Roman Kossak and James Schmerl
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568278
- eISBN:
- 9780191718199
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568278.001.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This book gives an account of the present state of research on lattices of elementary substructures and automorphisms of nonstandard models of arithmetic. Major representation theorems are proved, ...
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This book gives an account of the present state of research on lattices of elementary substructures and automorphisms of nonstandard models of arithmetic. Major representation theorems are proved, and the important particular case of countable recursively saturated models is discussed in detail. All necessary technical tools are developed. The list includes: constructions of elementary simple extensions; a partial classification of arithmetic types, in particular Gaifman's theory of definable types; forcing in arithmetic; elements of the Kirby-Paris combinatorial theory of cuts; Lascar's generic automorphisms; and applications of Abramson and Harrington's generalization of Ramsey's theorem. There are also chapters discussing ω1-like models with interesting second order properties, and a chapter on order types of nonstandard models.Less
This book gives an account of the present state of research on lattices of elementary substructures and automorphisms of nonstandard models of arithmetic. Major representation theorems are proved, and the important particular case of countable recursively saturated models is discussed in detail. All necessary technical tools are developed. The list includes: constructions of elementary simple extensions; a partial classification of arithmetic types, in particular Gaifman's theory of definable types; forcing in arithmetic; elements of the Kirby-Paris combinatorial theory of cuts; Lascar's generic automorphisms; and applications of Abramson and Harrington's generalization of Ramsey's theorem. There are also chapters discussing ω1-like models with interesting second order properties, and a chapter on order types of nonstandard models.
Michael Potter
- Published in print:
- 2002
- Published Online:
- May 2007
- ISBN:
- 9780199252619
- eISBN:
- 9780191712647
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199252619.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This book is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. It reassesses the brilliant ...
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This book is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. It reassesses the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as the understanding of mathematics. The book argues that through the problem of arithmetic participates in the larger puzzle of the relationship between thought, language, experience, and the world, we can distinguish accounts that look to each of these to supply the content we require: those that involve the structure of our experience of the world; those that explicitly involve our grasp of a ‘third realm’ of abstract objects distinct from the concrete objects of the empirical world and the ideas of the author's private Gedankenwelt; those that appeal to something non-physical that is nevertheless an aspect of reality in harmony with which the physical aspect of the world is configured; and finally those that involve only our grasp of language.Less
This book is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. It reassesses the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as the understanding of mathematics. The book argues that through the problem of arithmetic participates in the larger puzzle of the relationship between thought, language, experience, and the world, we can distinguish accounts that look to each of these to supply the content we require: those that involve the structure of our experience of the world; those that explicitly involve our grasp of a ‘third realm’ of abstract objects distinct from the concrete objects of the empirical world and the ideas of the author's private Gedankenwelt; those that appeal to something non-physical that is nevertheless an aspect of reality in harmony with which the physical aspect of the world is configured; and finally those that involve only our grasp of language.
David M. Armstrong
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199590612
- eISBN:
- 9780191723391
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199590612.003.0008
- Subject:
- Philosophy, Philosophy of Mind, Metaphysics/Epistemology
The notion of a truthmaker is introduced, and the importance of the notion for metaphysics is stressed. Russell was a pioneer. All truth is a matter of correspondence of a proposition to reality, so ...
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The notion of a truthmaker is introduced, and the importance of the notion for metaphysics is stressed. Russell was a pioneer. All truth is a matter of correspondence of a proposition to reality, so truthmaker Maximalism should be accepted. It need not be a one—one correspondence. ‘What are your truthmakers?’ is superior to Quine's question ‘What do you quantify over?’ Minimalist theories of truth, descending from Frank Ramsey, are rejected. Minimal truthmakers, however, are not rejected except in the case of infinities. The relation of truths to their truthmakers is an internal one, depending solely on the terms involved, truth and truthmaker. Truthbearers, that is truths, are true propositions, but propositions are no more than what is believed, supposes that, entertains that, etc., what philosophers call ‘intentional objects’. They can include impossibilities. There is no realm of propositions. The important Entailment Principle says that if a proposition entails some further proposition, then a truthmaker for the premise is also truthmaker for the conclusion. This casts significant light on the nature of valid argument.Less
The notion of a truthmaker is introduced, and the importance of the notion for metaphysics is stressed. Russell was a pioneer. All truth is a matter of correspondence of a proposition to reality, so truthmaker Maximalism should be accepted. It need not be a one—one correspondence. ‘What are your truthmakers?’ is superior to Quine's question ‘What do you quantify over?’ Minimalist theories of truth, descending from Frank Ramsey, are rejected. Minimal truthmakers, however, are not rejected except in the case of infinities. The relation of truths to their truthmakers is an internal one, depending solely on the terms involved, truth and truthmaker. Truthbearers, that is truths, are true propositions, but propositions are no more than what is believed, supposes that, entertains that, etc., what philosophers call ‘intentional objects’. They can include impossibilities. There is no realm of propositions. The important Entailment Principle says that if a proposition entails some further proposition, then a truthmaker for the premise is also truthmaker for the conclusion. This casts significant light on the nature of valid argument.
E. J. Lowe
- Published in print:
- 2005
- Published Online:
- May 2006
- ISBN:
- 9780199254392
- eISBN:
- 9780191603600
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199254397.003.0005
- Subject:
- Philosophy, Metaphysics/Epistemology
The formal ontological concept of an object is explicated and contrasted with that of a property. F. P. Ramsey’s objections to this distinction are challenged. The sense in which objects possess an ...
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The formal ontological concept of an object is explicated and contrasted with that of a property. F. P. Ramsey’s objections to this distinction are challenged. The sense in which objects possess an individuality not exhibited by entities of certain other types is discussed. The object/property distinction is distinguished from that between universals and particulars. The ontological status of events and processes, and that of abstract entities such as numbers, are examined. Gottlob Frege’s treatment of number and his object/concept distinction are criticized, and an alternative account of the ontological status of concepts is advanced.Less
The formal ontological concept of an object is explicated and contrasted with that of a property. F. P. Ramsey’s objections to this distinction are challenged. The sense in which objects possess an individuality not exhibited by entities of certain other types is discussed. The object/property distinction is distinguished from that between universals and particulars. The ontological status of events and processes, and that of abstract entities such as numbers, are examined. Gottlob Frege’s treatment of number and his object/concept distinction are criticized, and an alternative account of the ontological status of concepts is advanced.
E. J. Lowe
- Published in print:
- 2005
- Published Online:
- May 2006
- ISBN:
- 9780199254392
- eISBN:
- 9780191603600
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199254397.003.0007
- Subject:
- Philosophy, Metaphysics/Epistemology
F. P. Ramsey’s objections to the universal/particular distinction, especially as advocated by Bertrand Russell, are examined in depth and rebutted. At the same time, certain important lessons are ...
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F. P. Ramsey’s objections to the universal/particular distinction, especially as advocated by Bertrand Russell, are examined in depth and rebutted. At the same time, certain important lessons are drawn from his arguments concerning how best to articulate the distinction. In response to related arguments recently directed against the four-category ontology by Fraser MacBride, it is shown how each of the four categories can be uniquely identified in terms of the characteristic pattern of ontological dependence relations that its members bear to members of other ontological categories.Less
F. P. Ramsey’s objections to the universal/particular distinction, especially as advocated by Bertrand Russell, are examined in depth and rebutted. At the same time, certain important lessons are drawn from his arguments concerning how best to articulate the distinction. In response to related arguments recently directed against the four-category ontology by Fraser MacBride, it is shown how each of the four categories can be uniquely identified in terms of the characteristic pattern of ontological dependence relations that its members bear to members of other ontological categories.
Michio Morishima
- Published in print:
- 1969
- Published Online:
- November 2003
- ISBN:
- 9780198281641
- eISBN:
- 9780191596667
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198281641.003.0013
- Subject:
- Economics and Finance, Development, Growth, and Environmental
Chapter 10 was concerned with the Final State Turnpike Theorem on the assumptions that consumption of each good per worker is fixed throughout the planning period and that the authorities try to ...
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Chapter 10 was concerned with the Final State Turnpike Theorem on the assumptions that consumption of each good per worker is fixed throughout the planning period and that the authorities try to maximize the stocks of goods that they can bestow, at the horizon, upon the future citizens; this chapter looks at a Second Turnpike Theorem. The partial optimization for the sake of the future should more properly be superseded by a general mutual optimization, so that the benefits from the properties initially available are shared between the people living in the planning period and those after that; this would inevitably cause confrontation with one of the hardest problems of economics—the interpersonal and intertemporal comparisons of utilities. In this chapter, attempts to solve the crux of the problem are abandoned and the other extreme is addressed: the conditions are derived for Ramsey optimality as distinct from DOSSO efficiency, i.e. optimization is in favour of the people in the planning period, and the satisfaction of the future residents is pegged at a certain level, of which the present residents approve. Among all feasible programmes that leave, at the end of the planning period, necessary amounts of goods for the future residents, the question is whether the people living choose a single one that is most preferable from their own point of view, i.e. there is a switch over of ideology from abstinence for the future to satisfaction in the transient life. The different sections of the chapter include discussion of: two norms of optimum growth—the Golden Balanced Growth path and the Consumption Turnpike; the existence of the Consumption Turnpike; the Silvery Rule of Accumulation’ the singular case where there is no discrimination between the living and the coming people; the Consumption Turnpike Theorem—the cases of the subjective time‐preference factor not being greater than the growth factor of the population, and of the former being greater than the latter; and an example of a cyclic Ramsey‐optimum growth.Less
Chapter 10 was concerned with the Final State Turnpike Theorem on the assumptions that consumption of each good per worker is fixed throughout the planning period and that the authorities try to maximize the stocks of goods that they can bestow, at the horizon, upon the future citizens; this chapter looks at a Second Turnpike Theorem. The partial optimization for the sake of the future should more properly be superseded by a general mutual optimization, so that the benefits from the properties initially available are shared between the people living in the planning period and those after that; this would inevitably cause confrontation with one of the hardest problems of economics—the interpersonal and intertemporal comparisons of utilities. In this chapter, attempts to solve the crux of the problem are abandoned and the other extreme is addressed: the conditions are derived for Ramsey optimality as distinct from DOSSO efficiency, i.e. optimization is in favour of the people in the planning period, and the satisfaction of the future residents is pegged at a certain level, of which the present residents approve. Among all feasible programmes that leave, at the end of the planning period, necessary amounts of goods for the future residents, the question is whether the people living choose a single one that is most preferable from their own point of view, i.e. there is a switch over of ideology from abstinence for the future to satisfaction in the transient life. The different sections of the chapter include discussion of: two norms of optimum growth—the Golden Balanced Growth path and the Consumption Turnpike; the existence of the Consumption Turnpike; the Silvery Rule of Accumulation’ the singular case where there is no discrimination between the living and the coming people; the Consumption Turnpike Theorem—the cases of the subjective time‐preference factor not being greater than the growth factor of the population, and of the former being greater than the latter; and an example of a cyclic Ramsey‐optimum growth.
Cheryl Misak and Huw Price (eds)
- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780197266168
- eISBN:
- 9780191865237
- Item type:
- book
- Publisher:
- British Academy
- DOI:
- 10.5871/bacad/9780197266168.001.0001
- Subject:
- Philosophy, General
The pragmatist approach to philosophical problems focuses on the role of disputed notions—for example, truth, value, causation, probability, necessity—in our practices. The insight at the heart of ...
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The pragmatist approach to philosophical problems focuses on the role of disputed notions—for example, truth, value, causation, probability, necessity—in our practices. The insight at the heart of pragmatism is that our analysis of such philosophical concepts must start with, and remain linked to, human experience and inquiry.
As a self-conscious philosophical stance, pragmatism arose in America in the late nineteenth century, in the work of writers such as Charles Peirce, William James and John Dewey. While popular wisdom would have it that British philosophy thoroughly rejected that of its American cousins, that popular view is coming into dispute. Many distinguished British philosophers have also taken this practical turn, even if few have explicitly identified themselves as pragmatists. This book traces and assesses the influence of American pragmatism on British philosophy, with particular emphasis on Cambridge in the inter-war period (for instance, the work of Frank Ramsey and Ludwig Wittgenstein), on post-war Oxford (for instance, the work of Elizabeth Anscombe, P. F. Strawson and Michael Dummett), and on recent developments (for instance, the work of Simon Blackburn and Huw Price). There is a comprehensive introduction to the topic and the history of pragmatism, and Price and Blackburn, in their contributions, add their most recent thoughts to the debates.Less
The pragmatist approach to philosophical problems focuses on the role of disputed notions—for example, truth, value, causation, probability, necessity—in our practices. The insight at the heart of pragmatism is that our analysis of such philosophical concepts must start with, and remain linked to, human experience and inquiry.
As a self-conscious philosophical stance, pragmatism arose in America in the late nineteenth century, in the work of writers such as Charles Peirce, William James and John Dewey. While popular wisdom would have it that British philosophy thoroughly rejected that of its American cousins, that popular view is coming into dispute. Many distinguished British philosophers have also taken this practical turn, even if few have explicitly identified themselves as pragmatists. This book traces and assesses the influence of American pragmatism on British philosophy, with particular emphasis on Cambridge in the inter-war period (for instance, the work of Frank Ramsey and Ludwig Wittgenstein), on post-war Oxford (for instance, the work of Elizabeth Anscombe, P. F. Strawson and Michael Dummett), and on recent developments (for instance, the work of Simon Blackburn and Huw Price). There is a comprehensive introduction to the topic and the history of pragmatism, and Price and Blackburn, in their contributions, add their most recent thoughts to the debates.
Jon Williamson
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198530794
- eISBN:
- 9780191712982
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198530794.003.0009
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter develops an epistemic theory of causality. The origins of such a theory may be found in the writings of Kant and Ramsey. According to the epistemic theory, we think in terms of cause and ...
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This chapter develops an epistemic theory of causality. The origins of such a theory may be found in the writings of Kant and Ramsey. According to the epistemic theory, we think in terms of cause and effect because it is convenient to do so, not because our causal claims latch on to a physical causal connection. A formal causal epistemology is put forward, and it is argued that this approach provides a synthesis of the hypothetico-deductive and inductive accounts of causal discovery. Analogies between epistemic causality and objective Bayesianism are highlighted.Less
This chapter develops an epistemic theory of causality. The origins of such a theory may be found in the writings of Kant and Ramsey. According to the epistemic theory, we think in terms of cause and effect because it is convenient to do so, not because our causal claims latch on to a physical causal connection. A formal causal epistemology is put forward, and it is argued that this approach provides a synthesis of the hypothetico-deductive and inductive accounts of causal discovery. Analogies between epistemic causality and objective Bayesianism are highlighted.
Roman Kossak and James H. Schmerl
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568278
- eISBN:
- 9780191718199
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568278.003.0010
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter presents several constructions of ω1-like models with interesting second order properties. The list includes: recursively saturated rather classless models, rigid recursively saturated ...
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This chapter presents several constructions of ω1-like models with interesting second order properties. The list includes: recursively saturated rather classless models, rigid recursively saturated models, models whose additive reducts are isomorphic but whose multiplicative reducts are not, and very similar but nonisomorphic models. The chapter also presents two constructions used in completeness theorems for Peano Arithmetic with the Ramsey quantifier and the stationary quantifier.Less
This chapter presents several constructions of ω1-like models with interesting second order properties. The list includes: recursively saturated rather classless models, rigid recursively saturated models, models whose additive reducts are isomorphic but whose multiplicative reducts are not, and very similar but nonisomorphic models. The chapter also presents two constructions used in completeness theorems for Peano Arithmetic with the Ramsey quantifier and the stationary quantifier.
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.
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/9780199252619.003.0013
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This concluding chapter summarizes the discussion in the preceding chapters. The book sought an answer to the question: can we give an account of arithmetic which does not make it depend for its ...
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This concluding chapter summarizes the discussion in the preceding chapters. The book sought an answer to the question: can we give an account of arithmetic which does not make it depend for its truth on the way the world is? And if so, what constrains the world to conform to arithmetic? All the accounts we have considered have turned out to be flawed. But what is striking is how often an account was rejected not for philosophical reasons but for technical ones. It is shown that since the problem of arithmetic participates in the larger puzzle of the relationship between thought, language, experience, and the world, we can distinguish accounts that look to each of these to supply the content we require.Less
This concluding chapter summarizes the discussion in the preceding chapters. The book sought an answer to the question: can we give an account of arithmetic which does not make it depend for its truth on the way the world is? And if so, what constrains the world to conform to arithmetic? All the accounts we have considered have turned out to be flawed. But what is striking is how often an account was rejected not for philosophical reasons but for technical ones. It is shown that since the problem of arithmetic participates in the larger puzzle of the relationship between thought, language, experience, and the world, we can distinguish accounts that look to each of these to supply the content we require.
Roman Kossak and James H. Schmerl
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568278
- eISBN:
- 9780191718199
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568278.003.0005
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter makes use of an induced version of Ramsey's Theorem to prove several results: the Abramson-Harrington theorem on omitting large indiscernible sets and Hanf numbers for models of ...
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This chapter makes use of an induced version of Ramsey's Theorem to prove several results: the Abramson-Harrington theorem on omitting large indiscernible sets and Hanf numbers for models of arithmetic; a theorem characterizing the possible automorphism groups of models; and a theorem based on countable recursively saturated models being generated by a set of indiscernibles.Less
This chapter makes use of an induced version of Ramsey's Theorem to prove several results: the Abramson-Harrington theorem on omitting large indiscernible sets and Hanf numbers for models of arithmetic; a theorem characterizing the possible automorphism groups of models; and a theorem based on countable recursively saturated models being generated by a set of indiscernibles.
Christian Gollier
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691148762
- eISBN:
- 9781400845408
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691148762.003.0002
- Subject:
- Economics and Finance, Development, Growth, and Environmental
This chapter presents the main argument in favor of a positive discount rate. In a growing economy, future generations will consume more goods and services than we do. In this context, investing for ...
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This chapter presents the main argument in favor of a positive discount rate. In a growing economy, future generations will consume more goods and services than we do. In this context, investing for the future is equivalent to asking poor consumers to sacrifice more of their consumption for the benefit for wealthier people. Because of inequality aversion, one would be ready to do so only if the rate of return of these investment projects is large enough to compensate for the increased intertemporal inequalities that these projects would generate. The Ramsey rule quantifies this wealth effect. In fact, several experts have used the Ramsey rule to make recommendations on the choice of the discount rate to evaluate public policies, in particular toward climate change.Less
This chapter presents the main argument in favor of a positive discount rate. In a growing economy, future generations will consume more goods and services than we do. In this context, investing for the future is equivalent to asking poor consumers to sacrifice more of their consumption for the benefit for wealthier people. Because of inequality aversion, one would be ready to do so only if the rate of return of these investment projects is large enough to compensate for the increased intertemporal inequalities that these projects would generate. The Ramsey rule quantifies this wealth effect. In fact, several experts have used the Ramsey rule to make recommendations on the choice of the discount rate to evaluate public policies, in particular toward climate change.
Ian Rumfitt
- Published in print:
- 2011
- Published Online:
- May 2012
- ISBN:
- 9780199696482
- eISBN:
- 9780191738036
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199696482.003.0011
- Subject:
- Philosophy, Ancient Philosophy, Logic/Philosophy of Mathematics
This chapter develops F. P. Ramsey's theory of truth. Everyone knows that Ramsey had a theory of truth. Rather fewer people know that the theory came in two significantly different versions, and that ...
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This chapter develops F. P. Ramsey's theory of truth. Everyone knows that Ramsey had a theory of truth. Rather fewer people know that the theory came in two significantly different versions, and that the later and less famous version is more fertile than its predecessor. The more famous version is, of course, Ramsey's redundancy theory of truth, which he expounded in his great paper of 1927, ‘Facts and Propositions’. The Ramsey–Prior theory, contra Ramsey's original approach, confirms that the word ‘true’ has a determinate sense. It does so by specifying the contribution that the word makes to what is expressed by a statement that contains it. That specification vindicates the common-sense view that ‘true’ is grammatically and semantically a predicate.Less
This chapter develops F. P. Ramsey's theory of truth. Everyone knows that Ramsey had a theory of truth. Rather fewer people know that the theory came in two significantly different versions, and that the later and less famous version is more fertile than its predecessor. The more famous version is, of course, Ramsey's redundancy theory of truth, which he expounded in his great paper of 1927, ‘Facts and Propositions’. The Ramsey–Prior theory, contra Ramsey's original approach, confirms that the word ‘true’ has a determinate sense. It does so by specifying the contribution that the word makes to what is expressed by a statement that contains it. That specification vindicates the common-sense view that ‘true’ is grammatically and semantically a predicate.
Chris Jones
- Published in print:
- 2005
- Published Online:
- July 2005
- ISBN:
- 9780199281978
- eISBN:
- 9780191602535
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199281971.003.0009
- Subject:
- Economics and Finance, Public and Welfare
Rules for setting Ramsey (1927) optimal commodity taxes are derived in this chapter using the conventional welfare analysis presented in Ch. 6. When these tax rules apply, Diamond and Mirrlees (1971) ...
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Rules for setting Ramsey (1927) optimal commodity taxes are derived in this chapter using the conventional welfare analysis presented in Ch. 6. When these tax rules apply, Diamond and Mirrlees (1971) and Stiglitz and Dasgupta (1971) prove that the producer prices can be used as shadow prices in project evaluation if private profits are eliminated from consumer incomes. This result is demonstrated using shadow prices to value the changes in economic activity from a marginal tax change. It provides economic intuition that can be used, together with the generalized Hatta decomposition, to extend a number of the familiar optimal tax rules to economies with variable prices.Less
Rules for setting Ramsey (1927) optimal commodity taxes are derived in this chapter using the conventional welfare analysis presented in Ch. 6. When these tax rules apply, Diamond and Mirrlees (1971) and Stiglitz and Dasgupta (1971) prove that the producer prices can be used as shadow prices in project evaluation if private profits are eliminated from consumer incomes. This result is demonstrated using shadow prices to value the changes in economic activity from a marginal tax change. It provides economic intuition that can be used, together with the generalized Hatta decomposition, to extend a number of the familiar optimal tax rules to economies with variable prices.
Rowan Williams and Frances Young
- Published in print:
- 2008
- Published Online:
- January 2012
- ISBN:
- 9780197264348
- eISBN:
- 9780191734250
- Item type:
- chapter
- Publisher:
- British Academy
- DOI:
- 10.5871/bacad/9780197264348.003.0015
- Subject:
- History, Historiography
Maurice Frank Wiles (1923–2005), a Fellow of the British Academy, was an Anglican theologian who was able within that tradition to develop the field of ‘doctrinal criticism’. He began his career ...
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Maurice Frank Wiles (1923–2005), a Fellow of the British Academy, was an Anglican theologian who was able within that tradition to develop the field of ‘doctrinal criticism’. He began his career concentrating on the period of the early Fathers of the Church, and it was this grounding that sowed the seeds of his later work on modern doctrine. Arianism would remain a particular interest. Yet Wiles retained a profound respect for tradition and, like the Fathers, constantly measured his doctrinal critique against the experience of believers in life and worship, regarding theology as second-order discourse – reflection on the significance of what was primary for Christianity, such as the experience of salvation. During his student days two people particularly influenced him: Ian Ramsey, who was Chaplain of his college and his first Theology tutor; and Henry Chadwick, who encouraged his early research in the Church Fathers. The evolution of Wiles' thinking is perhaps best observed in the collection published as Working Papers in Doctrine.Less
Maurice Frank Wiles (1923–2005), a Fellow of the British Academy, was an Anglican theologian who was able within that tradition to develop the field of ‘doctrinal criticism’. He began his career concentrating on the period of the early Fathers of the Church, and it was this grounding that sowed the seeds of his later work on modern doctrine. Arianism would remain a particular interest. Yet Wiles retained a profound respect for tradition and, like the Fathers, constantly measured his doctrinal critique against the experience of believers in life and worship, regarding theology as second-order discourse – reflection on the significance of what was primary for Christianity, such as the experience of salvation. During his student days two people particularly influenced him: Ian Ramsey, who was Chaplain of his college and his first Theology tutor; and Henry Chadwick, who encouraged his early research in the Church Fathers. The evolution of Wiles' thinking is perhaps best observed in the collection published as Working Papers in Doctrine.
Vann McGee
- Published in print:
- 2004
- Published Online:
- May 2010
- ISBN:
- 9780199265176
- eISBN:
- 9780191713989
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199265176.003.0018
- Subject:
- Philosophy, Philosophy of Language, Logic/Philosophy of Mathematics
For accommodating defective utterances within compositional semantics, truth-value gaps (Kleene's 3-valued logic) and gluts (Priest's LP) are equally efficient, but in terms of classical logic gaps ...
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For accommodating defective utterances within compositional semantics, truth-value gaps (Kleene's 3-valued logic) and gluts (Priest's LP) are equally efficient, but in terms of classical logic gaps yield harmless incompleteness, whereas gluts precipitate collapse; ex contradictione quodlibet. The discrepancy is less deep than first appears, however. A dialetheist dual to van Fraassen's supervaluationism, implicit in Ramsey's ‘Theories,’ counts sentences true if they are true in at least one acceptable model. Divergent illucutionary norms compensate for differing semantics. Subvaluationists (so-called by Varzi) replace the supervaluationist maxim, ‘Do not assert what is untrue,’ by ‘Do not assert what is false.’ Both predict the same verbal behavior.Less
For accommodating defective utterances within compositional semantics, truth-value gaps (Kleene's 3-valued logic) and gluts (Priest's LP) are equally efficient, but in terms of classical logic gaps yield harmless incompleteness, whereas gluts precipitate collapse; ex contradictione quodlibet. The discrepancy is less deep than first appears, however. A dialetheist dual to van Fraassen's supervaluationism, implicit in Ramsey's ‘Theories,’ counts sentences true if they are true in at least one acceptable model. Divergent illucutionary norms compensate for differing semantics. Subvaluationists (so-called by Varzi) replace the supervaluationist maxim, ‘Do not assert what is untrue,’ by ‘Do not assert what is false.’ Both predict the same verbal behavior.
Norman F. Ramsey
- Published in print:
- 1986
- Published Online:
- September 2007
- ISBN:
- 9780198520214
- eISBN:
- 9780191706325
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198520214.003.0005
- Subject:
- Physics, Atomic, Laser, and Optical Physics
A brief history of early magnetic resonance methods is given. In 1938, Rabi published the description of the first successful magnetic resonance experiment which he had used with collaborators to ...
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A brief history of early magnetic resonance methods is given. In 1938, Rabi published the description of the first successful magnetic resonance experiment which he had used with collaborators to measure the nuclear magnetic moments in LiCl. With other collaborators, it became clear that the method provided precision radio-frequency and microwave spectroscopy. The theory of the method and the calculations of transition probabilities are given in detail. Although Rabi's method gives more accurate results than any previous method, the accuracy is limited by the fact that the accuracy increases with the length of the apparatus, but the length can not exceed ½ a wavelength of the oscillatory radiation without getting cancellations from the opposite phases. In 1949, Ramsey pointed out that this problem could be overcome by using two separated oscillatory field regions with each one less than ½ a wavelength long, but with the two regions being many wave lengths apart and with the oscillations in the two regions being coherently driven. This method (often called the Ramsey method) works well and provides resonances that can be hundreds of times narrower than that by Rabi's method. Sometimes the intensity of the resonances are increased by added space focusing or by the use of very slow molecules. Possible distortions of molecular beam resonances and means for preventing them are discussed.Less
A brief history of early magnetic resonance methods is given. In 1938, Rabi published the description of the first successful magnetic resonance experiment which he had used with collaborators to measure the nuclear magnetic moments in LiCl. With other collaborators, it became clear that the method provided precision radio-frequency and microwave spectroscopy. The theory of the method and the calculations of transition probabilities are given in detail. Although Rabi's method gives more accurate results than any previous method, the accuracy is limited by the fact that the accuracy increases with the length of the apparatus, but the length can not exceed ½ a wavelength of the oscillatory radiation without getting cancellations from the opposite phases. In 1949, Ramsey pointed out that this problem could be overcome by using two separated oscillatory field regions with each one less than ½ a wavelength long, but with the two regions being many wave lengths apart and with the oscillations in the two regions being coherently driven. This method (often called the Ramsey method) works well and provides resonances that can be hundreds of times narrower than that by Rabi's method. Sometimes the intensity of the resonances are increased by added space focusing or by the use of very slow molecules. Possible distortions of molecular beam resonances and means for preventing them are discussed.
Simon Blackburn
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199548057
- eISBN:
- 9780191594953
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199548057.003.0011
- Subject:
- Philosophy, Moral Philosophy, Metaphysics/Epistemology
In success semantics the notion of representation is linked to that of successful action. This chapter dissents from one popular way of expounding the connection, and suggests a different one making ...
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In success semantics the notion of representation is linked to that of successful action. This chapter dissents from one popular way of expounding the connection, and suggests a different one making a fuller use of decompositional semantics.Less
In success semantics the notion of representation is linked to that of successful action. This chapter dissents from one popular way of expounding the connection, and suggests a different one making a fuller use of decompositional semantics.
Maurice FitzGerald Scott
- Published in print:
- 1991
- Published Online:
- November 2003
- ISBN:
- 9780198287421
- eISBN:
- 9780191596872
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198287429.003.0008
- Subject:
- Economics and Finance, Development, Growth, and Environmental
Equations to determine the rate of investment are needed to close the model of Ch. 6. There seems to be no generally accepted theory of long‐run saving and investment. The capital stock adjustment ...
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Equations to determine the rate of investment are needed to close the model of Ch. 6. There seems to be no generally accepted theory of long‐run saving and investment. The capital stock adjustment principle makes investment respond to output, whereas we require causation to flow in the opposite direction. A simple Ramsey approach is adopted, faute de mieux, in which a utility function determines the rate of discount, which is equated to the marginal rate of return. There are then eight equations to determine eight endogenous variables.Less
Equations to determine the rate of investment are needed to close the model of Ch. 6. There seems to be no generally accepted theory of long‐run saving and investment. The capital stock adjustment principle makes investment respond to output, whereas we require causation to flow in the opposite direction. A simple Ramsey approach is adopted, faute de mieux, in which a utility function determines the rate of discount, which is equated to the marginal rate of return. There are then eight equations to determine eight endogenous variables.
