Stewart Shapiro
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199280391
- eISBN:
- 9780191707162
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199280391.003.0006
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
The present study, so far, has focused exclusively on vague predicates such as ‘bald’, ‘tall’, and predicates such as ‘determinately bald’ and ‘borderline bald‘. Intuitively, what makes a predicate ...
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The present study, so far, has focused exclusively on vague predicates such as ‘bald’, ‘tall’, and predicates such as ‘determinately bald’ and ‘borderline bald‘. Intuitively, what makes a predicate vague is that there is some indeterminacy over whether it applies to some objects: vague predicates have borderline cases. Some aggregates of sand are borderline heaps, some potential NBA players are borderline tall (for an NBA player), some men are borderline bald, and perhaps some men are borderline-borderline bald. At least prima facie, there also seem to be vague objects. This chapter looks at some variations on this theme, and then extends the model theory to handle them.Less
The present study, so far, has focused exclusively on vague predicates such as ‘bald’, ‘tall’, and predicates such as ‘determinately bald’ and ‘borderline bald‘. Intuitively, what makes a predicate vague is that there is some indeterminacy over whether it applies to some objects: vague predicates have borderline cases. Some aggregates of sand are borderline heaps, some potential NBA players are borderline tall (for an NBA player), some men are borderline bald, and perhaps some men are borderline-borderline bald. At least prima facie, there also seem to be vague objects. This chapter looks at some variations on this theme, and then extends the model theory to handle them.
Richard Tieszen
- Published in print:
- 2005
- Published Online:
- May 2010
- ISBN:
- 9780199272457
- eISBN:
- 9780191709951
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199272457.003.0009
- Subject:
- Philosophy, Philosophy of Mind
Edmund Husserl is one of only a few major philosophers in the last one hundred years or so who holds that it is possible to develop a philosophy of mind in which one can account for the consciousness ...
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Edmund Husserl is one of only a few major philosophers in the last one hundred years or so who holds that it is possible to develop a philosophy of mind in which one can account for the consciousness of abstract objects or ideal objects. This chapter discusses Husserl's ideas in connection with the views of Kurt Gödel and Roger Penrose. It presents an argument that leads from Gödel's incompleteness theorems to recognition of the awareness of abstract or ideal objects. Husserl's view, based on his ideas about intentionality and the phenomenological reduction, shows us how to open up a space for a phenomenology of the consciousness of abstract mathematical objects.Less
Edmund Husserl is one of only a few major philosophers in the last one hundred years or so who holds that it is possible to develop a philosophy of mind in which one can account for the consciousness of abstract objects or ideal objects. This chapter discusses Husserl's ideas in connection with the views of Kurt Gödel and Roger Penrose. It presents an argument that leads from Gödel's incompleteness theorems to recognition of the awareness of abstract or ideal objects. Husserl's view, based on his ideas about intentionality and the phenomenological reduction, shows us how to open up a space for a phenomenology of the consciousness of abstract mathematical objects.
E. J. Lowe
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199244997
- eISBN:
- 9780191597930
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199244995.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology
Begins with a defence of realist metaphysics against its many enemies. Metaphysics, it is argued, is an autonomous and indispensable intellectual discipline whose distinctive task is to chart the ...
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Begins with a defence of realist metaphysics against its many enemies. Metaphysics, it is argued, is an autonomous and indispensable intellectual discipline whose distinctive task is to chart the domain of real possibilities—a task which requires us to identify both the basic ontological categories into which all possible beings are divisible and the characteristic relations of ontological dependency in which beings of various ontological categories necessarily stand to one another. Central parts of this task are carried out in the rest of the book, which focuses especially on the key notions of substance, identity, and time. The unity of the concrete world as one world existing in time ultimately depends, it is argued, upon the existence of fundamental substances, which persist primitively through processes of qualitative change. And even abstract necessary beings, such as the objects of mathematics, ultimately depend for their existence, it is claimed, upon there being a concrete spatiotemporal world of enduring substances.Less
Begins with a defence of realist metaphysics against its many enemies. Metaphysics, it is argued, is an autonomous and indispensable intellectual discipline whose distinctive task is to chart the domain of real possibilities—a task which requires us to identify both the basic ontological categories into which all possible beings are divisible and the characteristic relations of ontological dependency in which beings of various ontological categories necessarily stand to one another. Central parts of this task are carried out in the rest of the book, which focuses especially on the key notions of substance, identity, and time. The unity of the concrete world as one world existing in time ultimately depends, it is argued, upon the existence of fundamental substances, which persist primitively through processes of qualitative change. And even abstract necessary beings, such as the objects of mathematics, ultimately depend for their existence, it is claimed, upon there being a concrete spatiotemporal world of enduring substances.
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.
TYLER BURGE
- Published in print:
- 2005
- Published Online:
- May 2010
- ISBN:
- 9780199278534
- eISBN:
- 9780191706943
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199278534.003.0009
- Subject:
- Philosophy, History of Philosophy, Philosophy of Language
Frege regarded the foundations of mathematics as self-evident. He maintained that reason could enable one to know of the existence and nature of both mind-independent abstract objects, such as the ...
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Frege regarded the foundations of mathematics as self-evident. He maintained that reason could enable one to know of the existence and nature of both mind-independent abstract objects, such as the numbers and thought contents, and mind-independent functions, such as the successor function. There is extensive discussion of evidence for, and the nature of, his Platonism; the view that abstract objects and functions are completely mind-independent of both minds and physical reality. This chapter explains how he squared his rationalism with his Platonism. The key idea is that Frege thought that mind is dependent for being what it is both on functioning to attain truth and to track accurately the basic structures of abstract, mind-independent objects (both logical objects and thought contents) and abstract, mind-independent functions.Less
Frege regarded the foundations of mathematics as self-evident. He maintained that reason could enable one to know of the existence and nature of both mind-independent abstract objects, such as the numbers and thought contents, and mind-independent functions, such as the successor function. There is extensive discussion of evidence for, and the nature of, his Platonism; the view that abstract objects and functions are completely mind-independent of both minds and physical reality. This chapter explains how he squared his rationalism with his Platonism. The key idea is that Frege thought that mind is dependent for being what it is both on functioning to attain truth and to track accurately the basic structures of abstract, mind-independent objects (both logical objects and thought contents) and abstract, mind-independent functions.
Christy Mag Uidhir (ed.)
- Published in print:
- 2013
- Published Online:
- January 2013
- ISBN:
- 9780199691494
- eISBN:
- 9780191746277
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199691494.001.0001
- Subject:
- Philosophy, Aesthetics, Metaphysics/Epistemology
The standard way of thinking about non-repeatable (single-instance) artworks such as paintings, drawings, and non-cast sculpture is that they are concrete things (i.e. material, causally efficacious, ...
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The standard way of thinking about non-repeatable (single-instance) artworks such as paintings, drawings, and non-cast sculpture is that they are concrete things (i.e. material, causally efficacious, located in space and time). For example, Da Vinci’s Mona Lisa is currently located in Paris, Richard Serra’s Tilted Arc weighs 73 tonnes, Vermeer’s The Concert was stolen in 1990, and Michaelangelo’s David was attacked with a hammer in 1991. By contrast, consider the current location of Melville’s Moby Dick or the weight of Yeats’s ‘Sailing to Byzantium’ or how one might go about stealing Puccini’s La Bohemme. The standard view of repeatable (multiple-instance) artworks such as novels, poems, plays, operas, films, and symphonies is that they must be abstract things (i.e. immaterial, casually inert, outside space-time). Although novels, poems, and symphonies may not appear to be stock abstract objects, most philosophers of art claim that for the basic intuitions, practices, and conventions surrounding such works to be preserved, repeatable artworks must be abstracta. The purpose of this volume is to examine how philosophical enquiry into the nature of art might productively inform or be productively informed by enquiry into the nature of abstracta taking place within other areas of philosophy such as metaphysics, philosophy of mathematics, epistemology, philosophy of science, and philosophy of mind and language. The aim is to provide a general methodological blueprint from which those within philosophy of art and those without can begin building responsible, and therefore mutually informative and productive, relationships between their respective fields.Less
The standard way of thinking about non-repeatable (single-instance) artworks such as paintings, drawings, and non-cast sculpture is that they are concrete things (i.e. material, causally efficacious, located in space and time). For example, Da Vinci’s Mona Lisa is currently located in Paris, Richard Serra’s Tilted Arc weighs 73 tonnes, Vermeer’s The Concert was stolen in 1990, and Michaelangelo’s David was attacked with a hammer in 1991. By contrast, consider the current location of Melville’s Moby Dick or the weight of Yeats’s ‘Sailing to Byzantium’ or how one might go about stealing Puccini’s La Bohemme. The standard view of repeatable (multiple-instance) artworks such as novels, poems, plays, operas, films, and symphonies is that they must be abstract things (i.e. immaterial, casually inert, outside space-time). Although novels, poems, and symphonies may not appear to be stock abstract objects, most philosophers of art claim that for the basic intuitions, practices, and conventions surrounding such works to be preserved, repeatable artworks must be abstracta. The purpose of this volume is to examine how philosophical enquiry into the nature of art might productively inform or be productively informed by enquiry into the nature of abstracta taking place within other areas of philosophy such as metaphysics, philosophy of mathematics, epistemology, philosophy of science, and philosophy of mind and language. The aim is to provide a general methodological blueprint from which those within philosophy of art and those without can begin building responsible, and therefore mutually informative and productive, relationships between their respective fields.
Kenneth P. Winkler
- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198235095
- eISBN:
- 9780191598685
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198235097.003.0002
- Subject:
- Philosophy, History of Philosophy
If representation is resemblance, how we do we think of groups or classes of things? According to a tradition Berkeley opposed—a tradition represented by Locke—we do so by forming abstract or ...
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If representation is resemblance, how we do we think of groups or classes of things? According to a tradition Berkeley opposed—a tradition represented by Locke—we do so by forming abstract or incomplete ideas. I show that Berkeley's opposition does not depend on his own personal failure to form abstract images, but on what he took to be the impersonal or objective impossibility of abstract objects. Berkeley himself accounts for general thinking not in terms of abstract or incomplete ideas, but in terms of our selective attention to ideas both concrete and determinate. Contentful thought about the natural world is impossible without ideas as objects, Berkeley believes, but ideas do not, in his view, completely fix the content of our thought.Less
If representation is resemblance, how we do we think of groups or classes of things? According to a tradition Berkeley opposed—a tradition represented by Locke—we do so by forming abstract or incomplete ideas. I show that Berkeley's opposition does not depend on his own personal failure to form abstract images, but on what he took to be the impersonal or objective impossibility of abstract objects. Berkeley himself accounts for general thinking not in terms of abstract or incomplete ideas, but in terms of our selective attention to ideas both concrete and determinate. Contentful thought about the natural world is impossible without ideas as objects, Berkeley believes, but ideas do not, in his view, completely fix the content of our thought.
Allan Hazlett
- Published in print:
- 2013
- Published Online:
- January 2013
- ISBN:
- 9780199691494
- eISBN:
- 9780191746277
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199691494.003.0008
- Subject:
- Philosophy, Aesthetics, Metaphysics/Epistemology
There seem to be repeatable artworks. Plays and musical works (like Hamlet or ‘Pictures at an Exhibition’) can be performed again and again; installations (like Sol LeWitt’s Wall Drawing #260) can be ...
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There seem to be repeatable artworks. Plays and musical works (like Hamlet or ‘Pictures at an Exhibition’) can be performed again and again; installations (like Sol LeWitt’s Wall Drawing #260) can be installed over and over; culinary dishes (like Jean-George Vongerichten’s tuna tartare) can be prepared many times. This chapter offers an argument against the existence of repeatable artworks. First, the chapter argues that an artwork is repeatable only if it is an abstract object. This jives with standard accounts of repeatable works, which take them to be abstracta. Second, it argues that abstract objects must have all their properties essentially. Finally, since repeatable artworks, if there are any, do not have all their properties essentially, the chapter concludes that there are no repeatable artworks.Less
There seem to be repeatable artworks. Plays and musical works (like Hamlet or ‘Pictures at an Exhibition’) can be performed again and again; installations (like Sol LeWitt’s Wall Drawing #260) can be installed over and over; culinary dishes (like Jean-George Vongerichten’s tuna tartare) can be prepared many times. This chapter offers an argument against the existence of repeatable artworks. First, the chapter argues that an artwork is repeatable only if it is an abstract object. This jives with standard accounts of repeatable works, which take them to be abstracta. Second, it argues that abstract objects must have all their properties essentially. Finally, since repeatable artworks, if there are any, do not have all their properties essentially, the chapter concludes that there are no repeatable artworks.
Charles Chihara
- Published in print:
- 2005
- Published Online:
- July 2005
- ISBN:
- 9780195148770
- eISBN:
- 9780199835560
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195148770.003.0015
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Nominalism is the view that abstract mathematical objects like numbers, functions, and sets do not exist. The chapter articulates and defends a variety of nominalism, based on a reading of ...
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Nominalism is the view that abstract mathematical objects like numbers, functions, and sets do not exist. The chapter articulates and defends a variety of nominalism, based on a reading of mathematical statements in terms of possible linguistic constructions. The chapter responds directly to a recent study of nominalism by Gideon Rosen and John Burgess, and develops a reply to the Quine-Putnam indispensability argument for the existence of mathematical objects.Less
Nominalism is the view that abstract mathematical objects like numbers, functions, and sets do not exist. The chapter articulates and defends a variety of nominalism, based on a reading of mathematical statements in terms of possible linguistic constructions. The chapter responds directly to a recent study of nominalism by Gideon Rosen and John Burgess, and develops a reply to the Quine-Putnam indispensability argument for the existence of mathematical objects.
John P. Burgess and Gideon Rosen
- Published in print:
- 1999
- Published Online:
- November 2003
- ISBN:
- 9780198250128
- eISBN:
- 9780191597138
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250126.003.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Begins by distinguishing different varieties of nominalism. All adherents of nominalism agree in rejecting mathematical and other abstract entities, and many have attempted to develop nominalist ...
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Begins by distinguishing different varieties of nominalism. All adherents of nominalism agree in rejecting mathematical and other abstract entities, and many have attempted to develop nominalist interpretations of scientific theories that appear to involve mathematical objects, with some (hermeneutic nominalists) claiming that these interpretations reveal what the theories really meant all along, and others (revolutionary nominalists) admitting that what they are developing are new, replacement theories. Before beginning our examination of these interpretative projects, we stop to examine critically their presuppositions, beginning with the distinction between abstract objects and concrete objects. We devote special attention to epistemological arguments and semantical arguments for nominalism, based on causal theories of knowledge and causal theories of reference. We also consider why more nominalists have not been content simply to adopt instrumentalism, which declares science to be a useful fiction, and offers no reinterpretation to turn theory into fact.Less
Begins by distinguishing different varieties of nominalism. All adherents of nominalism agree in rejecting mathematical and other abstract entities, and many have attempted to develop nominalist interpretations of scientific theories that appear to involve mathematical objects, with some (hermeneutic nominalists) claiming that these interpretations reveal what the theories really meant all along, and others (revolutionary nominalists) admitting that what they are developing are new, replacement theories. Before beginning our examination of these interpretative projects, we stop to examine critically their presuppositions, beginning with the distinction between abstract objects and concrete objects. We devote special attention to epistemological arguments and semantical arguments for nominalism, based on causal theories of knowledge and causal theories of reference. We also consider why more nominalists have not been content simply to adopt instrumentalism, which declares science to be a useful fiction, and offers no reinterpretation to turn theory into fact.
Scott Soames
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691160726
- eISBN:
- 9781400850464
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691160726.003.0010
- Subject:
- Philosophy, American Philosophy
This chapter examines the dispute between Quine and Carnap about how to understand ontological commitment and what ontology to adopt. The central dispute is over Carnap’s acceptance of abstract ...
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This chapter examines the dispute between Quine and Carnap about how to understand ontological commitment and what ontology to adopt. The central dispute is over Carnap’s acceptance of abstract objects, including numbers, properties, and propositions, which Quine characterizes in “On What There Is” (1948) as a form of Platonism. Carnap vigorously disagrees, responding in “Empiricism, Semantics, and Ontology” (1950, 1956). For him, commitments to these things are unproblematic consequences of accepting an optimal theoretical framework for doing science. Philosophers haven’t seen this because, he believes, they have approached ontology in an unscientific way.Less
This chapter examines the dispute between Quine and Carnap about how to understand ontological commitment and what ontology to adopt. The central dispute is over Carnap’s acceptance of abstract objects, including numbers, properties, and propositions, which Quine characterizes in “On What There Is” (1948) as a form of Platonism. Carnap vigorously disagrees, responding in “Empiricism, Semantics, and Ontology” (1950, 1956). For him, commitments to these things are unproblematic consequences of accepting an optimal theoretical framework for doing science. Philosophers haven’t seen this because, he believes, they have approached ontology in an unscientific way.
Alvin Plantinga
- Published in print:
- 1993
- Published Online:
- November 2003
- ISBN:
- 9780195078640
- eISBN:
- 9780199872213
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195078640.003.0006
- Subject:
- Philosophy, Metaphysics/Epistemology
In this chapter, I examine a priori knowledge from the perspective of my account of warrant. According to the epistemological tradition, what is known a priori is known, somehow, prior to or ...
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In this chapter, I examine a priori knowledge from the perspective of my account of warrant. According to the epistemological tradition, what is known a priori is known, somehow, prior to or independently of experience; in the first section of this chapter, I attempt to clarify this claim and describe some of the general features of a priori belief and knowledge. In the second section I argue, among other things, that a priori warrant (more precisely, intuitive warrant) is fallible and comes in degrees. I go on to consider an objection to the existence of a priori knowledge based on what has been called the causal requirement (roughly, the claim that any objects of which we have knowledge must be such that we stand in an appropriate causal relation with them). I argue that there is no plausible form of the causal requirement that constitutes a good objection to the existence of a priori knowledge; along the way, I offer an argument for the conclusion that propositions cannot be concrete objects of any sort, and point out that it is quite possible to think of abstract objects as capable of standing in causal relations with us.Less
In this chapter, I examine a priori knowledge from the perspective of my account of warrant. According to the epistemological tradition, what is known a priori is known, somehow, prior to or independently of experience; in the first section of this chapter, I attempt to clarify this claim and describe some of the general features of a priori belief and knowledge. In the second section I argue, among other things, that a priori warrant (more precisely, intuitive warrant) is fallible and comes in degrees. I go on to consider an objection to the existence of a priori knowledge based on what has been called the causal requirement (roughly, the claim that any objects of which we have knowledge must be such that we stand in an appropriate causal relation with them). I argue that there is no plausible form of the causal requirement that constitutes a good objection to the existence of a priori knowledge; along the way, I offer an argument for the conclusion that propositions cannot be concrete objects of any sort, and point out that it is quite possible to think of abstract objects as capable of standing in causal relations with us.
Linda Wetzel
- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262013017
- eISBN:
- 9780262259279
- Item type:
- book
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262013017.001.0001
- Subject:
- Philosophy, General
There is a widely recognized but infrequently discussed distinction between the spatiotemporal furniture of the world (tokens) and the types of which they are instances. Words come in both types and ...
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There is a widely recognized but infrequently discussed distinction between the spatiotemporal furniture of the world (tokens) and the types of which they are instances. Words come in both types and tokens — for example, there is only one word type “the,” but there are numerous tokens of it on this page — as do symphonies, bears, chess games, and many other types of things. This book examines the distinction between types and tokens and argues that types exist, even as abstract objects since they lack a unique spatiotemporal location. It demonstrates the ubiquity of references to (and quantifications over) types in science and ordinary language; types have to be reckoned with, and cannot simply be swept under the rug. The book argues that there are such things as types by undermining the epistemological arguments against abstract objects and offering extended original arguments demonstrating the failure of nominalistic attempts to paraphrase away such references to (and quantifications over) types. It then focuses on the relation between types and their tokens, especially for words, showing that there is nothing which all tokens of a type need to have in common other than being tokens of that type. Finally, the book considers an oft-overlooked problem for realism having to do with types occurring in other types (such as words in a sentence) and proposes an original solution, extending the discussion from words and expressions to other types that structurally involve other types (flags and stars and stripes; molecules and atoms; sonatas and notes).Less
There is a widely recognized but infrequently discussed distinction between the spatiotemporal furniture of the world (tokens) and the types of which they are instances. Words come in both types and tokens — for example, there is only one word type “the,” but there are numerous tokens of it on this page — as do symphonies, bears, chess games, and many other types of things. This book examines the distinction between types and tokens and argues that types exist, even as abstract objects since they lack a unique spatiotemporal location. It demonstrates the ubiquity of references to (and quantifications over) types in science and ordinary language; types have to be reckoned with, and cannot simply be swept under the rug. The book argues that there are such things as types by undermining the epistemological arguments against abstract objects and offering extended original arguments demonstrating the failure of nominalistic attempts to paraphrase away such references to (and quantifications over) types. It then focuses on the relation between types and their tokens, especially for words, showing that there is nothing which all tokens of a type need to have in common other than being tokens of that type. Finally, the book considers an oft-overlooked problem for realism having to do with types occurring in other types (such as words in a sentence) and proposes an original solution, extending the discussion from words and expressions to other types that structurally involve other types (flags and stars and stripes; molecules and atoms; sonatas and notes).
Friederike Moltmann
- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199608744
- eISBN:
- 9780191747700
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199608744.001.0001
- Subject:
- Philosophy, Philosophy of Language, Metaphysics/Epistemology
Abstract objects such as properties, propositions, numbers, degrees, and expression types are at the centre of many philosophical debates. Philosophers and linguists alike generally hold the view ...
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Abstract objects such as properties, propositions, numbers, degrees, and expression types are at the centre of many philosophical debates. Philosophers and linguists alike generally hold the view that natural language allows rather generously for reference to abstracts objects of the various sorts. The project of this book is to investigate in a fully systematic way whether and how natural language permits reference to abstract objects. For that purpose, the book will introduce a great range of new linguistic generalizations and make systematic use of recent semantic and syntactic theories. It will arrive at an ontology that differs rather radically from the one that philosophers, but also linguists, generally take natural language to involve. Reference to abstract objects is much more marginal than is generally thought. Instead of making reference to abstract objects, natural language, with its more central terms and constructions, makes reference to (concrete) particulars, especially tropes, as well as pluralities of particulars. Reference to abstract objects is generally reserved for syntactically complex and less central terms of the sort the property of being wise or the number eight.Less
Abstract objects such as properties, propositions, numbers, degrees, and expression types are at the centre of many philosophical debates. Philosophers and linguists alike generally hold the view that natural language allows rather generously for reference to abstracts objects of the various sorts. The project of this book is to investigate in a fully systematic way whether and how natural language permits reference to abstract objects. For that purpose, the book will introduce a great range of new linguistic generalizations and make systematic use of recent semantic and syntactic theories. It will arrive at an ontology that differs rather radically from the one that philosophers, but also linguists, generally take natural language to involve. Reference to abstract objects is much more marginal than is generally thought. Instead of making reference to abstract objects, natural language, with its more central terms and constructions, makes reference to (concrete) particulars, especially tropes, as well as pluralities of particulars. Reference to abstract objects is generally reserved for syntactically complex and less central terms of the sort the property of being wise or the number eight.
Crispin Wright
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780198236399
- eISBN:
- 9780191597565
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198236395.003.0007
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This paper starts by offering a brief reconstruction of the Neo‐Fregean approach as suggested in Frege's Conception of Numbers as Objects and distinguishes various challenges against the method of ...
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This paper starts by offering a brief reconstruction of the Neo‐Fregean approach as suggested in Frege's Conception of Numbers as Objects and distinguishes various challenges against the method of Abstraction. It then focuses on one line of criticism––Rejectionism––which is endorsed by Field in his Review of the previously mentioned book. The thought is to grant that the method of abstraction provides singular terms, however questions its ability to produce true statements. Furthermore, Field draws an analogy between the stipulation of Hume's Principle, which commits one to the existence of numbers and the ontological argument, which commits one to the existence of God. It is then shown that this analogy is amiss and that there is no real point of affinity with the Fregean platonist's ontological strategy and the ontological arguments. A further objection concerning the tacit ontological commitments on the right hand side of Abstraction Principle is discussed. The paper concludes considering ‘the onus of proof’ – issue for Nominalism‐Platonism debates.Less
This paper starts by offering a brief reconstruction of the Neo‐Fregean approach as suggested in Frege's Conception of Numbers as Objects and distinguishes various challenges against the method of Abstraction. It then focuses on one line of criticism––Rejectionism––which is endorsed by Field in his Review of the previously mentioned book. The thought is to grant that the method of abstraction provides singular terms, however questions its ability to produce true statements. Furthermore, Field draws an analogy between the stipulation of Hume's Principle, which commits one to the existence of numbers and the ontological argument, which commits one to the existence of God. It is then shown that this analogy is amiss and that there is no real point of affinity with the Fregean platonist's ontological strategy and the ontological arguments. A further objection concerning the tacit ontological commitments on the right hand side of Abstraction Principle is discussed. The paper concludes considering ‘the onus of proof’ – issue for Nominalism‐Platonism debates.
Colin McGinn
- Published in print:
- 2002
- Published Online:
- November 2003
- ISBN:
- 9780199251582
- eISBN:
- 9780191598012
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199251584.003.0011
- Subject:
- Philosophy, Metaphysics/Epistemology
McGinn's aim is two‐fold: to undermine both descriptive and causal theories of reference, and to argue for his preferred, ‘contextual’ theory of reference. McGinn is moved to this position by ...
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McGinn's aim is two‐fold: to undermine both descriptive and causal theories of reference, and to argue for his preferred, ‘contextual’ theory of reference. McGinn is moved to this position by emphasizing indexicals—which he takes to be the primary referential devices—rather than proper names. Linguistic reference, for McGinn, is a conventional activity governed by rules that prescribe the spatio‐temporal conditions of correct use; the semantic referent of a speaker's term is given by combining its linguistic meaning with the spatio‐temporal context in which the speaker is located. McGinn concludes his defence of this theory by demonstrating the plausibility of its implications for such topics as abstract objects, self‐reference, attribution, the language of thought hypothesis, truth, and the reducibility of reference.Less
McGinn's aim is two‐fold: to undermine both descriptive and causal theories of reference, and to argue for his preferred, ‘contextual’ theory of reference. McGinn is moved to this position by emphasizing indexicals—which he takes to be the primary referential devices—rather than proper names. Linguistic reference, for McGinn, is a conventional activity governed by rules that prescribe the spatio‐temporal conditions of correct use; the semantic referent of a speaker's term is given by combining its linguistic meaning with the spatio‐temporal context in which the speaker is located. McGinn concludes his defence of this theory by demonstrating the plausibility of its implications for such topics as abstract objects, self‐reference, attribution, the language of thought hypothesis, truth, and the reducibility of reference.
Linda Wetzel
- Published in print:
- 2009
- Published Online:
- August 2013
- ISBN:
- 9780262013017
- eISBN:
- 9780262259279
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262013017.003.0027
- Subject:
- Philosophy, General
This chapter presents some objections to the argument contending that if a conclusion is an immediate consequence of the data, the burden of proof lies on those who would deny it. The main objection ...
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This chapter presents some objections to the argument contending that if a conclusion is an immediate consequence of the data, the burden of proof lies on those who would deny it. The main objection posits that each claim appearing to refer to a type is merely a manner of speaking for a claim that does not actually refer to a type. Because such apparent references can be “paraphrased away,” they are harmless, and we need not suppose that types exist. In denying the existence of types, the main motivation is epistemological in nature: knowledge of types, which are abstract objects, is not possible since knowledge requires some sort of relationship, and abstract objects do not stand in causal relations with humans.Less
This chapter presents some objections to the argument contending that if a conclusion is an immediate consequence of the data, the burden of proof lies on those who would deny it. The main objection posits that each claim appearing to refer to a type is merely a manner of speaking for a claim that does not actually refer to a type. Because such apparent references can be “paraphrased away,” they are harmless, and we need not suppose that types exist. In denying the existence of types, the main motivation is epistemological in nature: knowledge of types, which are abstract objects, is not possible since knowledge requires some sort of relationship, and abstract objects do not stand in causal relations with humans.
Andrew Kania
- Published in print:
- 2013
- Published Online:
- January 2013
- ISBN:
- 9780199691494
- eISBN:
- 9780191746277
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199691494.003.0010
- Subject:
- Philosophy, Aesthetics, Metaphysics/Epistemology
Ontological theories of musical works fall into two broad classes, according to whether they take musical works to be abstract objects of some sort. The chapter uses the terms ‘Platonism’ and ...
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Ontological theories of musical works fall into two broad classes, according to whether they take musical works to be abstract objects of some sort. The chapter uses the terms ‘Platonism’ and ‘nominalism’ to refer to these two kinds of theory. It first considers recent debates within Platonism about musical works—the theory that musical works are abstract objects. It then considers reasons to be suspicious of such a view, motivating a consideration of nominalist theories of musical works. The chapter argues for two conclusions: first, that there are no compelling reasons to be a nominalist about musical works in particular, i.e. that nominalism about musical works rests on arguments for thoroughgoing nominalism, and, second, that if Platonism fails, fictionalism about musical works is to be preferred to other nominalist ontologies of musical works.Less
Ontological theories of musical works fall into two broad classes, according to whether they take musical works to be abstract objects of some sort. The chapter uses the terms ‘Platonism’ and ‘nominalism’ to refer to these two kinds of theory. It first considers recent debates within Platonism about musical works—the theory that musical works are abstract objects. It then considers reasons to be suspicious of such a view, motivating a consideration of nominalist theories of musical works. The chapter argues for two conclusions: first, that there are no compelling reasons to be a nominalist about musical works in particular, i.e. that nominalism about musical works rests on arguments for thoroughgoing nominalism, and, second, that if Platonism fails, fictionalism about musical works is to be preferred to other nominalist ontologies of musical works.
Alan Weir
- Published in print:
- 2005
- Published Online:
- July 2005
- ISBN:
- 9780195148770
- eISBN:
- 9780199835560
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195148770.003.0014
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Mathematics poses a difficult problem for methodological naturalists, those who embrace scientific method, and also for ontological naturalists who eschew non-physical entities such as Cartesian ...
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Mathematics poses a difficult problem for methodological naturalists, those who embrace scientific method, and also for ontological naturalists who eschew non-physical entities such as Cartesian souls. Mathematics seems both essential to science but also committed to abstract non-physical entities while methodologically it seems to have no place for experiment or empirical confirmation. The chapter critically reviews a number of responses naturalists have made including logicism, Quinean radical empiricism, and Penelope Maddy’s variant thereof and suggests some further problems both for ontological and for methodological naturalists.Less
Mathematics poses a difficult problem for methodological naturalists, those who embrace scientific method, and also for ontological naturalists who eschew non-physical entities such as Cartesian souls. Mathematics seems both essential to science but also committed to abstract non-physical entities while methodologically it seems to have no place for experiment or empirical confirmation. The chapter critically reviews a number of responses naturalists have made including logicism, Quinean radical empiricism, and Penelope Maddy’s variant thereof and suggests some further problems both for ontological and for methodological naturalists.
Christy Mag Uidhir
- Published in print:
- 2013
- Published Online:
- January 2013
- ISBN:
- 9780199691494
- eISBN:
- 9780191746277
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199691494.003.0001
- Subject:
- Philosophy, Aesthetics, Metaphysics/Epistemology
The introduction claims there is a tension between philosophical aesthetics and contemporary metaphysics with respect to the broad account of abstract objects as standardly employed. The issue of ...
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The introduction claims there is a tension between philosophical aesthetics and contemporary metaphysics with respect to the broad account of abstract objects as standardly employed. The issue of art-abstracta appears to give rise to what the author calls a paradox of standards: an art-ontological assumption (there are such things as art-abstracta), a metaphysical assumption (abstracta are non-spatiotemporal and causally inert), and an art-theoretical assumption (artworks must be created), though each standard if not foundational within its respective domain of enquiry, when taken together nevertheless form an inconsistent set. The author argues that the standardly available methods of resolving the paradox appear to be incommensurate with any minimally responsible art-realism. He then suggests an alternative account of how best to view the relationship between philosophical aesthetics and contemporary metaphysics to resolve the paradox of standards and discusses what consequences this relationship may have for the ontology of art.Less
The introduction claims there is a tension between philosophical aesthetics and contemporary metaphysics with respect to the broad account of abstract objects as standardly employed. The issue of art-abstracta appears to give rise to what the author calls a paradox of standards: an art-ontological assumption (there are such things as art-abstracta), a metaphysical assumption (abstracta are non-spatiotemporal and causally inert), and an art-theoretical assumption (artworks must be created), though each standard if not foundational within its respective domain of enquiry, when taken together nevertheless form an inconsistent set. The author argues that the standardly available methods of resolving the paradox appear to be incommensurate with any minimally responsible art-realism. He then suggests an alternative account of how best to view the relationship between philosophical aesthetics and contemporary metaphysics to resolve the paradox of standards and discusses what consequences this relationship may have for the ontology of art.
