Paul Horwich
- Published in print:
- 2005
- Published Online:
- September 2006
- ISBN:
- 9780199251247
- eISBN:
- 9780191603983
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019925124X.001.0001
- Subject:
- Philosophy, Philosophy of Language
The broad aim of this work is to explain how mere noises, marks, gestures, and mental/neural symbols are able to capture the world, that is, how words and sentences (in whatever medium) come to mean ...
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The broad aim of this work is to explain how mere noises, marks, gestures, and mental/neural symbols are able to capture the world, that is, how words and sentences (in whatever medium) come to mean what they do, to stand for certain things, to be true or false of reality. Paul Horwich’s answer takes off from Wittgenstein’s appealingly demystifying remark, that the meaning of a term is nothing over and above its use, and proceeds with a groundbreaking articulation and defence of that idea, showing how it can deal successfully with Quinean and Kripkean forms of scepticism about meaning, with the various normative features of thought and language, with the paradoxical phenomenon of vagueness, with the way that word-meanings combine to yield sentence-meanings, and with Chomsky-style models of the language faculty. The main lines of this theory were first suggested in Horwich’s 1998 book, Meaning. The present volume (which requires no familiarity with its predecessor) provides a host of improved, formulations, fresh arguments, responses to criticism, and extensions of the position into new areas.Less
The broad aim of this work is to explain how mere noises, marks, gestures, and mental/neural symbols are able to capture the world, that is, how words and sentences (in whatever medium) come to mean what they do, to stand for certain things, to be true or false of reality. Paul Horwich’s answer takes off from Wittgenstein’s appealingly demystifying remark, that the meaning of a term is nothing over and above its use, and proceeds with a groundbreaking articulation and defence of that idea, showing how it can deal successfully with Quinean and Kripkean forms of scepticism about meaning, with the various normative features of thought and language, with the paradoxical phenomenon of vagueness, with the way that word-meanings combine to yield sentence-meanings, and with Chomsky-style models of the language faculty. The main lines of this theory were first suggested in Horwich’s 1998 book, Meaning. The present volume (which requires no familiarity with its predecessor) provides a host of improved, formulations, fresh arguments, responses to criticism, and extensions of the position into new areas.
Gillian Russell
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199232192
- eISBN:
- 9780191715907
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199232192.001.0001
- Subject:
- Philosophy, Philosophy of Language
The analytic/synthetic distinction looks simple. It is a distinction between two different kinds of sentence: synthetic sentences are true in part because of the way the world is, and in part because ...
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The analytic/synthetic distinction looks simple. It is a distinction between two different kinds of sentence: synthetic sentences are true in part because of the way the world is, and in part because of what they mean, whereas analytic sentences — like all bachelors are unmarried and triangles have three sides — are different; they are true in virtue of meaning and so, no matter what the world is like, as long as the sentence means what it does, it will be true. The distinction seems powerful because analytic sentences seem to be knowable in a special way; one can know that all bachelors are unmarried, for example, just by thinking about what it means. But many 20th-century philosophers, with Quine in the lead, argued that there were no analytic sentences, that the idea of analyticity didn't even make sense and that the analytic/synthetic distinction was therefore an illusion. Others couldn't see how there could fail to be a distinction, however ingenious the arguments. But since the heyday of the debate, things have changed in the philosophy of language. Tools have been refined, confusions cleared up, and most significantly, many philosophers now accept a view of language — semantic externalism — on which it is possible to see how the distinction could fail. One might be tempted to think that ultimately the distinction has fallen for reasons other than those proposed in the original debate. This book argues that it hasn't. It uses the tools of contemporary philosophy of language to outline a view of analytic sentences which is compatible with semantic externalism, and defends that view against the old Quinean arguments. It then goes on to draw out some surprising epistemological consequences.Less
The analytic/synthetic distinction looks simple. It is a distinction between two different kinds of sentence: synthetic sentences are true in part because of the way the world is, and in part because of what they mean, whereas analytic sentences — like all bachelors are unmarried and triangles have three sides — are different; they are true in virtue of meaning and so, no matter what the world is like, as long as the sentence means what it does, it will be true. The distinction seems powerful because analytic sentences seem to be knowable in a special way; one can know that all bachelors are unmarried, for example, just by thinking about what it means. But many 20th-century philosophers, with Quine in the lead, argued that there were no analytic sentences, that the idea of analyticity didn't even make sense and that the analytic/synthetic distinction was therefore an illusion. Others couldn't see how there could fail to be a distinction, however ingenious the arguments. But since the heyday of the debate, things have changed in the philosophy of language. Tools have been refined, confusions cleared up, and most significantly, many philosophers now accept a view of language — semantic externalism — on which it is possible to see how the distinction could fail. One might be tempted to think that ultimately the distinction has fallen for reasons other than those proposed in the original debate. This book argues that it hasn't. It uses the tools of contemporary philosophy of language to outline a view of analytic sentences which is compatible with semantic externalism, and defends that view against the old Quinean arguments. It then goes on to draw out some surprising epistemological consequences.
Gary Kemp
- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199695621
- eISBN:
- 9780191738524
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199695621.001.0001
- Subject:
- Philosophy, Philosophy of Language, Metaphysics/Epistemology
So far as language and meaning are concerned, Donald Davidson and Willard Van Orman Quine are typically regarded as birds of a feather. This book urges first of all that they cannot be. Quine’s most ...
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So far as language and meaning are concerned, Donald Davidson and Willard Van Orman Quine are typically regarded as birds of a feather. This book urges first of all that they cannot be. Quine’s most basic and general philosophical commitment is to his methodological naturalism, which is incompatible with Davidson’s main commitments. In particular, it is not possible to endorse, from Quine’s perspective, the roles played by the concepts truth and reference in Davidson’s philosophy of language; Davidson’s employment of the concept of truth is from Quine’s point of view needlessly ambitious; and his use of the concept of reference cannot be divorced from unscientific ‘intuition’. Second, the book puts the case positively in favour of Quine’s naturalism and its corollary, naturalized epistemology. It is possible to give a consistent account of language without problematic uses of the concepts truth and reference, which in turn makes a strident naturalism much more plausible.Less
So far as language and meaning are concerned, Donald Davidson and Willard Van Orman Quine are typically regarded as birds of a feather. This book urges first of all that they cannot be. Quine’s most basic and general philosophical commitment is to his methodological naturalism, which is incompatible with Davidson’s main commitments. In particular, it is not possible to endorse, from Quine’s perspective, the roles played by the concepts truth and reference in Davidson’s philosophy of language; Davidson’s employment of the concept of truth is from Quine’s point of view needlessly ambitious; and his use of the concept of reference cannot be divorced from unscientific ‘intuition’. Second, the book puts the case positively in favour of Quine’s naturalism and its corollary, naturalized epistemology. It is possible to give a consistent account of language without problematic uses of the concepts truth and reference, which in turn makes a strident naturalism much more plausible.
D. M. Armstrong
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199590612
- eISBN:
- 9780191723391
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199590612.001.0001
- Subject:
- Philosophy, Philosophy of Mind, Metaphysics/Epistemology
This book tries to present in brief compass a metaphysical system, matured (as is hoped) over many years. By metaphysics is understood an account of the fundamental categories of being, such notions ...
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This book tries to present in brief compass a metaphysical system, matured (as is hoped) over many years. By metaphysics is understood an account of the fundamental categories of being, such notions as property, relation, causality. These notions are more abstract than the results of scientific inquiry, and are controversial among scientists as well as among philosophers. The book sprang from lectures given to graduate students, and has deliberately been kept at an informal level. It includes some explanations not required in a book for professional philosophers. The argument is developed in sixteen short chapters. It is argued that the world is a world of states of affairs, involving universals and particulars. The notion of finding suitable truthmakers for truths grows in importance as the book proceeds.Less
This book tries to present in brief compass a metaphysical system, matured (as is hoped) over many years. By metaphysics is understood an account of the fundamental categories of being, such notions as property, relation, causality. These notions are more abstract than the results of scientific inquiry, and are controversial among scientists as well as among philosophers. The book sprang from lectures given to graduate students, and has deliberately been kept at an informal level. It includes some explanations not required in a book for professional philosophers. The argument is developed in sixteen short chapters. It is argued that the world is a world of states of affairs, involving universals and particulars. The notion of finding suitable truthmakers for truths grows in importance as the book proceeds.
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/9780199590612.003.0001
- Subject:
- Philosophy, Philosophy of Mind, Metaphysics/Epistemology
The hypothesis is that space‐time is what there is. W.V. Quine's ‘abstract objects’ are rejected. What exists should play some causal role (Graham Oddie's Eleatic Principle). The nature of space‐time ...
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The hypothesis is that space‐time is what there is. W.V. Quine's ‘abstract objects’ are rejected. What exists should play some causal role (Graham Oddie's Eleatic Principle). The nature of space‐time is subject to scientific investigation (Wilfrid Sellars' distinction between the manifest and the scientific image of the world). Is there room for metaphysics? Yes, because a number of topic neutral notions (of which causality is an important instance) are contested by philosophers and scientists. As argued by C.B. Martin, metaphysics seeks a more abstract model of the world than that provided by science.Less
The hypothesis is that space‐time is what there is. W.V. Quine's ‘abstract objects’ are rejected. What exists should play some causal role (Graham Oddie's Eleatic Principle). The nature of space‐time is subject to scientific investigation (Wilfrid Sellars' distinction between the manifest and the scientific image of the world). Is there room for metaphysics? Yes, because a number of topic neutral notions (of which causality is an important instance) are contested by philosophers and scientists. As argued by C.B. Martin, metaphysics seeks a more abstract model of the world than that provided by science.
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/9780199590612.003.0012
- Subject:
- Philosophy, Philosophy of Mind, Metaphysics/Epistemology
Logical and mathematical truths differ from the empirical sciences in being necessary; they can be discovered a priori and in general can be proved (contra Quine). How is this possible? This problem ...
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Logical and mathematical truths differ from the empirical sciences in being necessary; they can be discovered a priori and in general can be proved (contra Quine). How is this possible? This problem is partly met by recognizing that the rational sciences are sciences of the possible. Only the mathematical structures that are instantiated in space‐time are existents. Furthermore, using the Entailment Principle, it is seen that only the logico‐mathematical axioms require truthmakers. We should recognize laws in these sciences, but laws that are necessary. Such laws will be truthmakers for truths about uninstantiated structures, for instance large infinite numbers. What is the source of these necessary laws? Perhaps it is a necessity in the nature of things.Less
Logical and mathematical truths differ from the empirical sciences in being necessary; they can be discovered a priori and in general can be proved (contra Quine). How is this possible? This problem is partly met by recognizing that the rational sciences are sciences of the possible. Only the mathematical structures that are instantiated in space‐time are existents. Furthermore, using the Entailment Principle, it is seen that only the logico‐mathematical axioms require truthmakers. We should recognize laws in these sciences, but laws that are necessary. Such laws will be truthmakers for truths about uninstantiated structures, for instance large infinite numbers. What is the source of these necessary laws? Perhaps it is a necessity in the nature of things.
Samuel Guttenplan
- Published in print:
- 2005
- Published Online:
- July 2005
- ISBN:
- 9780199280896
- eISBN:
- 9780191602627
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199280894.001.0001
- Subject:
- Philosophy, Philosophy of Language
Objects of Metaphor offers a philosophical account of the phenomenon of metaphor which is radically different from others in the literature. Yet for all its difference, the underlying ...
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Objects of Metaphor offers a philosophical account of the phenomenon of metaphor which is radically different from others in the literature. Yet for all its difference, the underlying rationale of the account is genuinely ecumenical. If one adopts its perspective, one should be able to understand the substantial correctness of many other accounts, while at the same time seeing why they are not in the end completely correct. The origins of the account lie in an examination of the conception of predication. Unreflectively thought of as a task accomplished by words, it is argued that predication, or something very much like it, can also be accomplished by non-word objects (‘objects’ here include events, states of affairs, situations, actions and the like). Liberated in this way from words, predication becomes one central element in the account of metaphor. The other element is the move from language to objects which, adapting an idea of Quine’s, is thought of as the limiting case of semantic descent. Whilst the Objects of Metaphor account presents other accounts in a new light, its main importance lies in what it says about metaphor itself. Powerful and flexible enough to cope with the syntactic complexity typical of genuine metaphor, it offers novel conceptions of both the relationship between simile and metaphor and the notion of dead metaphor. Additionally, it shows why metaphor is a robust theoretic kind, related to other tropes such as synecdoche and metonymy, but not to be confused with tropes generally, or with the figurative and non-literal.Less
Objects of Metaphor offers a philosophical account of the phenomenon of metaphor which is radically different from others in the literature. Yet for all its difference, the underlying rationale of the account is genuinely ecumenical. If one adopts its perspective, one should be able to understand the substantial correctness of many other accounts, while at the same time seeing why they are not in the end completely correct. The origins of the account lie in an examination of the conception of predication. Unreflectively thought of as a task accomplished by words, it is argued that predication, or something very much like it, can also be accomplished by non-word objects (‘objects’ here include events, states of affairs, situations, actions and the like). Liberated in this way from words, predication becomes one central element in the account of metaphor. The other element is the move from language to objects which, adapting an idea of Quine’s, is thought of as the limiting case of semantic descent. Whilst the Objects of Metaphor account presents other accounts in a new light, its main importance lies in what it says about metaphor itself. Powerful and flexible enough to cope with the syntactic complexity typical of genuine metaphor, it offers novel conceptions of both the relationship between simile and metaphor and the notion of dead metaphor. Additionally, it shows why metaphor is a robust theoretic kind, related to other tropes such as synecdoche and metonymy, but not to be confused with tropes generally, or with the figurative and non-literal.
Donald Davidson
- Published in print:
- 2005
- Published Online:
- July 2005
- ISBN:
- 9780198237570
- eISBN:
- 9780191602610
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019823757X.003.0006
- Subject:
- Philosophy, General
This essay explores Quine’s concept of truth. Quine substitutes radical translation for translation which aims to preserve ‘meaning’. Although radical translation does not always preserve truth ...
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This essay explores Quine’s concept of truth. Quine substitutes radical translation for translation which aims to preserve ‘meaning’. Although radical translation does not always preserve truth value, much less meaning, truth is nevertheless very much in view in the practice of radical translation. Meaning, as preserved by radical interpretation, is needed to apply our truth predicate to any speech but our own, and we need truth to understand meaning. Such basic relations between truth and meaning are incompatible with a deflationary attitude toward the concept of truth.Less
This essay explores Quine’s concept of truth. Quine substitutes radical translation for translation which aims to preserve ‘meaning’. Although radical translation does not always preserve truth value, much less meaning, truth is nevertheless very much in view in the practice of radical translation. Meaning, as preserved by radical interpretation, is needed to apply our truth predicate to any speech but our own, and we need truth to understand meaning. Such basic relations between truth and meaning are incompatible with a deflationary attitude toward the concept of truth.
Alan Millar
- Published in print:
- 1991
- Published Online:
- October 2011
- ISBN:
- 9780198242703
- eISBN:
- 9780191680540
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198242703.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Mind
There is a tendency in current philosophical thought to treat sensory experiences as a peculiar species of propositional attitude. This book argues against this view. While allowing that experiences ...
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There is a tendency in current philosophical thought to treat sensory experiences as a peculiar species of propositional attitude. This book argues against this view. While allowing that experiences may in some sense bear propositional content, it presents a view of sensory experiences as a species of psychological state. The book applies the resulting analytical framework to a discussion of justified belief, dealing, firstly, with how beliefs may derive justification from other beliefs, and secondly, with how current sensory experiences may contribute to the justification of a person's beliefs. A key theme in the book's general approach is that justified belief results from the competent exercise of conceptual capacities, some of which involve an ability to respond appropriately to current experience. In working out this approach the book develops a view of concepts and their mastery; explores the role of groundless beliefs drawing on suggestions of Wittgenstein; illuminates aspects of the thought of Locke, Hume, Quine, and Goldman; and finally offers a response to a sophisticated variety of scepticism.Less
There is a tendency in current philosophical thought to treat sensory experiences as a peculiar species of propositional attitude. This book argues against this view. While allowing that experiences may in some sense bear propositional content, it presents a view of sensory experiences as a species of psychological state. The book applies the resulting analytical framework to a discussion of justified belief, dealing, firstly, with how beliefs may derive justification from other beliefs, and secondly, with how current sensory experiences may contribute to the justification of a person's beliefs. A key theme in the book's general approach is that justified belief results from the competent exercise of conceptual capacities, some of which involve an ability to respond appropriately to current experience. In working out this approach the book develops a view of concepts and their mastery; explores the role of groundless beliefs drawing on suggestions of Wittgenstein; illuminates aspects of the thought of Locke, Hume, Quine, and Goldman; and finally offers a response to a sophisticated variety of scepticism.
Hartry Field
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199242894
- eISBN:
- 9780191597381
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199242895.001.0001
- Subject:
- Philosophy, General
This is a collection of papers, written over many years, with substantial postscripts tying them together and giving an updated perspective on them. The first five are on the notions of truth and ...
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This is a collection of papers, written over many years, with substantial postscripts tying them together and giving an updated perspective on them. The first five are on the notions of truth and truth‐conditions, and their role in a theory of meaning and of the content of our mental states. The next five deal with what I call ‘factually defective discourse’—discourse that gives rise to issues about which, it is tempting to say that, there is no fact of the matter as to the right answer; one particular kind of factually defective discourse is called ‘indeterminacy’, and it gets the bulk of the attention. The final bunch of papers deal with issues about objectivity, closely related to issues about factual defectiveness; two deal with the question of whether the axioms of mathematics are as objective as is often assumed, and one deals with the question of whether our epistemological methods are as objective as they are usually assumed to be.Less
This is a collection of papers, written over many years, with substantial postscripts tying them together and giving an updated perspective on them. The first five are on the notions of truth and truth‐conditions, and their role in a theory of meaning and of the content of our mental states. The next five deal with what I call ‘factually defective discourse’—discourse that gives rise to issues about which, it is tempting to say that, there is no fact of the matter as to the right answer; one particular kind of factually defective discourse is called ‘indeterminacy’, and it gets the bulk of the attention. The final bunch of papers deal with issues about objectivity, closely related to issues about factual defectiveness; two deal with the question of whether the axioms of mathematics are as objective as is often assumed, and one deals with the question of whether our epistemological methods are as objective as they are usually assumed to be.
Penelope Maddy
- Published in print:
- 1992
- Published Online:
- November 2003
- ISBN:
- 9780198240358
- eISBN:
- 9780191597978
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019824035X.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Many mathematicians understand their work as an effort to describe the denizens and features of an abstract mathematical world or worlds. Most philosophers of mathematics consider views of this sort ...
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Many mathematicians understand their work as an effort to describe the denizens and features of an abstract mathematical world or worlds. Most philosophers of mathematics consider views of this sort highly problematic, largely due to two stark difficulties laid out by Benacerraf: first, if mathematical things are abstract, and thus not to be found in space and time, how can we come to know anything about them? Second, how can mathematics be the study of certain particular things, when all that seems to matter mathematically are various structural features and relations? The goal of this book is to develop a philosophically defensible version of the mathematician's pre‐theoretic realism (sometimes called ‘Platonism’) about mathematical things. Beginning from an analysis of the strengths and weaknesses of Quine's and Gödel's versions of mathematical realism, I propose an alternative called ‘set theoretic realism’ and argue that it avoids both of Benacerraf's problems. In their place, I raise a new problem: given that some open questions of mathematics (like Cantor's Continuum Hypothesis) cannot be settled on the basis of the standard axioms, how are we rationally to evaluate new candidates for axiomatic status (such as Gödel's Axiom of Constructibility or various large cardinal axioms)? Set theoretic realism and its realistic cousins are not the only positions that face this important new challenge—various popular versions of nominalism and structuralism do as well—which suggests that it taps into a fundamental issue.Less
Many mathematicians understand their work as an effort to describe the denizens and features of an abstract mathematical world or worlds. Most philosophers of mathematics consider views of this sort highly problematic, largely due to two stark difficulties laid out by Benacerraf: first, if mathematical things are abstract, and thus not to be found in space and time, how can we come to know anything about them? Second, how can mathematics be the study of certain particular things, when all that seems to matter mathematically are various structural features and relations? The goal of this book is to develop a philosophically defensible version of the mathematician's pre‐theoretic realism (sometimes called ‘Platonism’) about mathematical things. Beginning from an analysis of the strengths and weaknesses of Quine's and Gödel's versions of mathematical realism, I propose an alternative called ‘set theoretic realism’ and argue that it avoids both of Benacerraf's problems. In their place, I raise a new problem: given that some open questions of mathematics (like Cantor's Continuum Hypothesis) cannot be settled on the basis of the standard axioms, how are we rationally to evaluate new candidates for axiomatic status (such as Gödel's Axiom of Constructibility or various large cardinal axioms)? Set theoretic realism and its realistic cousins are not the only positions that face this important new challenge—various popular versions of nominalism and structuralism do as well—which suggests that it taps into a fundamental issue.
Stewart Shapiro
- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198250296
- eISBN:
- 9780191598388
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250290.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
A language is second‐order, or higher‐order, if it has bound variables that range over properties or sets of the items in the range of the ordinary, first‐order variables. This book presents a formal ...
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A language is second‐order, or higher‐order, if it has bound variables that range over properties or sets of the items in the range of the ordinary, first‐order variables. This book presents a formal development of second‐ and higher‐order logic and an extended argument that higher‐order systems have an important role to play in the philosophy and foundations of mathematics. The development includes the languages, deductive systems, and model‐theoretic semantics for higher‐order languages, and the basic and advanced results in its meta‐theory: completeness, compactness, and the Löwenheim–Skolem theorems for Henkin semantics, and the failure of those results for standard semantics. Argues that second‐order theories and formalizations, with standard semantics, provide better models of important aspects of mathematics than their first‐order counterparts. Despite the fact that Quine is the main opponent of second‐order logic (arguing that second‐order logic is set‐theory in disguise), the present argument is broadly Quinean, proposing that there is no sharp line dividing mathematics from logic, especially the logic of mathematics. Also surveys the historical development in logic, tracing the emergence of first‐order logic as the de facto standard among logicians and philosophers. The connection between formal deduction and reasoning is related to Wittgensteinian issues concerning rule‐following. The book closes with an examination of several alternatives to second‐order logic: first‐order set theory, infinitary languages, and systems that are, in a sense, intermediate between first order and second order.Less
A language is second‐order, or higher‐order, if it has bound variables that range over properties or sets of the items in the range of the ordinary, first‐order variables. This book presents a formal development of second‐ and higher‐order logic and an extended argument that higher‐order systems have an important role to play in the philosophy and foundations of mathematics. The development includes the languages, deductive systems, and model‐theoretic semantics for higher‐order languages, and the basic and advanced results in its meta‐theory: completeness, compactness, and the Löwenheim–Skolem theorems for Henkin semantics, and the failure of those results for standard semantics. Argues that second‐order theories and formalizations, with standard semantics, provide better models of important aspects of mathematics than their first‐order counterparts. Despite the fact that Quine is the main opponent of second‐order logic (arguing that second‐order logic is set‐theory in disguise), the present argument is broadly Quinean, proposing that there is no sharp line dividing mathematics from logic, especially the logic of mathematics. Also surveys the historical development in logic, tracing the emergence of first‐order logic as the de facto standard among logicians and philosophers. The connection between formal deduction and reasoning is related to Wittgensteinian issues concerning rule‐following. The book closes with an examination of several alternatives to second‐order logic: first‐order set theory, infinitary languages, and systems that are, in a sense, intermediate between first order and second order.
Frank Jackson
- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198250616
- eISBN:
- 9780191597787
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250614.001.0001
- Subject:
- Philosophy, General
Conceptual analysis is currently out of favour, especially in North America. This is partly through misunderstanding of its nature. Properly understood, conceptual analysis is not a mysterious ...
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Conceptual analysis is currently out of favour, especially in North America. This is partly through misunderstanding of its nature. Properly understood, conceptual analysis is not a mysterious activity discredited by Quine that seeks after the a priori in some hard‐to‐understand sense. It is, rather, something familiar to everyone, philosophers and non‐philosophers alike—or so I argue. Another reason for its unpopularity is a failure to appreciate the need for conceptual analysis. The cost of repudiating it has not been sufficiently appreciated; without it, we cannot address a whole raft of important questions.I have always been suspicious of excessively abstract theorizing in philosophy. I think that an important test of metaphilosophical claims is whether they make good sense in the context of particular problems. The discussion in the book is, accordingly, anchored in particular philosophical debates. The basic framework is developed in the first three chapters via a consideration of the role of conceptual analysis in the debate over the doctrine in metaphysics known as physicalism, with digressions on free will, meaning, personal identity, motion, and change, and then applied in the last three chapters to current debates over colour and ethics.Less
Conceptual analysis is currently out of favour, especially in North America. This is partly through misunderstanding of its nature. Properly understood, conceptual analysis is not a mysterious activity discredited by Quine that seeks after the a priori in some hard‐to‐understand sense. It is, rather, something familiar to everyone, philosophers and non‐philosophers alike—or so I argue. Another reason for its unpopularity is a failure to appreciate the need for conceptual analysis. The cost of repudiating it has not been sufficiently appreciated; without it, we cannot address a whole raft of important questions.
I have always been suspicious of excessively abstract theorizing in philosophy. I think that an important test of metaphilosophical claims is whether they make good sense in the context of particular problems. The discussion in the book is, accordingly, anchored in particular philosophical debates. The basic framework is developed in the first three chapters via a consideration of the role of conceptual analysis in the debate over the doctrine in metaphysics known as physicalism, with digressions on free will, meaning, personal identity, motion, and change, and then applied in the last three chapters to current debates over colour and ethics.
Colin McGinn
- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780199241811
- eISBN:
- 9780191598029
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199241813.001.0001
- Subject:
- Philosophy, General
This book discusses the nature of identity, existence, predication, necessity, and truth. Its main claims are that identity, existence, and truth are logical properties, that predicates are singular ...
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This book discusses the nature of identity, existence, predication, necessity, and truth. Its main claims are that identity, existence, and truth are logical properties, that predicates are singular terms that refer to properties, and that necessity (and other modalities) are modes of instantiation of properties by objects. The book develops a realist anti‐naturalist stance on logical properties, which takes logical notions at face value, and refuses to reduce them to other notions. Two further contentions central to this work are, first, that the quantifier has been overrated as an instrument of logico‐linguistic analysis; and secondly, that past attempts to define logical notions such as identity or existence have been largely unsuccessful.Less
This book discusses the nature of identity, existence, predication, necessity, and truth. Its main claims are that identity, existence, and truth are logical properties, that predicates are singular terms that refer to properties, and that necessity (and other modalities) are modes of instantiation of properties by objects. The book develops a realist anti‐naturalist stance on logical properties, which takes logical notions at face value, and refuses to reduce them to other notions. Two further contentions central to this work are, first, that the quantifier has been overrated as an instrument of logico‐linguistic analysis; and secondly, that past attempts to define logical notions such as identity or existence have been largely unsuccessful.
Charles S. Chihara
- Published in print:
- 1991
- Published Online:
- November 2003
- ISBN:
- 9780198239758
- eISBN:
- 9780191597190
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198239750.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
A continuation of the study of mathematical existence begun in Ontology and the Vicious‐Circle Principle (published in 1973); in the present work, Quine's indispensability argument is rebutted by the ...
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A continuation of the study of mathematical existence begun in Ontology and the Vicious‐Circle Principle (published in 1973); in the present work, Quine's indispensability argument is rebutted by the development of a new nominalistic version of mathematics (the Constructibility Theory) that is specified as an axiomatized theory formalized in a many‐sorted first‐order language. What is new in the present work is its abandonment of the predicative restrictions of the earlier work and its much greater attention to the applications of mathematics in science and everyday life. The book also contains detailed discussions of rival views (Mathematical Structuralism, Field's Instrumentalism, Burgess's Moderate Realism, Maddy's Set Theoretical Realism, and Kitcher's Ideal Agent account of mathematics), in which many comparisons with the Constructibility Theory are made.Less
A continuation of the study of mathematical existence begun in Ontology and the Vicious‐Circle Principle (published in 1973); in the present work, Quine's indispensability argument is rebutted by the development of a new nominalistic version of mathematics (the Constructibility Theory) that is specified as an axiomatized theory formalized in a many‐sorted first‐order language. What is new in the present work is its abandonment of the predicative restrictions of the earlier work and its much greater attention to the applications of mathematics in science and everyday life. The book also contains detailed discussions of rival views (Mathematical Structuralism, Field's Instrumentalism, Burgess's Moderate Realism, Maddy's Set Theoretical Realism, and Kitcher's Ideal Agent account of mathematics), in which many comparisons with the Constructibility Theory are made.
Mark Colyvan
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780195137545
- eISBN:
- 9780199833139
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019513754X.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Looks at the Quine–Putnam indispensability argument in the philosophy of mathematics. This argument urges us to place mathematical entities on the same ontological footing as other theoretical ...
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Looks at the Quine–Putnam indispensability argument in the philosophy of mathematics. This argument urges us to place mathematical entities on the same ontological footing as other theoretical entities indispensable to our best scientific theories. The indispensability argument has come under serious scrutiny in recent times, with many influential philosophers unconvinced of its cogency. This book outlines the indispensability argument in considerable detail, before defending it against various challenges.Although the focus is squarely on the indispensability argument, in order to appreciate the argument's full force, it is necessary to consider many other interesting and related topics. These include questions about ontological commitments and the applications of mathematics to physical theories. Of particular interest here is the Quinean backdrop from which the indispensability argument emerges. This backdrop consists of the doctrines of holism and naturalism. The latter is crucial to the whole indispensability debate, so a considerable portion of this work is spent discussing naturalism.Less
Looks at the Quine–Putnam indispensability argument in the philosophy of mathematics. This argument urges us to place mathematical entities on the same ontological footing as other theoretical entities indispensable to our best scientific theories. The indispensability argument has come under serious scrutiny in recent times, with many influential philosophers unconvinced of its cogency. This book outlines the indispensability argument in considerable detail, before defending it against various challenges.
Although the focus is squarely on the indispensability argument, in order to appreciate the argument's full force, it is necessary to consider many other interesting and related topics. These include questions about ontological commitments and the applications of mathematics to physical theories. Of particular interest here is the Quinean backdrop from which the indispensability argument emerges. This backdrop consists of the doctrines of holism and naturalism. The latter is crucial to the whole indispensability debate, so a considerable portion of this work is spent discussing naturalism.
Timothy McCarthy
- Published in print:
- 2002
- Published Online:
- November 2003
- ISBN:
- 9780195145069
- eISBN:
- 9780199833436
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195145062.001.0001
- Subject:
- Philosophy, Philosophy of Language
Attempts to offer a response to Quine's arguments for the indeterminacy of reference and translation by developing an original theory of radical interpretation, i.e. the project of characterising ...
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Attempts to offer a response to Quine's arguments for the indeterminacy of reference and translation by developing an original theory of radical interpretation, i.e. the project of characterising from scratch the language and attitudes of an unknown agent or population. Ch. 1 situates the theory put forward in the context of the recent history of the subject and offers arguments against its main competitors, namely, Kripkean theories of reference and Dummettian verificationist accounts. Ch. 2 introduces the constitutive principles of McCarthy's own theory of radical interpretation, exploiting the constraints on interpretation suggested by Davidson and Lewis as the starting point of discussion. Chs 3 and 4 apply McCarthy's framework to theories of reference and the interpretation problem for the philosophy of logic, offering original accounts of how the reference of expressions in specific problem categories, in particular, proper names, observational predicates, and natural kind terms, is determined, and how the logical devices of a language can be characterized on the basis of data provided by an interpretation of its speakers.Less
Attempts to offer a response to Quine's arguments for the indeterminacy of reference and translation by developing an original theory of radical interpretation, i.e. the project of characterising from scratch the language and attitudes of an unknown agent or population. Ch. 1 situates the theory put forward in the context of the recent history of the subject and offers arguments against its main competitors, namely, Kripkean theories of reference and Dummettian verificationist accounts. Ch. 2 introduces the constitutive principles of McCarthy's own theory of radical interpretation, exploiting the constraints on interpretation suggested by Davidson and Lewis as the starting point of discussion. Chs 3 and 4 apply McCarthy's framework to theories of reference and the interpretation problem for the philosophy of logic, offering original accounts of how the reference of expressions in specific problem categories, in particular, proper names, observational predicates, and natural kind terms, is determined, and how the logical devices of a language can be characterized on the basis of data provided by an interpretation of its speakers.
Michael Dummett
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198236214
- eISBN:
- 9780191597350
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198236212.001.0001
- Subject:
- Philosophy, Philosophy of Language
The book contains articles in metaphysics and philosophy of language written between 1975 and 1992. Dummett defends the verificationist theory of meaning, according to which in order to know the ...
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The book contains articles in metaphysics and philosophy of language written between 1975 and 1992. Dummett defends the verificationist theory of meaning, according to which in order to know the meaning of a statement one must be in possession of a procedure to verify it. He also argues for the link between bivalence and the metaphysical doctrine of realism. Other topics discussed include refutation of instrumentalism, mathematical applicability, backward causation, and the analysis of the concept of existence.Less
The book contains articles in metaphysics and philosophy of language written between 1975 and 1992. Dummett defends the verificationist theory of meaning, according to which in order to know the meaning of a statement one must be in possession of a procedure to verify it. He also argues for the link between bivalence and the metaphysical doctrine of realism. Other topics discussed include refutation of instrumentalism, mathematical applicability, backward causation, and the analysis of the concept of existence.
Lorraine Code
- Published in print:
- 2006
- Published Online:
- September 2006
- ISBN:
- 9780195159431
- eISBN:
- 9780199786411
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195159438.003.0003
- Subject:
- Philosophy, Feminist Philosophy
Starting with a critical reading of the promise of Quinean naturalized epistemology for feminist and other post-colonial theories of knowledge, this chapter instead proposes an ecological naturalism ...
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Starting with a critical reading of the promise of Quinean naturalized epistemology for feminist and other post-colonial theories of knowledge, this chapter instead proposes an ecological naturalism centred on a conception of the natural and of natural knowledge-making derived from the science of ecology. For Quinean naturalism, laboratory-based cognitive science is the place to study how human beings “naturally” know; yet its promise is vitiated by the artificiality of its regulative conception of “the natural”. Its reliance on a residual positivist-empiricism blocks its capacity to relinquish the epistemological imaginary of mastery and control, to engage with specific, diverse human knowings, and to address the politics of knowledge. Although ecological science counts as a “weak” science by orthodox positivist standards (following Kristin Schrader-Frechette and Sharon Kingsland), this so-called weakness becomes a strength in the enhanced capacity it offers to know interpretively, non-reductively, and responsibly.Less
Starting with a critical reading of the promise of Quinean naturalized epistemology for feminist and other post-colonial theories of knowledge, this chapter instead proposes an ecological naturalism centred on a conception of the natural and of natural knowledge-making derived from the science of ecology. For Quinean naturalism, laboratory-based cognitive science is the place to study how human beings “naturally” know; yet its promise is vitiated by the artificiality of its regulative conception of “the natural”. Its reliance on a residual positivist-empiricism blocks its capacity to relinquish the epistemological imaginary of mastery and control, to engage with specific, diverse human knowings, and to address the politics of knowledge. Although ecological science counts as a “weak” science by orthodox positivist standards (following Kristin Schrader-Frechette and Sharon Kingsland), this so-called weakness becomes a strength in the enhanced capacity it offers to know interpretively, non-reductively, and responsibly.
Michael D. Resnik
- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198250142
- eISBN:
- 9780191598296
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250142.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Mathematics is regarded as our most developed science, and yet philosophical troubles surface as soon as we inquire about its subject matter partly because mathematics itself says nothing about the ...
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Mathematics is regarded as our most developed science, and yet philosophical troubles surface as soon as we inquire about its subject matter partly because mathematics itself says nothing about the metaphysical nature of its objects. Taking mathematics at face value seems to favour the Platonist view according to which mathematics concerns causally inert objects existing outside space‐time, but this view seems to preclude any account of how we acquire mathematical knowledge without using some mysterious intellectual intuition. In this book, I defend a version of mathematical realism, motivated by the indispensability of mathematics in science, according to which (1) mathematical objects exist independently of us and our constructions, (2) much of contemporary mathematics is true, and (3) mathematical truths obtain independently of our beliefs, theories, and proofs.The ontological component of my realism is a form of structuralism according to which mathematical objects are featureless, abstract positions in structures, or patterns, and like geometric points, their identities are fixed only through their relationships to each other. Structuralism is also part of my epistemology in that material objects ‘fit’ simple patterns, and in doing so, they ‘fill’ the positions of simple mathematical structures. We may perceive the arrangements of objects but we cannot perceive their positions i.e. the abstract, non‐spatiotemporal mathematical objects, and the problem then consists in explaining how we can form beliefs about them.Answering this question introduces a central notion of my epistemology, that of a posit: by representing and designing patterned objects our ancestors posited geometric objects as sui generis and started describing them by describing the patterns in which they are positions. Since positing mathematical objects, like positing new scientific entities, is an activity similar to making up a story, one might wonder how such an activity can lead to mathematical knowledge and truth, but I believe that our ancestors were justified in introducing mathematical objects and we are justified in retaining them, by pragmatic and global considerations: mathematics has proved immensely fruitful for science, technology, and practical life, and doing without it is now virtually impossible.This account of justification introduces a further problem: if our justification for believing in mathematical truths is global and pragmatic, then it might turn out that one is not justified in accepting a mathematical claim unless it is accepted by science, and this is clearly at odds with the practice of mathematics where we hardly ever invoke such global considerations in order to justify a mathematical claim. In mathematics, we usually employ a local conception of evidence made up mainly of a priori proofs. However, arguing from the perspective of a Quinean epistemic holism, I claim that this feature of the practice should not make us conclude that mathematics is an a priori science, disconnected evidentially from both observation and natural science, for observation is relevant to mathematics, and technological and scientific success forms a vital part of our justification for believing in the truth of mathematics.Less
Mathematics is regarded as our most developed science, and yet philosophical troubles surface as soon as we inquire about its subject matter partly because mathematics itself says nothing about the metaphysical nature of its objects. Taking mathematics at face value seems to favour the Platonist view according to which mathematics concerns causally inert objects existing outside space‐time, but this view seems to preclude any account of how we acquire mathematical knowledge without using some mysterious intellectual intuition. In this book, I defend a version of mathematical realism, motivated by the indispensability of mathematics in science, according to which (1) mathematical objects exist independently of us and our constructions, (2) much of contemporary mathematics is true, and (3) mathematical truths obtain independently of our beliefs, theories, and proofs.
The ontological component of my realism is a form of structuralism according to which mathematical objects are featureless, abstract positions in structures, or patterns, and like geometric points, their identities are fixed only through their relationships to each other. Structuralism is also part of my epistemology in that material objects ‘fit’ simple patterns, and in doing so, they ‘fill’ the positions of simple mathematical structures. We may perceive the arrangements of objects but we cannot perceive their positions i.e. the abstract, non‐spatiotemporal mathematical objects, and the problem then consists in explaining how we can form beliefs about them.
Answering this question introduces a central notion of my epistemology, that of a posit: by representing and designing patterned objects our ancestors posited geometric objects as sui generis and started describing them by describing the patterns in which they are positions. Since positing mathematical objects, like positing new scientific entities, is an activity similar to making up a story, one might wonder how such an activity can lead to mathematical knowledge and truth, but I believe that our ancestors were justified in introducing mathematical objects and we are justified in retaining them, by pragmatic and global considerations: mathematics has proved immensely fruitful for science, technology, and practical life, and doing without it is now virtually impossible.
This account of justification introduces a further problem: if our justification for believing in mathematical truths is global and pragmatic, then it might turn out that one is not justified in accepting a mathematical claim unless it is accepted by science, and this is clearly at odds with the practice of mathematics where we hardly ever invoke such global considerations in order to justify a mathematical claim. In mathematics, we usually employ a local conception of evidence made up mainly of a priori proofs. However, arguing from the perspective of a Quinean epistemic holism, I claim that this feature of the practice should not make us conclude that mathematics is an a priori science, disconnected evidentially from both observation and natural science, for observation is relevant to mathematics, and technological and scientific success forms a vital part of our justification for believing in the truth of mathematics.
