George J. Mailath and Larry Samuelson
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780195300796
- eISBN:
- 9780199783700
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195300796.003.0007
- Subject:
- Economics and Finance, Behavioural Economics
This chapter provides the basic technical tools for working with games of imperfect public monitoring, with games of perfect monitoring as a special case. It introduces the central notions of a ...
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This chapter provides the basic technical tools for working with games of imperfect public monitoring, with games of perfect monitoring as a special case. It introduces the central notions of a public strategy and perfect public equilibrium (PPE), and shows that PPE has a recursive structure. Readers particularly interested in imperfect public monitoring can move straight from Chapter 2 to this chapter. This chapter develops and illustrates the ideas of decomposability, enforceability, and self-generation, the basic tools for working with games of incomplete information, as well as presenting the bang-bang theorem.Less
This chapter provides the basic technical tools for working with games of imperfect public monitoring, with games of perfect monitoring as a special case. It introduces the central notions of a public strategy and perfect public equilibrium (PPE), and shows that PPE has a recursive structure. Readers particularly interested in imperfect public monitoring can move straight from Chapter 2 to this chapter. This chapter develops and illustrates the ideas of decomposability, enforceability, and self-generation, the basic tools for working with games of incomplete information, as well as presenting the bang-bang theorem.
Frederick L. Coolidge and Thomas Wynn
- Published in print:
- 2009
- Published Online:
- May 2010
- ISBN:
- 9780199545872
- eISBN:
- 9780191720369
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199545872.003.0013
- Subject:
- Linguistics, Sociolinguistics / Anthropological Linguistics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics
Recursion is considered to be the hallmark of modern language. This chapter addresses fundamental questions about its evolutionary emergence: ‘What is the relationship of recursion to modern language ...
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Recursion is considered to be the hallmark of modern language. This chapter addresses fundamental questions about its evolutionary emergence: ‘What is the relationship of recursion to modern language and thinking?’ and ‘What might be the mechanism or subspecies of recursion that bestows its advantages to cognition?’ In addressing these questions, empirical evidence is presented which shows that recursion requires not only greater working memory capacity but also greater phonological storage capacity. The chapter proposes that recursion arose as a function of an increase in phonological storage capacity and/or working memory capacity. These capacities were enhanced by a genetic neural mutation that occurred sometime between 150,000 and 30,000 years ago. That change made possible longer recursive and canonical utterances and a consequent increase in the complexity and information content of sentences.Less
Recursion is considered to be the hallmark of modern language. This chapter addresses fundamental questions about its evolutionary emergence: ‘What is the relationship of recursion to modern language and thinking?’ and ‘What might be the mechanism or subspecies of recursion that bestows its advantages to cognition?’ In addressing these questions, empirical evidence is presented which shows that recursion requires not only greater working memory capacity but also greater phonological storage capacity. The chapter proposes that recursion arose as a function of an increase in phonological storage capacity and/or working memory capacity. These capacities were enhanced by a genetic neural mutation that occurred sometime between 150,000 and 30,000 years ago. That change made possible longer recursive and canonical utterances and a consequent increase in the complexity and information content of sentences.
Thomas Streicher
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566519
- eISBN:
- 9780191713927
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566519.003.0005
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy
This chapter discusses a notion of universe in toposes, which from a logical point of view gives rise to an extension of Higher Order Intuitionistic Arithmetic (HAH). In this way, one can construct ...
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This chapter discusses a notion of universe in toposes, which from a logical point of view gives rise to an extension of Higher Order Intuitionistic Arithmetic (HAH). In this way, one can construct families of types in the universe by structural recursion and quantify over such families. Further, it shows that (hierarchies of) such universes do exist in all sheaf and realizability toposes. They do not exist instead either in the free topos or in the Vω+ω model of Zermelo set theory. Though universes in the category Set are necessarily of strongly inaccessible cardinality, it remains an open question as to whether toposes with a universe allow one to construct internal models of Intuitionistic Zermelo Fraenkel set theory (IZF).Less
This chapter discusses a notion of universe in toposes, which from a logical point of view gives rise to an extension of Higher Order Intuitionistic Arithmetic (HAH). In this way, one can construct families of types in the universe by structural recursion and quantify over such families. Further, it shows that (hierarchies of) such universes do exist in all sheaf and realizability toposes. They do not exist instead either in the free topos or in the Vω+ω model of Zermelo set theory. Though universes in the category Set are necessarily of strongly inaccessible cardinality, it remains an open question as to whether toposes with a universe allow one to construct internal models of Intuitionistic Zermelo Fraenkel set theory (IZF).
Michael Potter
- Published in print:
- 2002
- Published Online:
- May 2007
- ISBN:
- 9780199252619
- eISBN:
- 9780191712647
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199252619.003.0004
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
Dedekind was explicit, as Frege was, that ‘arithmetic is part of logic’, by which he meant to imply that he considered ‘the number concept entirely independent of the notions or intuitions of space ...
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Dedekind was explicit, as Frege was, that ‘arithmetic is part of logic’, by which he meant to imply that he considered ‘the number concept entirely independent of the notions or intuitions of space and time’. Moreover, he did not limit himself to justifying the necessity of arithmetic; he shared Frege's view of the importance of explaining its applicability, as the title of his monograph — Was sind und was sollen die Zahlen? (What are numbers and what are they for?) — makes clear. Although there are considerable similarities between the two treatments, there are also marked differences, not just in the technical details of their developments of arithmetic within logic but in the way they tackled the dual problems of establishing the existence of the number sequence and uniqueness of the number sequence. In particular, although Dedekind's characterization of the natural numbers faced a version of the Julius Caesar problem just as Frege's did, Dedekind solved it in a very different way, which allowed him to avoid the problem of extraneous properties.Less
Dedekind was explicit, as Frege was, that ‘arithmetic is part of logic’, by which he meant to imply that he considered ‘the number concept entirely independent of the notions or intuitions of space and time’. Moreover, he did not limit himself to justifying the necessity of arithmetic; he shared Frege's view of the importance of explaining its applicability, as the title of his monograph — Was sind und was sollen die Zahlen? (What are numbers and what are they for?) — makes clear. Although there are considerable similarities between the two treatments, there are also marked differences, not just in the technical details of their developments of arithmetic within logic but in the way they tackled the dual problems of establishing the existence of the number sequence and uniqueness of the number sequence. In particular, although Dedekind's characterization of the natural numbers faced a version of the Julius Caesar problem just as Frege's did, Dedekind solved it in a very different way, which allowed him to avoid the problem of extraneous properties.
Debraj Ray
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199207954
- eISBN:
- 9780191709104
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199207954.003.0007
- Subject:
- Economics and Finance, Financial Economics
This chapter takes up the more general problem of coalition formation when the symmetry assumption is dropped. The analysis is necessarily complex and several new considerations arise. The chapter ...
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This chapter takes up the more general problem of coalition formation when the symmetry assumption is dropped. The analysis is necessarily complex and several new considerations arise. The chapter proceeds in two main steps. First, a theory of coalition formation is developed for the theory for situations in which there are no payoff externalities across coalitions. The Markovian equilibrium payoffs for such games have a simple structure: they are unique for each set of active players, and they are amenable to computation by the use of a recursive algorithm. The efficiency properties of such equilibria are discussed in detail. The second step extends the theory to cover externalities across coalitions. The chapter therefore obtains a fairly general theory of coalition formation when commitments to form coalitions are irreversible.Less
This chapter takes up the more general problem of coalition formation when the symmetry assumption is dropped. The analysis is necessarily complex and several new considerations arise. The chapter proceeds in two main steps. First, a theory of coalition formation is developed for the theory for situations in which there are no payoff externalities across coalitions. The Markovian equilibrium payoffs for such games have a simple structure: they are unique for each set of active players, and they are amenable to computation by the use of a recursive algorithm. The efficiency properties of such equilibria are discussed in detail. The second step extends the theory to cover externalities across coalitions. The chapter therefore obtains a fairly general theory of coalition formation when commitments to form coalitions are irreversible.
Steven Pinker and Ray Jackendoff
- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780195305432
- eISBN:
- 9780199866953
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195305432.003.0007
- Subject:
- Psychology, Cognitive Psychology, Cognitive Models and Architectures
Hauser, Chomsky, and Fitch (HCF) proposed that recursion is the only thing that distinguishes language (a) from other human capacities, and (b) from the capacities of animals. These factors are ...
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Hauser, Chomsky, and Fitch (HCF) proposed that recursion is the only thing that distinguishes language (a) from other human capacities, and (b) from the capacities of animals. These factors are independent. The narrow faculty of language might include more than recursion, falsifying (a). Or it might consist only of recursion, although parts of the broad faculty might be uniquely human as well, falsifying (b). This chapter presents a view that is contrasted with HCF's above. It shows that there is considerably more of language that is special, though still a plausible product of the processes of evolution. It assesses the key bodies of evidence, coming to a different reading from HCF's. The chapter organizes the discussion by distinguishing the conceptual, sensorimotor, and specifically linguistic aspects of the broad language faculty in turn.Less
Hauser, Chomsky, and Fitch (HCF) proposed that recursion is the only thing that distinguishes language (a) from other human capacities, and (b) from the capacities of animals. These factors are independent. The narrow faculty of language might include more than recursion, falsifying (a). Or it might consist only of recursion, although parts of the broad faculty might be uniquely human as well, falsifying (b). This chapter presents a view that is contrasted with HCF's above. It shows that there is considerably more of language that is special, though still a plausible product of the processes of evolution. It assesses the key bodies of evidence, coming to a different reading from HCF's. The chapter organizes the discussion by distinguishing the conceptual, sensorimotor, and specifically linguistic aspects of the broad language faculty in turn.
K. Velupillai
- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198295273
- eISBN:
- 9780191596988
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198295278.001.0001
- Subject:
- Economics and Finance, Macro- and Monetary Economics
In a discipline such as economics, increasingly devoted to its computational content, the mathematical underpinnings of the computability assumptions of economic fundamentals have not been ...
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In a discipline such as economics, increasingly devoted to its computational content, the mathematical underpinnings of the computability assumptions of economic fundamentals have not been investigated systematically or reasonably exhaustively. In this book, such an attempt is made for the first time. Choice theory, adaptively rational behaviour, induction, learning, arithmetical games, computational complexity of decision processes, growth theory, and the theory of economic fluctuations are given recursion theoretic (i.e, computable) interpretations. Economic theoretic questions, posed recursion theoretically, lead to answers that are ambiguous: undecidable choices, uncomputable learning processes, algorithmically unplayable games, etc., become standard answers. The book also claims that a recursion theoretic formalization of economic analysis makes the subject intrinsically inductive and computational.Less
In a discipline such as economics, increasingly devoted to its computational content, the mathematical underpinnings of the computability assumptions of economic fundamentals have not been investigated systematically or reasonably exhaustively. In this book, such an attempt is made for the first time. Choice theory, adaptively rational behaviour, induction, learning, arithmetical games, computational complexity of decision processes, growth theory, and the theory of economic fluctuations are given recursion theoretic (i.e, computable) interpretations. Economic theoretic questions, posed recursion theoretically, lead to answers that are ambiguous: undecidable choices, uncomputable learning processes, algorithmically unplayable games, etc., become standard answers. The book also claims that a recursion theoretic formalization of economic analysis makes the subject intrinsically inductive and computational.
Christopher I. Beckwith
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691155319
- eISBN:
- 9781400845170
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691155319.003.0002
- Subject:
- History, World Medieval History
This chapter examines the recursive argument method of medieval science. The distinctive argument method used in scientific literature from the High Middle Ages to the Enlightenment was the ...
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This chapter examines the recursive argument method of medieval science. The distinctive argument method used in scientific literature from the High Middle Ages to the Enlightenment was the “scientific method” until the scientific revolution. It is traditionally known in earlier scholarly literature as the “scholastic method” or quaestiones disputatae “disputed questions” method. Unfortunately, because of increasing scholarly confusion about the origins and meaning of the traditional term “scholastic method,” and even of the term quaestiones disputatae, it has been necessary to adopt a purely descriptive term, namely recursive argument method, also called recursive method or recursive argument. Many medieval scholars who wrote works using the recursive argument method also wrote treatises. The chapter compares the recursive argument with the treatise and dialogue argument structures and considers diffrent types of formal recursion.Less
This chapter examines the recursive argument method of medieval science. The distinctive argument method used in scientific literature from the High Middle Ages to the Enlightenment was the “scientific method” until the scientific revolution. It is traditionally known in earlier scholarly literature as the “scholastic method” or quaestiones disputatae “disputed questions” method. Unfortunately, because of increasing scholarly confusion about the origins and meaning of the traditional term “scholastic method,” and even of the term quaestiones disputatae, it has been necessary to adopt a purely descriptive term, namely recursive argument method, also called recursive method or recursive argument. Many medieval scholars who wrote works using the recursive argument method also wrote treatises. The chapter compares the recursive argument with the treatise and dialogue argument structures and considers diffrent types of formal recursion.
Christopher I. Beckwith
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691155319
- eISBN:
- 9781400845170
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691155319.003.0004
- Subject:
- History, World Medieval History
This chapter examines Buddhist Central Asia's invention of the recursive argument method. Some Buddhist teachings, which are found in all Buddhist traditions—indicating that they may be inherited ...
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This chapter examines Buddhist Central Asia's invention of the recursive argument method. Some Buddhist teachings, which are found in all Buddhist traditions—indicating that they may be inherited from early Buddhism—contain embedded sets in the form of linked lists, which are suggestive of recursion. The Buddhist fondness for explicitly numbered sets and lists is traditionally ascribed to Siddhārtha Gautama, or Śākyamuni Buddha, himself. The chapter first considers the enduring influence of Hellenism after Alexander's conquest and colonization of Bactria and Gandhāra before presenting examples of the Central Asian Buddhist recursive argument.Less
This chapter examines Buddhist Central Asia's invention of the recursive argument method. Some Buddhist teachings, which are found in all Buddhist traditions—indicating that they may be inherited from early Buddhism—contain embedded sets in the form of linked lists, which are suggestive of recursion. The Buddhist fondness for explicitly numbered sets and lists is traditionally ascribed to Siddhārtha Gautama, or Śākyamuni Buddha, himself. The chapter first considers the enduring influence of Hellenism after Alexander's conquest and colonization of Bactria and Gandhāra before presenting examples of the Central Asian Buddhist recursive argument.
Kumaraswamy Velupillai
- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198295273
- eISBN:
- 9780191596988
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198295278.003.0002
- Subject:
- Economics and Finance, Macro- and Monetary Economics
In this chapter, a first, tentative attempt is made to define the nature and scope of what is meant by computable economics. From a study of the way economics was mathematized in the modern era, – ...
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In this chapter, a first, tentative attempt is made to define the nature and scope of what is meant by computable economics. From a study of the way economics was mathematized in the modern era, – i.e., since about the late 1920s – I try to extract those studies and examples that attempted recursion theoretic characterizations of economic theoretic problems. These are then distilled and codified as early examples of computable economics. The chapter also discusses, more specifically but concisely, the contributions of Herbert Simon from a recursion theoretic point of view.Less
In this chapter, a first, tentative attempt is made to define the nature and scope of what is meant by computable economics. From a study of the way economics was mathematized in the modern era, – i.e., since about the late 1920s – I try to extract those studies and examples that attempted recursion theoretic characterizations of economic theoretic problems. These are then distilled and codified as early examples of computable economics. The chapter also discusses, more specifically but concisely, the contributions of Herbert Simon from a recursion theoretic point of view.
John M. Anderson
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199608331
- eISBN:
- 9780191732119
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199608331.003.0007
- Subject:
- Linguistics, Syntax and Morphology, Phonetics / Phonology
This chapter examines structural properties that in some form seem to be central to syntax, but at most marginal in phonology. Firstly, it looks at the presence of lexical derivation involving ...
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This chapter examines structural properties that in some form seem to be central to syntax, but at most marginal in phonology. Firstly, it looks at the presence of lexical derivation involving syntactic categories, expressed by affixation, internal modification, conversion, or compounding, or merely by distribution. Change of category is incompatible with the expression of phonology. Lexical structures can display recursion, and syntactic recursion is the second topic of the chapter, where a distinction between direct and indirect recursion is made. At most, only direct recursion is associated with phonological structures, again because of incompatibility with their implementation. Similarly, phonology displays ambidependency, but rejects non-projectivity and associated long-distance dependencies. The need for non-projectivity and how it can be constrained is dis cussed.Less
This chapter examines structural properties that in some form seem to be central to syntax, but at most marginal in phonology. Firstly, it looks at the presence of lexical derivation involving syntactic categories, expressed by affixation, internal modification, conversion, or compounding, or merely by distribution. Change of category is incompatible with the expression of phonology. Lexical structures can display recursion, and syntactic recursion is the second topic of the chapter, where a distinction between direct and indirect recursion is made. At most, only direct recursion is associated with phonological structures, again because of incompatibility with their implementation. Similarly, phonology displays ambidependency, but rejects non-projectivity and associated long-distance dependencies. The need for non-projectivity and how it can be constrained is dis cussed.
Hidetoshi Nishimori and Gerardo Ortiz
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199577224
- eISBN:
- 9780191722943
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577224.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Mean-field theory is usually taken as a first step toward understanding critical phenomena, providing an overview that reveals qualitative behaviour of physical quantities. However, it is necessary ...
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Mean-field theory is usually taken as a first step toward understanding critical phenomena, providing an overview that reveals qualitative behaviour of physical quantities. However, it is necessary to proceed beyond the mean-field theory to better understand the situation, both qualitatively and quantitatively, when fluctuations play vital roles leading to exponents that cannot be explained by dimensional analysis, thus introducing anomalous dimensions. The present chapter explains the basic concepts of the renormalization group and scaling theory, which allow us to analyze critical phenomena with fluctuations systematically taken into account. The essential step in a renormalization group calculation consists of establishing recursion relations between the parameters defining the Hamiltonian of the system. These recursion or renormalization group equations define a flow with well-defined fixed points. Details other than the values of the relevant operators have no influence on the critical exponents and this represents universality.Less
Mean-field theory is usually taken as a first step toward understanding critical phenomena, providing an overview that reveals qualitative behaviour of physical quantities. However, it is necessary to proceed beyond the mean-field theory to better understand the situation, both qualitatively and quantitatively, when fluctuations play vital roles leading to exponents that cannot be explained by dimensional analysis, thus introducing anomalous dimensions. The present chapter explains the basic concepts of the renormalization group and scaling theory, which allow us to analyze critical phenomena with fluctuations systematically taken into account. The essential step in a renormalization group calculation consists of establishing recursion relations between the parameters defining the Hamiltonian of the system. These recursion or renormalization group equations define a flow with well-defined fixed points. Details other than the values of the relevant operators have no influence on the critical exponents and this represents universality.
Michael Potter
- Published in print:
- 2004
- Published Online:
- September 2011
- ISBN:
- 9780199269730
- eISBN:
- 9780191699443
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269730.003.0008
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
It has to be shown that the axioms of ZU guarantee the existence of structures with the familiar properties the natural, rational, and real numbers are expected to have. This chapter makes a start on ...
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It has to be shown that the axioms of ZU guarantee the existence of structures with the familiar properties the natural, rational, and real numbers are expected to have. This chapter makes a start on this project by considering natural numbers.Less
It has to be shown that the axioms of ZU guarantee the existence of structures with the familiar properties the natural, rational, and real numbers are expected to have. This chapter makes a start on this project by considering natural numbers.
Michael Potter
- Published in print:
- 2004
- Published Online:
- September 2011
- ISBN:
- 9780199269730
- eISBN:
- 9780191699443
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199269730.003.0016
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
The simple and general principles of induction are powerful tools for proving things about the natural numbers. This chapter investigates ways in which they can be generalized to apply to a very much ...
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The simple and general principles of induction are powerful tools for proving things about the natural numbers. This chapter investigates ways in which they can be generalized to apply to a very much wider class of ordered sets than the subsets of ω. The basis of this study is the observation that a version of induction can be applied to any ordered set with a property called well-ordering. The strategy is to apply much the same techniques to the study of isomorphism between well-ordered sets used in Chapter 9 to investigate equinumerosity between sets. Just as that work led to an arithmetic of cardinals, what this chapter does is lead to an arithmetic of ordinals.Less
The simple and general principles of induction are powerful tools for proving things about the natural numbers. This chapter investigates ways in which they can be generalized to apply to a very much wider class of ordered sets than the subsets of ω. The basis of this study is the observation that a version of induction can be applied to any ordered set with a property called well-ordering. The strategy is to apply much the same techniques to the study of isomorphism between well-ordered sets used in Chapter 9 to investigate equinumerosity between sets. Just as that work led to an arithmetic of cardinals, what this chapter does is lead to an arithmetic of ordinals.
Brandon C. Wheeler, William A. Searcy, Morten H. Christiansen, Michael C. Corballis, Julia Fischer, Christoph Grüter, Daniel Margoliash, Michael J. Owren, Tabitha Price, Robert Seyfarth, and Markus Wild
- Published in print:
- 2011
- Published Online:
- May 2016
- ISBN:
- 9780262016636
- eISBN:
- 9780262298988
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262016636.003.0013
- Subject:
- Psychology, Social Psychology
This chapter reviews what has been learned about animal thinking from the study of animal communication and considers what we might hope to learn in the future. It begins with a discussion on the ...
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This chapter reviews what has been learned about animal thinking from the study of animal communication and considers what we might hope to learn in the future. It begins with a discussion on the importance of informational versus non-informational interpretations of animal communication and then considers what inferences can be drawn about the cognitive requirements of communication from the communicative abilities of simple organisms. It discusses the importance of context to the meaning of animal signals and the possibility of asymmetries in the neural processes underlying production versus reception. Current theories on the evolution of human language are reviewed and how the study of animal communication informs these theories.Less
This chapter reviews what has been learned about animal thinking from the study of animal communication and considers what we might hope to learn in the future. It begins with a discussion on the importance of informational versus non-informational interpretations of animal communication and then considers what inferences can be drawn about the cognitive requirements of communication from the communicative abilities of simple organisms. It discusses the importance of context to the meaning of animal signals and the possibility of asymmetries in the neural processes underlying production versus reception. Current theories on the evolution of human language are reviewed and how the study of animal communication informs these theories.
John Collins
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199694846
- eISBN:
- 9780191732027
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199694846.003.0007
- Subject:
- Philosophy, Philosophy of Language, Philosophy of Mind
The last chapter fielded a range of potential philosophical objections to the account of unity offered in chapter 5. I also trust that it clarified a range of background issues pertaining to the ...
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The last chapter fielded a range of potential philosophical objections to the account of unity offered in chapter 5. I also trust that it clarified a range of background issues pertaining to the purpose and scope of semantic inquiry, at least as I conceive of it. In this final chapter, I shall address a range of issues that arise in linguistics to do with the status and interpretation of Merge. I shall be especially concerned to defend the primitive status of Merge from critics, such as Jackendoff, and those who seek to analyse it into more primitive components, such as Hornstein. Although these issues may be initially oblique to some readers, I hope that their interest will quickly become apparent. Any interdisciplinary work is obliged to justify itself in all the relevant disciplines, not just the one.Less
The last chapter fielded a range of potential philosophical objections to the account of unity offered in chapter 5. I also trust that it clarified a range of background issues pertaining to the purpose and scope of semantic inquiry, at least as I conceive of it. In this final chapter, I shall address a range of issues that arise in linguistics to do with the status and interpretation of Merge. I shall be especially concerned to defend the primitive status of Merge from critics, such as Jackendoff, and those who seek to analyse it into more primitive components, such as Hornstein. Although these issues may be initially oblique to some readers, I hope that their interest will quickly become apparent. Any interdisciplinary work is obliged to justify itself in all the relevant disciplines, not just the one.
LUTZ MARTEN
- Published in print:
- 2002
- Published Online:
- January 2010
- ISBN:
- 9780199250639
- eISBN:
- 9780191719479
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199250639.003.0005
- Subject:
- Linguistics, Semantics and Pragmatics, Syntax and Morphology
This chapter is concerned with the interpretation of underspecified verbs. It shows that standard model-theoretic approaches cannot be extended to this dynamic view of verbs since they presuppose a ...
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This chapter is concerned with the interpretation of underspecified verbs. It shows that standard model-theoretic approaches cannot be extended to this dynamic view of verbs since they presuppose a static notion of semantic arity which is specified in advance in the model against which the sentence is evaluated. This is demonstrated by discussing two approaches to the semantics of adjuncts (based on Dowty 1979 and McConnell-Ginet 1982). The chapter then introduces the notions of mental representation and pragmatic enrichment, and argues against this background that a proper understanding of underspecified verbs, and hence VP adjunction, can better be attained by a pragmatic analysis of verb phrase interpretation. Under this view verbs address mental concepts only indirectly, and the eventual, communicated concept is constructed in an ad hoc fashion in the utterance context with recourse to the pragmatic principle of relevance. The interpretation of verbs is thus seen in parallel to other processes of meaning construction, including non-literal meaning (cf. Carston 1996). Furthermore, since the eventual valency of a verb results from its meaning in context, it can equally only be determined with recourse to pragmatic knowledge. In other words, the establishment of basic predicate-argument structure is subject to pragmatic constraints on meaning construction. A result of this view is that there is no well-defined syntactic level of logical form as an interface between syntax and pragmatics, since the establishment of VPs — syntactic structures — presupposes the application of non-syntactic, pragmatic knowledge.Less
This chapter is concerned with the interpretation of underspecified verbs. It shows that standard model-theoretic approaches cannot be extended to this dynamic view of verbs since they presuppose a static notion of semantic arity which is specified in advance in the model against which the sentence is evaluated. This is demonstrated by discussing two approaches to the semantics of adjuncts (based on Dowty 1979 and McConnell-Ginet 1982). The chapter then introduces the notions of mental representation and pragmatic enrichment, and argues against this background that a proper understanding of underspecified verbs, and hence VP adjunction, can better be attained by a pragmatic analysis of verb phrase interpretation. Under this view verbs address mental concepts only indirectly, and the eventual, communicated concept is constructed in an ad hoc fashion in the utterance context with recourse to the pragmatic principle of relevance. The interpretation of verbs is thus seen in parallel to other processes of meaning construction, including non-literal meaning (cf. Carston 1996). Furthermore, since the eventual valency of a verb results from its meaning in context, it can equally only be determined with recourse to pragmatic knowledge. In other words, the establishment of basic predicate-argument structure is subject to pragmatic constraints on meaning construction. A result of this view is that there is no well-defined syntactic level of logical form as an interface between syntax and pragmatics, since the establishment of VPs — syntactic structures — presupposes the application of non-syntactic, pragmatic knowledge.
Gerjan van Schaaik
- Published in print:
- 2020
- Published Online:
- September 2020
- ISBN:
- 9780198851509
- eISBN:
- 9780191886102
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198851509.001.0001
- Subject:
- Linguistics, Phonetics / Phonology, Syntax and Morphology
The point of departure of this book is the fundamental observation that actual conversations tend to consist of loosely connected, compact, and meaningful chunks built on a noun phrase, rather than ...
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The point of departure of this book is the fundamental observation that actual conversations tend to consist of loosely connected, compact, and meaningful chunks built on a noun phrase, rather than fully fledged sentences. Therefore, after the treatment of elementary matters such as the Turkish alphabet and pronunciation in part I, the main points of part II are the structure of noun phrases and their function in nominal, existential, and verbal sentences, while part III presents their adjuncts and modifiers. The verbal system is extensively discussed in part IV, and in part V on sentence structure the grammatical phenomena presented so far are wrapped up. The first five parts of the book, taken together, provide for all-round operational knowledge of Turkish on a basic level. Part VI deals with the ways in which complex words are constructed, and constitutes a bridge to the advanced matter treated in parts VII and VIII. These latter parts deal with advanced topics such as relative clauses, subordination, embedded clauses, clausal complements, and the finer points of the verbal system. An important advantage of this book is its revealing new content: the section on syllable structure explains how loanwords adapt to Turkish; other topics include: the use of pronouns in invectives; verbal objects classified in terms of case marking; extensive treatment of the optative (highly relevant in day-to-day conversation); recursion and lexicalization in compounds; stacking of passives; the Başı-Bozuk and Focus-Locus constructions; relativization on possessive, dative, locative, and ablative objects, instrumentals and adverbial adjuncts; pseudo-relative clauses; typology of clausal complements; periphrastic constructions and double negation.Less
The point of departure of this book is the fundamental observation that actual conversations tend to consist of loosely connected, compact, and meaningful chunks built on a noun phrase, rather than fully fledged sentences. Therefore, after the treatment of elementary matters such as the Turkish alphabet and pronunciation in part I, the main points of part II are the structure of noun phrases and their function in nominal, existential, and verbal sentences, while part III presents their adjuncts and modifiers. The verbal system is extensively discussed in part IV, and in part V on sentence structure the grammatical phenomena presented so far are wrapped up. The first five parts of the book, taken together, provide for all-round operational knowledge of Turkish on a basic level. Part VI deals with the ways in which complex words are constructed, and constitutes a bridge to the advanced matter treated in parts VII and VIII. These latter parts deal with advanced topics such as relative clauses, subordination, embedded clauses, clausal complements, and the finer points of the verbal system. An important advantage of this book is its revealing new content: the section on syllable structure explains how loanwords adapt to Turkish; other topics include: the use of pronouns in invectives; verbal objects classified in terms of case marking; extensive treatment of the optative (highly relevant in day-to-day conversation); recursion and lexicalization in compounds; stacking of passives; the Başı-Bozuk and Focus-Locus constructions; relativization on possessive, dative, locative, and ablative objects, instrumentals and adverbial adjuncts; pseudo-relative clauses; typology of clausal complements; periphrastic constructions and double negation.
John R Taylor
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199290802
- eISBN:
- 9780191741388
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199290802.003.0002
- Subject:
- Linguistics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics
Presents and critically examines the view that knowledge of a language can partitioned into a mental lexicon (which lists the words) and a syntax (which lists the rules for combining the words). ...
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Presents and critically examines the view that knowledge of a language can partitioned into a mental lexicon (which lists the words) and a syntax (which lists the rules for combining the words). Contrary to the entailments of the model, rules may have only limited applicability, and full compositionality is rare.Less
Presents and critically examines the view that knowledge of a language can partitioned into a mental lexicon (which lists the words) and a syntax (which lists the rules for combining the words). Contrary to the entailments of the model, rules may have only limited applicability, and full compositionality is rare.
Raymond M. Smullyan
- Published in print:
- 1993
- Published Online:
- November 2020
- ISBN:
- 9780195082326
- eISBN:
- 9780197560426
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195082326.003.0013
- Subject:
- Computer Science, Mathematical Theory of Computation
We have proved that every completely E.I. pair of r.e. sets is D.U. In the next chapter we will show the stronger result that every E.I. pair of r.e. sets is D.U. The proof of this is based on the ...
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We have proved that every completely E.I. pair of r.e. sets is D.U. In the next chapter we will show the stronger result that every E.I. pair of r.e. sets is D.U. The proof of this is based on the double recursion theorem of this chapter. Our original formulation of the double recursion theorem (T.F.S.) required the recursive pairing function J(x,y), not only for its proof, but for its very statement. In this chapter, we give an improved version whose statement and proof are independent of J, K and L. In Part III of this chapter, we compare our new version with the original J, K and L version and show that they are easily interderivable. §1. The Weak Double Recursion Theorem. Consider two r.e. relations, M1(x,y, z) and M2(x, y, z). For any number b, the relation M1(x,y,b) is an r.e. relation between x and y, and so by the weak recursion theorem (Theorem 1, Chapter 8), there is a number a such that ωa = x : M1(x, a, b). Likewise, for any number a, the relation M2(x,a,y) is an r.e. relation between x and y, and so there is a number b such that ωb, = x : M2(x,a,b). Our next theorem tells us that we can choose a and b so that both these conditions hold simultaneously.
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We have proved that every completely E.I. pair of r.e. sets is D.U. In the next chapter we will show the stronger result that every E.I. pair of r.e. sets is D.U. The proof of this is based on the double recursion theorem of this chapter. Our original formulation of the double recursion theorem (T.F.S.) required the recursive pairing function J(x,y), not only for its proof, but for its very statement. In this chapter, we give an improved version whose statement and proof are independent of J, K and L. In Part III of this chapter, we compare our new version with the original J, K and L version and show that they are easily interderivable. §1. The Weak Double Recursion Theorem. Consider two r.e. relations, M1(x,y, z) and M2(x, y, z). For any number b, the relation M1(x,y,b) is an r.e. relation between x and y, and so by the weak recursion theorem (Theorem 1, Chapter 8), there is a number a such that ωa = x : M1(x, a, b). Likewise, for any number a, the relation M2(x,a,y) is an r.e. relation between x and y, and so there is a number b such that ωb, = x : M2(x,a,b). Our next theorem tells us that we can choose a and b so that both these conditions hold simultaneously.
