Andy Clark
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195333213
- eISBN:
- 9780199868858
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195333213.003.0010
- Subject:
- Philosophy, Philosophy of Mind
This chapter presents some concluding thoughts. It argues that work on embodiment, action, and cognitive extension likewise invites us to view mind and cognition in a new and illuminating manner. The ...
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This chapter presents some concluding thoughts. It argues that work on embodiment, action, and cognitive extension likewise invites us to view mind and cognition in a new and illuminating manner. The human mind emerges at the productive interface of brain, body, and social and material world. Unravelling the workings of these embodied, embedded, and sometimes extended minds requires an unusual mix of neuroscience, computational, dynamical, and information-theoretic understandings, ‘brute’ physiology, ecological sensitivity, and attention to the stacked designer cocoons in which we grow, work, think, and act.Less
This chapter presents some concluding thoughts. It argues that work on embodiment, action, and cognitive extension likewise invites us to view mind and cognition in a new and illuminating manner. The human mind emerges at the productive interface of brain, body, and social and material world. Unravelling the workings of these embodied, embedded, and sometimes extended minds requires an unusual mix of neuroscience, computational, dynamical, and information-theoretic understandings, ‘brute’ physiology, ecological sensitivity, and attention to the stacked designer cocoons in which we grow, work, think, and act.
Roman Kossak and James H. Schmerl
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568278
- eISBN:
- 9780191718199
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568278.003.0002
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter introduces some techniques for constructing elementary simple extensions. In particular, it includes proof of the existence of superminimal elementary end extensions of countable models ...
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This chapter introduces some techniques for constructing elementary simple extensions. In particular, it includes proof of the existence of superminimal elementary end extensions of countable models and a construction of a Jónsson model. The MacDowell-Specker Theorem is proved and some of its consequences derived, including results on conservative extensions, rather classless models and amalgamations. The chapter concludes with a discussion of nonelementary extensions and the theorem of Wilkie on end extensions which are not σ1-elementary.Less
This chapter introduces some techniques for constructing elementary simple extensions. In particular, it includes proof of the existence of superminimal elementary end extensions of countable models and a construction of a Jónsson model. The MacDowell-Specker Theorem is proved and some of its consequences derived, including results on conservative extensions, rather classless models and amalgamations. The chapter concludes with a discussion of nonelementary extensions and the theorem of Wilkie on end extensions which are not σ1-elementary.
Wallace Matson
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199812691
- eISBN:
- 9780199919420
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199812691.003.0021
- Subject:
- Philosophy, History of Philosophy
Spinoza, more concerned than Hobbes with the ancient conception of the role of philosophy in delineating the Good Life, made Substance, God, and Nature into synonyms. God is eternal, free, and ...
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Spinoza, more concerned than Hobbes with the ancient conception of the role of philosophy in delineating the Good Life, made Substance, God, and Nature into synonyms. God is eternal, free, and all-powerful, but in no way personal, operating for no end, but from the necessity of its nature. Nothing is contingent. This entity, of whose infinite Attributes we know two, Thought and Extension, and whose Modes are the particular things (including us) of our experience, is all there is. Mind and Body are “the same thing, expressed in two ways.” A particular mind is composed of Ideas –beliefs, active entities, not the “dumb pictures on a tablet” of Descartes. Some ideas are adequate, others are inadequate, “confused and fragmentary.” The more we replace our inadequate ideas by adequate ones, the closer we attain to blessedness, and indeed share in the eternity of God.Less
Spinoza, more concerned than Hobbes with the ancient conception of the role of philosophy in delineating the Good Life, made Substance, God, and Nature into synonyms. God is eternal, free, and all-powerful, but in no way personal, operating for no end, but from the necessity of its nature. Nothing is contingent. This entity, of whose infinite Attributes we know two, Thought and Extension, and whose Modes are the particular things (including us) of our experience, is all there is. Mind and Body are “the same thing, expressed in two ways.” A particular mind is composed of Ideas –beliefs, active entities, not the “dumb pictures on a tablet” of Descartes. Some ideas are adequate, others are inadequate, “confused and fragmentary.” The more we replace our inadequate ideas by adequate ones, the closer we attain to blessedness, and indeed share in the eternity of God.
Katherine Hawley
- Published in print:
- 2004
- Published Online:
- October 2011
- ISBN:
- 9780199275434
- eISBN:
- 9780191699818
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199275434.001.0001
- Subject:
- Philosophy, Metaphysics/Epistemology
How do things persist? Are material objects spread out through time just as they are spread out through space? Or is temporal persistence quite different from spatial extension? This key question ...
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How do things persist? Are material objects spread out through time just as they are spread out through space? Or is temporal persistence quite different from spatial extension? This key question lies at the heart of any metaphysical exploration of the material world, and it plays a crucial part in debates about personal identity and survival. This book explores and compares three theories of persistence — endurance, perdurance, and stage theories — investigating the ways in which they attempt to account for the world around us. Having provided valuable clarification of its two main rivals, the book concludes by advocating stage theory. Such a basic issue about the nature of the physical world naturally has close ties with other central philosophical problems. This book includes discussions of change and parthood, of how we refer to material objects at different times, of the doctrine of Humean supervenience, and of the modal features of material things. In particular, it contains new accounts of the nature of worldly vagueness, and of what binds material things together over time, distinguishing the career of a natural object from an arbitrary sequence of events. Each chapter concludes with a reflection about the impact of these metaphysical debates upon questions about our personal identity and survival.Less
How do things persist? Are material objects spread out through time just as they are spread out through space? Or is temporal persistence quite different from spatial extension? This key question lies at the heart of any metaphysical exploration of the material world, and it plays a crucial part in debates about personal identity and survival. This book explores and compares three theories of persistence — endurance, perdurance, and stage theories — investigating the ways in which they attempt to account for the world around us. Having provided valuable clarification of its two main rivals, the book concludes by advocating stage theory. Such a basic issue about the nature of the physical world naturally has close ties with other central philosophical problems. This book includes discussions of change and parthood, of how we refer to material objects at different times, of the doctrine of Humean supervenience, and of the modal features of material things. In particular, it contains new accounts of the nature of worldly vagueness, and of what binds material things together over time, distinguishing the career of a natural object from an arbitrary sequence of events. Each chapter concludes with a reflection about the impact of these metaphysical debates upon questions about our personal identity and survival.
Alfredo Bellen and Marino Zennaro
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198506546
- eISBN:
- 9780191709609
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506546.003.0005
- Subject:
- Mathematics, Numerical Analysis
This chapter presents the continuous Runge-Kutta methods for ODEs. In addition to providing the basics for the construction of the standard approach for DDEs, it constitutes one of the first ...
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This chapter presents the continuous Runge-Kutta methods for ODEs. In addition to providing the basics for the construction of the standard approach for DDEs, it constitutes one of the first systematic collections of results on continuous Runge-Kutta methods. All the results in the literature are homogenized under a unifying point of view. The methods are divided in two classes, namely the first and the second class. The first class includes continuous extensions of Runge-Kutta methods constructed using the already available stage values. The second class includes the continuous extensions that make use of additional stage values. Special attention is given to the natural continuous extensions for which a kind of superconvergence result is given in the application to problems with driving equation.Less
This chapter presents the continuous Runge-Kutta methods for ODEs. In addition to providing the basics for the construction of the standard approach for DDEs, it constitutes one of the first systematic collections of results on continuous Runge-Kutta methods. All the results in the literature are homogenized under a unifying point of view. The methods are divided in two classes, namely the first and the second class. The first class includes continuous extensions of Runge-Kutta methods constructed using the already available stage values. The second class includes the continuous extensions that make use of additional stage values. Special attention is given to the natural continuous extensions for which a kind of superconvergence result is given in the application to problems with driving equation.
Mark Wilson
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199269259
- eISBN:
- 9780191710155
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269259.003.0008
- Subject:
- Philosophy, Philosophy of Language
This chapter investigates the implications of these conclusions with respect to rule-following and rigor's implementation. It begins with a survey of common philosophical tensions over these topics ...
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This chapter investigates the implications of these conclusions with respect to rule-following and rigor's implementation. It begins with a survey of common philosophical tensions over these topics and recommends a seasonal sensitivity with respect to the competing demands that syntax and ‘semantic picture’ place upon a usage. The historical travails of Oliver Heaviside's operational calculus provide a vivid illustration of how reasonable standards of rigor must adapt and shift over time.Less
This chapter investigates the implications of these conclusions with respect to rule-following and rigor's implementation. It begins with a survey of common philosophical tensions over these topics and recommends a seasonal sensitivity with respect to the competing demands that syntax and ‘semantic picture’ place upon a usage. The historical travails of Oliver Heaviside's operational calculus provide a vivid illustration of how reasonable standards of rigor must adapt and shift over time.
Silvio Cruschina
- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199759613
- eISBN:
- 9780199932658
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199759613.003.0007
- Subject:
- Linguistics, Syntax and Morphology
This chapter summarizes the main points and findings of the book. The book discusses the notion of discourse‐related features and their relevance for linguistic theory and parametric variation. The ...
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This chapter summarizes the main points and findings of the book. The book discusses the notion of discourse‐related features and their relevance for linguistic theory and parametric variation. The principal aim is to determine the syntax of the functional projections associated with these types of features and to account for the marked word orders, in particular the fronting phenomena, found in Romance. The analysis carried out leads us to the conclusion that information structure categories play an active role in the syntax in the form of discourse-related features able to trigger specific syntactic operations. In addition, it reveals that the association of focus with both overt and covert operators is one of the most important factors in the regulation and assessment of the information structure of the sentence and, accordingly, of marked word orders.Less
This chapter summarizes the main points and findings of the book. The book discusses the notion of discourse‐related features and their relevance for linguistic theory and parametric variation. The principal aim is to determine the syntax of the functional projections associated with these types of features and to account for the marked word orders, in particular the fronting phenomena, found in Romance. The analysis carried out leads us to the conclusion that information structure categories play an active role in the syntax in the form of discourse-related features able to trigger specific syntactic operations. In addition, it reveals that the association of focus with both overt and covert operators is one of the most important factors in the regulation and assessment of the information structure of the sentence and, accordingly, of marked word orders.
Leon Ehrenpreis
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198509783
- eISBN:
- 9780191709166
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509783.003.0009
- Subject:
- Mathematics, Mathematical Physics
This chapter shows how the book's main theory allows for the treatment of extension problems for partial differential equations. The culmination of this is a solution of the asymptotic edge of the ...
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This chapter shows how the book's main theory allows for the treatment of extension problems for partial differential equations. The culmination of this is a solution of the asymptotic edge of the wedge theorem — a problem that was posed by Nirenberg and C. Fefferman.Less
This chapter shows how the book's main theory allows for the treatment of extension problems for partial differential equations. The culmination of this is a solution of the asymptotic edge of the wedge theorem — a problem that was posed by Nirenberg and C. Fefferman.
Terry Lyons and Zhongmin Qian
- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198506485
- eISBN:
- 9780191709395
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506485.003.0003
- Subject:
- Mathematics, Probability / Statistics
This chapter defines rough paths. If the path has good smoothness properties, then its chords (the Abelian version of the description) provide an adequate description and can be used to predict its ...
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This chapter defines rough paths. If the path has good smoothness properties, then its chords (the Abelian version of the description) provide an adequate description and can be used to predict its effects on a controlled system. A rough path uses a nilpotent group element, computed using Chen iterated integrals as an extended description. The chapter introduces the notion of a control and proves several basic results for paths whose nilpotent descriptors are appropriately controlled, and gives the formal definition of a rough path. Key theorems are proved. In particular, the extension theorem allowing one to compute all iterated integrals of a rough path, and the notion of an almost multiplicative functional, which is important for the development of an integration theory, are both introduced.Less
This chapter defines rough paths. If the path has good smoothness properties, then its chords (the Abelian version of the description) provide an adequate description and can be used to predict its effects on a controlled system. A rough path uses a nilpotent group element, computed using Chen iterated integrals as an extended description. The chapter introduces the notion of a control and proves several basic results for paths whose nilpotent descriptors are appropriately controlled, and gives the formal definition of a rough path. Key theorems are proved. In particular, the extension theorem allowing one to compute all iterated integrals of a rough path, and the notion of an almost multiplicative functional, which is important for the development of an integration theory, are both introduced.
Mathew Penrose
- Published in print:
- 2003
- Published Online:
- September 2007
- ISBN:
- 9780198506263
- eISBN:
- 9780191707858
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198506263.003.0003
- Subject:
- Mathematics, Probability / Statistics
This chapter is concerned with the number of embedded copies of a given finite graph γ in the random geometric graph G(n,r) (for example the number of edges or triangles). It is shown that if γ has k ...
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This chapter is concerned with the number of embedded copies of a given finite graph γ in the random geometric graph G(n,r) (for example the number of edges or triangles). It is shown that if γ has k vertices and if r is chosen so that the number of copies of γ has mean value approaching a constant, then it is asymptotically Poisson distributed; if its mean tends to infinity, then after scaling and centring it is asymptotically normal. Similar results are given for the number of isolated components of G(n,r) isomorphic to γ. Multivariate extensions are also presented, with explicit formulae for limiting means and covariances.Less
This chapter is concerned with the number of embedded copies of a given finite graph γ in the random geometric graph G(n,r) (for example the number of edges or triangles). It is shown that if γ has k vertices and if r is chosen so that the number of copies of γ has mean value approaching a constant, then it is asymptotically Poisson distributed; if its mean tends to infinity, then after scaling and centring it is asymptotically normal. Similar results are given for the number of isolated components of G(n,r) isomorphic to γ. Multivariate extensions are also presented, with explicit formulae for limiting means and covariances.
Edwin L. Battistella
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195367126
- eISBN:
- 9780199867356
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195367126.003.0014
- Subject:
- Linguistics, English Language
This chapter takes up the emergence of correspondence education as a means of serving workers and others to whom traditional university education was unavailable.
This chapter takes up the emergence of correspondence education as a means of serving workers and others to whom traditional university education was unavailable.
Pieter A. M. Seuren
- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780199559473
- eISBN:
- 9780191721137
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199559473.003.0006
- Subject:
- Linguistics, Semantics and Pragmatics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics
The Fregean and the modern schemata for extensions and intensions of terms, predicates, and propositions are subjected to a new critique and are revised accordingly, whereby an intensional ontology ...
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The Fregean and the modern schemata for extensions and intensions of terms, predicates, and propositions are subjected to a new critique and are revised accordingly, whereby an intensional ontology of virtual objects and facts is developed, in the light of the original Fregean problem of substitution salva veritate. Categories of reference values are defined for terms and for propositional structures.Less
The Fregean and the modern schemata for extensions and intensions of terms, predicates, and propositions are subjected to a new critique and are revised accordingly, whereby an intensional ontology of virtual objects and facts is developed, in the light of the original Fregean problem of substitution salva veritate. Categories of reference values are defined for terms and for propositional structures.
John L. Bell
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198568520
- eISBN:
- 9780191717581
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568520.003.0007
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
The technique of iterating Boolean extensions is introduced in this chapter and applied to prove the independence of Souslin’s hypothesis concerning the structure of densely ordered sets.
The technique of iterating Boolean extensions is introduced in this chapter and applied to prove the independence of Souslin’s hypothesis concerning the structure of densely ordered sets.
Roman Kossak and James H. Schmerl
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568278
- eISBN:
- 9780191718199
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568278.003.0007
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter presents the theorem of Kirby and Paris characterizing strong cuts in models of arithmetic. In the build up to the theorem, semiregular and regular cuts are also discussed. Other results ...
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This chapter presents the theorem of Kirby and Paris characterizing strong cuts in models of arithmetic. In the build up to the theorem, semiregular and regular cuts are also discussed. Other results in this chapter include a theorem on nonconservative minimal extensions and two important model theoretic characterizations of Peano Arithmetic, one due to Kaye and one to Wilkie.Less
This chapter presents the theorem of Kirby and Paris characterizing strong cuts in models of arithmetic. In the build up to the theorem, semiregular and regular cuts are also discussed. Other results in this chapter include a theorem on nonconservative minimal extensions and two important model theoretic characterizations of Peano Arithmetic, one due to Kaye and one to Wilkie.
Alan Barnard
- Published in print:
- 2007
- Published Online:
- January 2012
- ISBN:
- 9780197264140
- eISBN:
- 9780191734489
- Item type:
- chapter
- Publisher:
- British Academy
- DOI:
- 10.5871/bacad/9780197264140.003.0002
- Subject:
- Archaeology, Prehistoric Archaeology
This chapter begins by outlining two proposed modes of thought, which are characterized by opposite perceptions in at least four domains: saving versus consumption (which reflect notions of time and ...
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This chapter begins by outlining two proposed modes of thought, which are characterized by opposite perceptions in at least four domains: saving versus consumption (which reflect notions of time and work); decision-making and political hierarchy; degree and kind of kin category extension; and notions of land, place, and settlement. All of these have implications for understanding group structure, transhumance, migration, and so on. The chapter then addresses the question of whether Mesolithic thought persisted into the Neolithic. It argues that mode of thought is much slower to change than mode of production. Social relations retain the structures of hunter-gatherer times if these are deeply rooted in cultural understandings of sociality. The existence nearby of agro-pastoralists does not make former hunter-gatherers think more like agro-pastoralists; it may even accentuate the differences in their thinking by making each side more aware of what makes them, say, Mesolithic or Neolithic.Less
This chapter begins by outlining two proposed modes of thought, which are characterized by opposite perceptions in at least four domains: saving versus consumption (which reflect notions of time and work); decision-making and political hierarchy; degree and kind of kin category extension; and notions of land, place, and settlement. All of these have implications for understanding group structure, transhumance, migration, and so on. The chapter then addresses the question of whether Mesolithic thought persisted into the Neolithic. It argues that mode of thought is much slower to change than mode of production. Social relations retain the structures of hunter-gatherer times if these are deeply rooted in cultural understandings of sociality. The existence nearby of agro-pastoralists does not make former hunter-gatherers think more like agro-pastoralists; it may even accentuate the differences in their thinking by making each side more aware of what makes them, say, Mesolithic or Neolithic.
Ronald W. Langacker
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780195331967
- eISBN:
- 9780199868209
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195331967.003.0010
- Subject:
- Linguistics, Syntax and Morphology
Personal pronouns and proper names are inherently grounded. The structure of other nominals tends to reflect semantic function, with the head noun as core, grounding as the outermost layer, and ...
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Personal pronouns and proper names are inherently grounded. The structure of other nominals tends to reflect semantic function, with the head noun as core, grounding as the outermost layer, and modifiers in between. Noun modification is varied both semantically and in its structural implementation. When nominal and relational expressions combine grammatically, there is often a discrepancy between the nominal expression's profile and the entity which participates most directly in the relationship—its active zone with respect to that relationship. Noun classes have varying degrees of semantic motivation. Distributional classes, defined by participation in particular patterns, may be semantically arbitrary. While gender-type classes have semantic prototypes, the class as a whole is defined by a consistent set of grammatical behaviors. In a usage based approach, such classes are characterized by families of constructional schemas. Noun classifiers likewise have prototypical values semantically extended to a range of other cases. They represent a distinct kind of nominal structure in which the classifier functions as a schematic head noun. Classifiers are related to quantifier constructions allowing the unitization of a mass. Nouns bear various kinds of grammatical markings. Most intrinsic to nouns are elements deriving them from other classes. There is no sharp distinction between such derivation and noun inflection. Markings of gender and number are intermediate. More extrinsic are markings indicating a nominal's role in higher-level grammatical constructions. These are meaningful in a symbolic account of grammar. Such an account accommodates both agreement—the multiple realization of semantic specifications—and cases where multiple specifications are realized by a single, unanalyzable form. Analyzability is a matter of degree.Less
Personal pronouns and proper names are inherently grounded. The structure of other nominals tends to reflect semantic function, with the head noun as core, grounding as the outermost layer, and modifiers in between. Noun modification is varied both semantically and in its structural implementation. When nominal and relational expressions combine grammatically, there is often a discrepancy between the nominal expression's profile and the entity which participates most directly in the relationship—its active zone with respect to that relationship. Noun classes have varying degrees of semantic motivation. Distributional classes, defined by participation in particular patterns, may be semantically arbitrary. While gender-type classes have semantic prototypes, the class as a whole is defined by a consistent set of grammatical behaviors. In a usage based approach, such classes are characterized by families of constructional schemas. Noun classifiers likewise have prototypical values semantically extended to a range of other cases. They represent a distinct kind of nominal structure in which the classifier functions as a schematic head noun. Classifiers are related to quantifier constructions allowing the unitization of a mass. Nouns bear various kinds of grammatical markings. Most intrinsic to nouns are elements deriving them from other classes. There is no sharp distinction between such derivation and noun inflection. Markings of gender and number are intermediate. More extrinsic are markings indicating a nominal's role in higher-level grammatical constructions. These are meaningful in a symbolic account of grammar. Such an account accommodates both agreement—the multiple realization of semantic specifications—and cases where multiple specifications are realized by a single, unanalyzable form. Analyzability is a matter of degree.
Ronald W. Langacker
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780195331967
- eISBN:
- 9780199868209
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195331967.003.0005
- Subject:
- Linguistics, Syntax and Morphology
Despite being polar opposites conceptually, the two most fundamental grammatical classes—noun and verb—show extensive parallelism. One similarity is that both divide into two major subclasses: count ...
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Despite being polar opposites conceptually, the two most fundamental grammatical classes—noun and verb—show extensive parallelism. One similarity is that both divide into two major subclasses: count vs. mass for nouns, perfective vs. imperfective for verbs. Allowing for the intrinsic conceptual difference between nouns and verbs, these oppositions are precisely the same. The essential feature of count nouns and perfective verbs is that the profiled thing or process is construed as being bounded within the immediate scope in a particular cognitive domain: the domain of instantiation, characterized as the domain where instances of a type are primarily conceived as residing and are distinguished from one another by their locations. For nouns, the domain of instantiation varies, although space is prototypical; for verbs, the relevant domain is always time. Correlated with bounding are other distinguishing properties: internal heterogeneity (for count and perfective) vs. homogeneity (for mass and imperfective); contractibility (the property of masses and imperfectives whereby any subpart of an instance is itself an instance of its type); and expansibility (whereby combining two mass or imperfective instances yields a single, larger instance). Count vs. mass and perfective vs. imperfective are not rigid lexical distinctions, but are malleable owing to alternate construals as well as systematic patterns of extension. The conceptual characterization of perfective and imperfective verbs explains their contrasting behavior with respect to the English progressive and present tense.Less
Despite being polar opposites conceptually, the two most fundamental grammatical classes—noun and verb—show extensive parallelism. One similarity is that both divide into two major subclasses: count vs. mass for nouns, perfective vs. imperfective for verbs. Allowing for the intrinsic conceptual difference between nouns and verbs, these oppositions are precisely the same. The essential feature of count nouns and perfective verbs is that the profiled thing or process is construed as being bounded within the immediate scope in a particular cognitive domain: the domain of instantiation, characterized as the domain where instances of a type are primarily conceived as residing and are distinguished from one another by their locations. For nouns, the domain of instantiation varies, although space is prototypical; for verbs, the relevant domain is always time. Correlated with bounding are other distinguishing properties: internal heterogeneity (for count and perfective) vs. homogeneity (for mass and imperfective); contractibility (the property of masses and imperfectives whereby any subpart of an instance is itself an instance of its type); and expansibility (whereby combining two mass or imperfective instances yields a single, larger instance). Count vs. mass and perfective vs. imperfective are not rigid lexical distinctions, but are malleable owing to alternate construals as well as systematic patterns of extension. The conceptual characterization of perfective and imperfective verbs explains their contrasting behavior with respect to the English progressive and present tense.
Ronald W. Langacker
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780195331967
- eISBN:
- 9780199868209
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195331967.003.0008
- Subject:
- Linguistics, Syntax and Morphology
Language is both cognitive and sociocultural, consisting in conventionally sanctioned patterns of communicative activity. These patterns take the form of schemas abstracted from usage events by the ...
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Language is both cognitive and sociocultural, consisting in conventionally sanctioned patterns of communicative activity. These patterns take the form of schemas abstracted from usage events by the reinforcement of recurring commonalities. Conventional linguistic units are linked by relationships of composition and categorization (either elaboration or extension) and thus form intersecting networks of great complexity. Expressions are interpreted and assessed for well-formedness through categorization by linguistic units. Through a process of interactive activation, particular units are selected to categorize particular facets of an expression. The total set of categorizing relationships constitutes the expression's structural description, and whether the categorizations involve elaboration or extension determines its degree of conventionality. Despite the absence of explicit prohibitions, this model affords an account of distribution, restrictions, and judgments of ungrammaticality. One aspect of grammatical constructions is their characterization at different levels of specificity, including constructional subschemas incorporating specific lexical items. And since one aspect of lexical items is their occurrence in particular constructions, lexicon and grammar are overlapping rather than disjoint. The model accommodates degrees and kinds of regularity, which decomposes into generality, productivity, and compositionality. Regularities include higher-order generalizations, where sets of categorizations or lexical behaviors are themselves schematized to form productive patterns. Among the phenomena described in this manner are patterns of phonological extension (phonological rules), patterns of semantic extension (e.g. general metonymies), and patterns of morphological realization (like conjugation classes).Less
Language is both cognitive and sociocultural, consisting in conventionally sanctioned patterns of communicative activity. These patterns take the form of schemas abstracted from usage events by the reinforcement of recurring commonalities. Conventional linguistic units are linked by relationships of composition and categorization (either elaboration or extension) and thus form intersecting networks of great complexity. Expressions are interpreted and assessed for well-formedness through categorization by linguistic units. Through a process of interactive activation, particular units are selected to categorize particular facets of an expression. The total set of categorizing relationships constitutes the expression's structural description, and whether the categorizations involve elaboration or extension determines its degree of conventionality. Despite the absence of explicit prohibitions, this model affords an account of distribution, restrictions, and judgments of ungrammaticality. One aspect of grammatical constructions is their characterization at different levels of specificity, including constructional subschemas incorporating specific lexical items. And since one aspect of lexical items is their occurrence in particular constructions, lexicon and grammar are overlapping rather than disjoint. The model accommodates degrees and kinds of regularity, which decomposes into generality, productivity, and compositionality. Regularities include higher-order generalizations, where sets of categorizations or lexical behaviors are themselves schematized to form productive patterns. Among the phenomena described in this manner are patterns of phonological extension (phonological rules), patterns of semantic extension (e.g. general metonymies), and patterns of morphological realization (like conjugation classes).
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/9780199278534.003.0008
- Subject:
- Philosophy, History of Philosophy, Philosophy of Language
This chapter traces historically Frege's uncertainty about how to complete his logicist project by invoking extensions of concepts. The uncertainty is placed in the context of his view that experts ...
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This chapter traces historically Frege's uncertainty about how to complete his logicist project by invoking extensions of concepts. The uncertainty is placed in the context of his view that experts can incompletely understand the senses of mathematical expressions. Frege's discussions of incomplete understanding are surveyed. It appears that for some years Frege attempted to avoid invoking extensions of concepts by appealing to contextual definition. By contrast, during the same period, Frege was working out the approach that he eventually took in Basic Laws of Arithmetic, in which he attempted to justify, on purely logical grounds, the existence of infinitely many logical objects; the numbers, taken as extensions of concepts. Much of his thinking centered on how to understand the singular term ‘the concept F’. Frege's justification ultimately centered on his attempt to justify Law V, the principle that leads to contradiction in Russell's paradox. He tried to justify Law V by holding that reference to concepts on the left side of the principle's bi-conditional has the same sense as reference to extensions of concepts on the right side. Frege's claiming that the purported logical law was, in effect, a tautology, while at the same time being uncertain about whether to believe the (claimed) tautology, is explained with Frege's notion of incomplete understanding. Frege never regarded Law V as obvious, not even when he thought it to be self-evident. Self-evident propositions could come to be obvious only when completely understood, and complete understanding required mastery of theory, not simply immediate insight.Less
This chapter traces historically Frege's uncertainty about how to complete his logicist project by invoking extensions of concepts. The uncertainty is placed in the context of his view that experts can incompletely understand the senses of mathematical expressions. Frege's discussions of incomplete understanding are surveyed. It appears that for some years Frege attempted to avoid invoking extensions of concepts by appealing to contextual definition. By contrast, during the same period, Frege was working out the approach that he eventually took in Basic Laws of Arithmetic, in which he attempted to justify, on purely logical grounds, the existence of infinitely many logical objects; the numbers, taken as extensions of concepts. Much of his thinking centered on how to understand the singular term ‘the concept F’. Frege's justification ultimately centered on his attempt to justify Law V, the principle that leads to contradiction in Russell's paradox. He tried to justify Law V by holding that reference to concepts on the left side of the principle's bi-conditional has the same sense as reference to extensions of concepts on the right side. Frege's claiming that the purported logical law was, in effect, a tautology, while at the same time being uncertain about whether to believe the (claimed) tautology, is explained with Frege's notion of incomplete understanding. Frege never regarded Law V as obvious, not even when he thought it to be self-evident. Self-evident propositions could come to be obvious only when completely understood, and complete understanding required mastery of theory, not simply immediate insight.
Geert Booij
- Published in print:
- 2007
- Published Online:
- September 2007
- ISBN:
- 9780199226245
- eISBN:
- 9780191710360
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199226245.003.009
- Subject:
- Linguistics, Syntax and Morphology
The semantic interpretation of complex words is governed by the general principle of compositionality. The semantic scope of morphosyntactic properties of words may be larger than the word on which ...
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The semantic interpretation of complex words is governed by the general principle of compositionality. The semantic scope of morphosyntactic properties of words may be larger than the word on which they are marked. Polysemy is a pervasive phenomenon on the domain of word formation, and can be explained through general mechanisms of meaning extension such as metaphor and metonymy.Less
The semantic interpretation of complex words is governed by the general principle of compositionality. The semantic scope of morphosyntactic properties of words may be larger than the word on which they are marked. Polysemy is a pervasive phenomenon on the domain of word formation, and can be explained through general mechanisms of meaning extension such as metaphor and metonymy.
