removal developed at Yosemite, Yellowstone, and Glacier national parks from the early 1870s to the 1930s.Less
This book examines the ideal of wilderness preservation in the United States from the antebellum era to the first half of the twentieth century, showing how the early conception of the wilderness as the place where Indians lived (or should live) gave way to the idealization of uninhabited wilderness. It focuses on specific policies of Indian removal developed at Yosemite, Yellowstone, and Glacier national parks from the early 1870s to the 1930s.
Paul Weirich
- Published in print:
- 2004
- Published Online:
- November 2004
- ISBN:
- 9780195171259
- eISBN:
- 9780199834976
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019517125X.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Decision theory aims at a general account of rationality covering humans but to begin makes idealizations about decision problems and agents' resources and circumstances. It treats inerrant agents ...
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Decision theory aims at a general account of rationality covering humans but to begin makes idealizations about decision problems and agents' resources and circumstances. It treats inerrant agents with unlimited cognitive power facing tractable decision problems. This book systematically rolls back idealizations and without loss of precision treats errant agents with limited cognitive abilities facing decision problems without a stable top option. It recommends choices that maximize utility using quantizations of beliefs and desires in cases where probabilities and utilities are indeterminate and using higher-order utility analysis in cases of limited access to probabilities and utilities. For agents burdened with mistakes, it advocates reasonable attempts to correct unacceptable mistakes before deciding. In decision problems without a stable top option, a topic of game theory, it proposes maximizing self-conditional utility among self-supporting options. In games of strategy, the new principles lead to solutions that are Pareto optimal among equilibria composed of jointly self-supporting strategies. Offering an account of bounded rationality, the bookmakes large strides toward realism in decision theory.Less
Decision theory aims at a general account of rationality covering humans but to begin makes idealizations about decision problems and agents' resources and circumstances. It treats inerrant agents with unlimited cognitive power facing tractable decision problems. This book systematically rolls back idealizations and without loss of precision treats errant agents with limited cognitive abilities facing decision problems without a stable top option. It recommends choices that maximize utility using quantizations of beliefs and desires in cases where probabilities and utilities are indeterminate and using higher-order utility analysis in cases of limited access to probabilities and utilities. For agents burdened with mistakes, it advocates reasonable attempts to correct unacceptable mistakes before deciding. In decision problems without a stable top option, a topic of game theory, it proposes maximizing self-conditional utility among self-supporting options. In games of strategy, the new principles lead to solutions that are Pareto optimal among equilibria composed of jointly self-supporting strategies. Offering an account of bounded rationality, the bookmakes large strides toward realism in decision theory.
Paul Weirich
- Published in print:
- 2004
- Published Online:
- November 2004
- ISBN:
- 9780195171259
- eISBN:
- 9780199834976
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019517125X.003.0010
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This chapter combines adjustments for removal of idealizations. It recommends maximizing self-conditional utility among self-supporting options, using a quantization of conscious beliefs and desires, ...
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This chapter combines adjustments for removal of idealizations. It recommends maximizing self-conditional utility among self-supporting options, using a quantization of conscious beliefs and desires, after making reasonable efforts to form and become aware of relevant beliefs and desires, acquire pertinent a priori knowledge, and correct unacceptable mistakes. Future work on realistic decision theory will explore planning, time preference, attitudes to risk, and equilibrium in cooperative games.Less
This chapter combines adjustments for removal of idealizations. It recommends maximizing self-conditional utility among self-supporting options, using a quantization of conscious beliefs and desires, after making reasonable efforts to form and become aware of relevant beliefs and desires, acquire pertinent a priori knowledge, and correct unacceptable mistakes. Future work on realistic decision theory will explore planning, time preference, attitudes to risk, and equilibrium in cooperative games.
Lawrence Sklar
- Published in print:
- 2002
- Published Online:
- November 2003
- ISBN:
- 9780199251575
- eISBN:
- 9780191598449
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199251576.001.0001
- Subject:
- Philosophy, Philosophy of Science
Sceptics have often cast doubt on the legitimacy of claims to the effect that our best scientific theories are true. One ground for such scepticism is the fact that our theories advert to the ...
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Sceptics have often cast doubt on the legitimacy of claims to the effect that our best scientific theories are true. One ground for such scepticism is the fact that our theories advert to the existence and nature of unobservable entities and features of the world. Another ground for such scepticism is the fact that our theories rest upon our idealization of the world in their descriptions and explanations. A third ground for scepticism is the claim that all of our theories are but transient. If we expect even our best theories to ultimately be replaced, how can we think of them as truly describing the world? Each kind of sceptical argument plays a role within the scientific project of theory construction and evaluation itself. But there are clear and important differences between the kinds of internal role such arguments play within science and the way that they function in the more abstract philosophical context.Less
Sceptics have often cast doubt on the legitimacy of claims to the effect that our best scientific theories are true. One ground for such scepticism is the fact that our theories advert to the existence and nature of unobservable entities and features of the world. Another ground for such scepticism is the fact that our theories rest upon our idealization of the world in their descriptions and explanations. A third ground for scepticism is the claim that all of our theories are but transient. If we expect even our best theories to ultimately be replaced, how can we think of them as truly describing the world? Each kind of sceptical argument plays a role within the scientific project of theory construction and evaluation itself. But there are clear and important differences between the kinds of internal role such arguments play within science and the way that they function in the more abstract philosophical context.
David Christensen
- Published in print:
- 2004
- Published Online:
- July 2005
- ISBN:
- 9780199263257
- eISBN:
- 9780191602603
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199263256.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Are rational beliefs constrained by formal logic? This book argues that if beliefs are seen in a binary way (either one believes a proposition or one doesn't), then the standard constraints of ...
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Are rational beliefs constrained by formal logic? This book argues that if beliefs are seen in a binary way (either one believes a proposition or one doesn't), then the standard constraints of ’deductive cogency’ (i.e. deductive consistency and deductive closure) are incompatible with epistemic rationality. If, however, beliefs are seen as graded, or coming in degrees, a probabilistic constraint (based on standard logic) is imposed by ideal rationality. This constraint, probabilistic coherence, explains both the appeal of the standard deductive constraints and the power of deductive arguments. Moreover, it can be defended without taking degrees of belief (as many decision-theoretic philosophers have) to be somehow defined or constituted by preferences. Although probabilistic coherence is humanly unattainable, this does not undermine its normative status as a constraint in a suitably idealized understanding of epistemic rationality.Less
Are rational beliefs constrained by formal logic? This book argues that if beliefs are seen in a binary way (either one believes a proposition or one doesn't), then the standard constraints of ’deductive cogency’ (i.e. deductive consistency and deductive closure) are incompatible with epistemic rationality. If, however, beliefs are seen as graded, or coming in degrees, a probabilistic constraint (based on standard logic) is imposed by ideal rationality. This constraint, probabilistic coherence, explains both the appeal of the standard deductive constraints and the power of deductive arguments. Moreover, it can be defended without taking degrees of belief (as many decision-theoretic philosophers have) to be somehow defined or constituted by preferences. Although probabilistic coherence is humanly unattainable, this does not undermine its normative status as a constraint in a suitably idealized understanding of epistemic rationality.
Lawrence Sklar
- Published in print:
- 2002
- Published Online:
- November 2003
- ISBN:
- 9780199251575
- eISBN:
- 9780191598449
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199251576.003.0006
- Subject:
- Philosophy, Philosophy of Science
Abstract, philosophical scepticism about the truth of theories can rest on doubts about positing unobservables, doubts arising out of the role played by idealization in theories, and doubts arising ...
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Abstract, philosophical scepticism about the truth of theories can rest on doubts about positing unobservables, doubts arising out of the role played by idealization in theories, and doubts arising from the transient place of our theories in our corpus of accepted theories. But each of these kinds of scepticism can play a role within scientific theory construction and evaluation. As a local project within ongoing science, each mode of sceptical argument has a far richer and more interesting structure than is evident from the role played by these arguments in abstract philosophy.Less
Abstract, philosophical scepticism about the truth of theories can rest on doubts about positing unobservables, doubts arising out of the role played by idealization in theories, and doubts arising from the transient place of our theories in our corpus of accepted theories. But each of these kinds of scepticism can play a role within scientific theory construction and evaluation. As a local project within ongoing science, each mode of sceptical argument has a far richer and more interesting structure than is evident from the role played by these arguments in abstract philosophy.
Steven Horst
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780195317114
- eISBN:
- 9780199871520
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195317114.003.0008
- Subject:
- Philosophy, Philosophy of Mind
This chapter examines two forms of pluralism in philosophy of mind that are suggested by explanatory pluralism in philosophy of science. The first is a radical ontological pluralism suggested by John ...
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This chapter examines two forms of pluralism in philosophy of mind that are suggested by explanatory pluralism in philosophy of science. The first is a radical ontological pluralism suggested by John Dupré. It holds that the explanatory pluralism of the sciences is due to a prior and profligate ontological plurality in nature itself. The second is a view called Cognitive Pluralism. This is the view that theory pluralism is a predictable consequence of our cognitive architecture and of the nature of scientific models, which are partial, domain‐specific, and idealized and employ proprietary representational systems. A model‐based account of cognition in general, and scientific understanding as a special case, is used to account for theory pluralism.Less
This chapter examines two forms of pluralism in philosophy of mind that are suggested by explanatory pluralism in philosophy of science. The first is a radical ontological pluralism suggested by John Dupré. It holds that the explanatory pluralism of the sciences is due to a prior and profligate ontological plurality in nature itself. The second is a view called Cognitive Pluralism. This is the view that theory pluralism is a predictable consequence of our cognitive architecture and of the nature of scientific models, which are partial, domain‐specific, and idealized and employ proprietary representational systems. A model‐based account of cognition in general, and scientific understanding as a special case, is used to account for theory pluralism.
Steven Horst
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780195317114
- eISBN:
- 9780199871520
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195317114.003.0009
- Subject:
- Philosophy, Philosophy of Mind
This chapter argues for the plausibility of Cognitive Pluralism as a general principle of cognitive architecture, and argues further that scientific pluralism is plausibly seen as a special case of ...
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This chapter argues for the plausibility of Cognitive Pluralism as a general principle of cognitive architecture, and argues further that scientific pluralism is plausibly seen as a special case of this general principle. Cognitive Pluralism is compared with existing ideas of modularity.Less
This chapter argues for the plausibility of Cognitive Pluralism as a general principle of cognitive architecture, and argues further that scientific pluralism is plausibly seen as a special case of this general principle. Cognitive Pluralism is compared with existing ideas of modularity.
Mary Leng
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199280797
- eISBN:
- 9780191723452
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199280797.003.0005
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, Metaphysics/Epistemology
This chapter considers a tension between Quine's naturalism and his confirmational holism that has been pointed out by Penelope Maddy, amongst others. Naturalism requires us to look to science to ...
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This chapter considers a tension between Quine's naturalism and his confirmational holism that has been pointed out by Penelope Maddy, amongst others. Naturalism requires us to look to science to discover what we ought to believe, and holism requires us to accept the truth of our best scientific theories. But as Maddy has pointed out, there are cases where scientists hold back from believing all the claims of their theories. Scientists might simply be wrong here—our naturalism does not require us to accept, uncritically, the attitudes scientists take to their own theories. However, it is argued that reflection on the role various theoretical assumptions play in our scientific theories shows that the attitude taken by these scientists may be reasonable. Confirmational holism is therefore rejected—the question of which among our theoretical assumptions becomes a question of how best to understand the successful use of these assumptions.Less
This chapter considers a tension between Quine's naturalism and his confirmational holism that has been pointed out by Penelope Maddy, amongst others. Naturalism requires us to look to science to discover what we ought to believe, and holism requires us to accept the truth of our best scientific theories. But as Maddy has pointed out, there are cases where scientists hold back from believing all the claims of their theories. Scientists might simply be wrong here—our naturalism does not require us to accept, uncritically, the attitudes scientists take to their own theories. However, it is argued that reflection on the role various theoretical assumptions play in our scientific theories shows that the attitude taken by these scientists may be reasonable. Confirmational holism is therefore rejected—the question of which among our theoretical assumptions becomes a question of how best to understand the successful use of these assumptions.
Matthew Fox
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199211920
- eISBN:
- 9780191705854
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199211920.003.0004
- Subject:
- Classical Studies, Ancient Greek, Roman, and Early Christian Philosophy
The chapter is the first in a series of detailed readings of individual philosophical dialogues. De republica is examined as an attempt to ground political theory in Roman history, but one that ...
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The chapter is the first in a series of detailed readings of individual philosophical dialogues. De republica is examined as an attempt to ground political theory in Roman history, but one that produces ambiguous results. Close reading of the work suggests that although Cicero can conceive of an idealized Rome where political decisions and philosophical insight work together, he also makes clear that the realities of Roman history do not support such an idealization. The notion of ironic history is introduced to describe historical representations that question their own validity.Less
The chapter is the first in a series of detailed readings of individual philosophical dialogues. De republica is examined as an attempt to ground political theory in Roman history, but one that produces ambiguous results. Close reading of the work suggests that although Cicero can conceive of an idealized Rome where political decisions and philosophical insight work together, he also makes clear that the realities of Roman history do not support such an idealization. The notion of ironic history is introduced to describe historical representations that question their own validity.
Alan Weir
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199541492
- eISBN:
- 9780191594915
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199541492.001.0001
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics
This book defends an anti-platonist philosophy of mathematics derived from game formalism. Classic formalists claimed implausibly that mathematical utterances are truth-valueless moves in a game. ...
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This book defends an anti-platonist philosophy of mathematics derived from game formalism. Classic formalists claimed implausibly that mathematical utterances are truth-valueless moves in a game. This study aims to develop a more satisfactory successor to game formalism utilizing a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance. This framework allows for sentences whose truth-conditions are not representational, which are made true or false by conditions residing in the circumstances of utterances but not transparently in the sense. Applications to projectivism and fiction pave the way for the claim that mathematical utterances are made true or false by the existence of concrete proofs or refutations, though these truth-making conditions form no part of their sense or informational content. The position is compared with rivals, an account of the applicability of mathematics developed, and a new account of the nature of idealization proffered in which it is argued that the finitistic limitations Gödel placed on proofs are without rational justification. Finally a non-classical logical system is provided in which excluded middle fails, yet enough logical power remains to recapture the results of standard mathematics.Less
This book defends an anti-platonist philosophy of mathematics derived from game formalism. Classic formalists claimed implausibly that mathematical utterances are truth-valueless moves in a game. This study aims to develop a more satisfactory successor to game formalism utilizing a widely accepted, broadly neo-Fregean framework, in which the proposition expressed by an utterance is a function of both sense and background circumstance. This framework allows for sentences whose truth-conditions are not representational, which are made true or false by conditions residing in the circumstances of utterances but not transparently in the sense. Applications to projectivism and fiction pave the way for the claim that mathematical utterances are made true or false by the existence of concrete proofs or refutations, though these truth-making conditions form no part of their sense or informational content. The position is compared with rivals, an account of the applicability of mathematics developed, and a new account of the nature of idealization proffered in which it is argued that the finitistic limitations Gödel placed on proofs are without rational justification. Finally a non-classical logical system is provided in which excluded middle fails, yet enough logical power remains to recapture the results of standard mathematics.
Nancy Cartwright
- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198235071
- eISBN:
- 9780191597169
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198235070.003.0006
- Subject:
- Philosophy, Philosophy of Science
Modern science relies heavily on Galilean idealization, which establishes ceteris paribus laws—laws about what happens when a factor operates unimpeded. But these laws are of little direct use since ...
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Modern science relies heavily on Galilean idealization, which establishes ceteris paribus laws—laws about what happens when a factor operates unimpeded. But these laws are of little direct use since factors seldom do operate unimpeded. The follow‐up to Galilean idealization is abstraction—we talk simply of what the factor does. The best way to understand this abstraction is as an ascription of a capacity, not in terms of any kind of laws. Even the process of ‘de‐idealization’ or of ‘concretization’ that results in a concrete phenomenological law inevitably involves further concepts in the capacity family.Less
Modern science relies heavily on Galilean idealization, which establishes ceteris paribus laws—laws about what happens when a factor operates unimpeded. But these laws are of little direct use since factors seldom do operate unimpeded. The follow‐up to Galilean idealization is abstraction—we talk simply of what the factor does. The best way to understand this abstraction is as an ascription of a capacity, not in terms of any kind of laws. Even the process of ‘de‐idealization’ or of ‘concretization’ that results in a concrete phenomenological law inevitably involves further concepts in the capacity family.
RICHARD WHITTINGTON and MICHAEL MAYER
- Published in print:
- 2002
- Published Online:
- January 2010
- ISBN:
- 9780199251049
- eISBN:
- 9780191714382
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199251049.003.0003
- Subject:
- Business and Management, Strategy
This chapter begins by introducing the large industrial corporation — for some, a crowning achievement of 20th-century capitalism, for others now just a redundant remnant. It examines the debates ...
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This chapter begins by introducing the large industrial corporation — for some, a crowning achievement of 20th-century capitalism, for others now just a redundant remnant. It examines the debates surrounding the strategies by which the large corporation grew and the structures by which it was managed. On diversification, it begins by considering the patchy evidence on diversification trends and performance in the United States and Europe, particularly in the light of arguments concerning a general downscoping of contemporary business. It then pitches economic arguments principally from the market-power perspective and the resource-based view of the firm against more sociological arguments pointing to managerial interests and hubris and the changing role of financial markets. It then considers the place of the multi-divisional. It examines its idealisation as the embodiment of modern bureaucratic rationality, superior to its centralised functional and chaotic holding company alternatives.Less
This chapter begins by introducing the large industrial corporation — for some, a crowning achievement of 20th-century capitalism, for others now just a redundant remnant. It examines the debates surrounding the strategies by which the large corporation grew and the structures by which it was managed. On diversification, it begins by considering the patchy evidence on diversification trends and performance in the United States and Europe, particularly in the light of arguments concerning a general downscoping of contemporary business. It then pitches economic arguments principally from the market-power perspective and the resource-based view of the firm against more sociological arguments pointing to managerial interests and hubris and the changing role of financial markets. It then considers the place of the multi-divisional. It examines its idealisation as the embodiment of modern bureaucratic rationality, superior to its centralised functional and chaotic holding company alternatives.
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/9780199273669.003.0021
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Rudimentary logic falls short of classical logic in a number of ways. To bridge the gap, the Second Philosopher follows Frege and imposes a number of restrictions and idealizations: she treats only ...
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Rudimentary logic falls short of classical logic in a number of ways. To bridge the gap, the Second Philosopher follows Frege and imposes a number of restrictions and idealizations: she treats only well-functioning language, where terms refer and paradoxical predicates don't arise; vagueness is idealized away with the assumption that all properties and relations have sharp boundaries; complex ground-consequent dependencies are replaced by a material conditional. Many deviant logics (free logic, logics of vagueness, relevance logic) are then straightforwardly understood as rejections of one or another of these simplifications. As with any scientific modeling, the question is whether or not those simplifications are effective and benign in a given application; these are the proper terms of debate between these deviant logicians and the classicist. Other deviant logics (intuitionism, quantum logic, dialetheism) go deeper, rejecting elements of rudimentary logic itself. The Second Philosopher finds no evidence that any of these are viable candidates for the underlying logic of the world.Less
Rudimentary logic falls short of classical logic in a number of ways. To bridge the gap, the Second Philosopher follows Frege and imposes a number of restrictions and idealizations: she treats only well-functioning language, where terms refer and paradoxical predicates don't arise; vagueness is idealized away with the assumption that all properties and relations have sharp boundaries; complex ground-consequent dependencies are replaced by a material conditional. Many deviant logics (free logic, logics of vagueness, relevance logic) are then straightforwardly understood as rejections of one or another of these simplifications. As with any scientific modeling, the question is whether or not those simplifications are effective and benign in a given application; these are the proper terms of debate between these deviant logicians and the classicist. Other deviant logics (intuitionism, quantum logic, dialetheism) go deeper, rejecting elements of rudimentary logic itself. The Second Philosopher finds no evidence that any of these are viable candidates for the underlying logic of the world.
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.
Alan Weir
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199541492
- eISBN:
- 9780191594915
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199541492.003.0001
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics
The introduction sets out the attractions and drawbacks of mathematical platonism, then gives an overview of the anti-platonistic argument of the book, paying particular attention to the difficulties ...
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The introduction sets out the attractions and drawbacks of mathematical platonism, then gives an overview of the anti-platonistic argument of the book, paying particular attention to the difficulties a naturalized epistemology faces in accounting for platonism. Chapter 1's distinctions between methodological and ontological naturalism and between informational and metaphysical content are sketched. The content of the remaining chapters is described in turn: Chapter 2 deals with ‘hermeneutic anti-realisms’, anti-realisms which do not deny that the discourse in question is truth-valued; Chapter 3 with the neo-formalist position championed in the book; Chapter 4 looks at objections to neo-formalism and comparisons with other views; Chapter 5 tackles the applicability of mathematics. Chapter 6 develops a concretist syntax, and distinguishes a legitimate from an illegitimate way to idealize such syntax, the former explored in Chapter 7 which additionally argues for infinitary idealizations; Chapter 8 concentrates on key logical issues.Less
The introduction sets out the attractions and drawbacks of mathematical platonism, then gives an overview of the anti-platonistic argument of the book, paying particular attention to the difficulties a naturalized epistemology faces in accounting for platonism. Chapter 1's distinctions between methodological and ontological naturalism and between informational and metaphysical content are sketched. The content of the remaining chapters is described in turn: Chapter 2 deals with ‘hermeneutic anti-realisms’, anti-realisms which do not deny that the discourse in question is truth-valued; Chapter 3 with the neo-formalist position championed in the book; Chapter 4 looks at objections to neo-formalism and comparisons with other views; Chapter 5 tackles the applicability of mathematics. Chapter 6 develops a concretist syntax, and distinguishes a legitimate from an illegitimate way to idealize such syntax, the former explored in Chapter 7 which additionally argues for infinitary idealizations; Chapter 8 concentrates on key logical issues.
Alan Weir
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199541492
- eISBN:
- 9780191594915
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199541492.003.0007
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics
This chapter attempts to carry out the task promised earlier: a purely concretist syntax and proof theory, where abstract types are replaced by concrete ‘tipes’, construed as fusions of concrete ...
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This chapter attempts to carry out the task promised earlier: a purely concretist syntax and proof theory, where abstract types are replaced by concrete ‘tipes’, construed as fusions of concrete tokens. The conclusion is drawn that there are only finitely many sentences and proofs in actual human languages, and since no appeal to possibility beyond everyday uncontentious uses is made this seems to drive us towards a strict finitism. In particular, how can those concrete utterances which, given limits on the size of graspable proofs, can have no concrete proof or disproof, have determinate truth values? Recourse to ‘in principle possibility’ and idealized beings is rejected as no more acceptable in this domain than appeal to supernatural beings is in biology. A different model of idealization is needed.Less
This chapter attempts to carry out the task promised earlier: a purely concretist syntax and proof theory, where abstract types are replaced by concrete ‘tipes’, construed as fusions of concrete tokens. The conclusion is drawn that there are only finitely many sentences and proofs in actual human languages, and since no appeal to possibility beyond everyday uncontentious uses is made this seems to drive us towards a strict finitism. In particular, how can those concrete utterances which, given limits on the size of graspable proofs, can have no concrete proof or disproof, have determinate truth values? Recourse to ‘in principle possibility’ and idealized beings is rejected as no more acceptable in this domain than appeal to supernatural beings is in biology. A different model of idealization is needed.
Alan Weir
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199541492
- eISBN:
- 9780191594915
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199541492.003.0008
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics
Idealization in grammar is taken as a starting point. Grammatical theory is interpreted as an ‘injective idealization’, from the fragmentary corpus of concrete utterances into an infinite ...
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Idealization in grammar is taken as a starting point. Grammatical theory is interpreted as an ‘injective idealization’, from the fragmentary corpus of concrete utterances into an infinite mathematical domain. Formalization in mathematics should be viewed as a similar injective mapping from patchy concrete utterances into a formal structure, carried out for a variety of reasons including conceptual innovation and, especially, in order to carry out theoretical investigations into provability and truth. These can only be at conceived at the level of formal languages, though we can we read back results into concrete utterances. If the idealization is legitimate and we can demonstrate, e.g. negation-completeness in the idealization, this suffices to justify excluded middle, even where no concrete proof or refutation is possible. Neo-formalism is entitled to utilize any such applied theorem so long as there is reason to believe there is a concrete proof of it. There is no rational justification for restricting the idealization to mathematical structures whose elements are finite; thus the restrictions inherent in limitative results such as Gödel's are ill-motivated in foundational studies.Less
Idealization in grammar is taken as a starting point. Grammatical theory is interpreted as an ‘injective idealization’, from the fragmentary corpus of concrete utterances into an infinite mathematical domain. Formalization in mathematics should be viewed as a similar injective mapping from patchy concrete utterances into a formal structure, carried out for a variety of reasons including conceptual innovation and, especially, in order to carry out theoretical investigations into provability and truth. These can only be at conceived at the level of formal languages, though we can we read back results into concrete utterances. If the idealization is legitimate and we can demonstrate, e.g. negation-completeness in the idealization, this suffices to justify excluded middle, even where no concrete proof or refutation is possible. Neo-formalism is entitled to utilize any such applied theorem so long as there is reason to believe there is a concrete proof of it. There is no rational justification for restricting the idealization to mathematical structures whose elements are finite; thus the restrictions inherent in limitative results such as Gödel's are ill-motivated in foundational studies.
Derek Hirst and Steven N. Zwicker
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199655373
- eISBN:
- 9780191742118
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199655373.001.0001
- Subject:
- Literature, 17th-century and Restoration Literature, Poetry
This book studies the poetry and polemics of one of the greatest of early modern writers, a poet of immense lyric talent and political importance. The book situates these writings and this writer ...
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This book studies the poetry and polemics of one of the greatest of early modern writers, a poet of immense lyric talent and political importance. The book situates these writings and this writer within the patronage networks and political upheavals of mid-seventeenth-century England. It tracks his negotiations among personalities and events; it explores his idealizations, attachments, and subversions; and it speculates on the meaning of the narratives that he told of himself within his writings — what we call Andrew Marvell’s ‘imagined life’. The book draws the figure of this imagined life from the repeated traces that Marvell left of lyric yearning and satiric anger, and it suggests how these were rooted both in the body and in the imagination. The book sheds new light on some of Marvell’s most familiar poems — Upon Appleton House, The Garden, To His Coy Mistress, and An Horatian Ode; but at its centre is an extended reading of Marvell’s The unfortunate Lover, his least familiar and surely his most mysterious lyric, and his most sustained narrative of the self. By attending to the lyric, the polemical, and the parliamentary careers together, this book offers a reading of Marvell and his writings as an interpretable whole.Less
This book studies the poetry and polemics of one of the greatest of early modern writers, a poet of immense lyric talent and political importance. The book situates these writings and this writer within the patronage networks and political upheavals of mid-seventeenth-century England. It tracks his negotiations among personalities and events; it explores his idealizations, attachments, and subversions; and it speculates on the meaning of the narratives that he told of himself within his writings — what we call Andrew Marvell’s ‘imagined life’. The book draws the figure of this imagined life from the repeated traces that Marvell left of lyric yearning and satiric anger, and it suggests how these were rooted both in the body and in the imagination. The book sheds new light on some of Marvell’s most familiar poems — Upon Appleton House, The Garden, To His Coy Mistress, and An Horatian Ode; but at its centre is an extended reading of Marvell’s The unfortunate Lover, his least familiar and surely his most mysterious lyric, and his most sustained narrative of the self. By attending to the lyric, the polemical, and the parliamentary careers together, this book offers a reading of Marvell and his writings as an interpretable whole.
Richard Tieszen
- Published in print:
- 2005
- Published Online:
- May 2010
- ISBN:
- 9780199272457
- eISBN:
- 9780191709951
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199272457.003.0009
- Subject:
- Philosophy, Philosophy of Mind
Edmund Husserl is one of only a few major philosophers in the last one hundred years or so who holds that it is possible to develop a philosophy of mind in which one can account for the consciousness ...
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Edmund Husserl is one of only a few major philosophers in the last one hundred years or so who holds that it is possible to develop a philosophy of mind in which one can account for the consciousness of abstract objects or ideal objects. This chapter discusses Husserl's ideas in connection with the views of Kurt Gödel and Roger Penrose. It presents an argument that leads from Gödel's incompleteness theorems to recognition of the awareness of abstract or ideal objects. Husserl's view, based on his ideas about intentionality and the phenomenological reduction, shows us how to open up a space for a phenomenology of the consciousness of abstract mathematical objects.Less
Edmund Husserl is one of only a few major philosophers in the last one hundred years or so who holds that it is possible to develop a philosophy of mind in which one can account for the consciousness of abstract objects or ideal objects. This chapter discusses Husserl's ideas in connection with the views of Kurt Gödel and Roger Penrose. It presents an argument that leads from Gödel's incompleteness theorems to recognition of the awareness of abstract or ideal objects. Husserl's view, based on his ideas about intentionality and the phenomenological reduction, shows us how to open up a space for a phenomenology of the consciousness of abstract mathematical objects.
