John C. Lennox and Derek J. S. Robinson
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198507284
- eISBN:
- 9780191709326
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507284.003.0005
- Subject:
- Mathematics, Pure Mathematics
This chapter details the ranks of an abelian group. It also talks about the structure of soluble groups with finite rank, minimax groups, and residual finiteness.
This chapter details the ranks of an abelian group. It also talks about the structure of soluble groups with finite rank, minimax groups, and residual finiteness.
John C. Lennox and Derek J. S. Robinson
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198507284
- eISBN:
- 9780191709326
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507284.003.0007
- Subject:
- Mathematics, Pure Mathematics
This chapter discusses simple modules over polycyclic groups, the Jategaonkar-Roseblade theorem, the Artin-Rees property, and residual finiteness. It also talks about the Frattini subgroup.
This chapter discusses simple modules over polycyclic groups, the Jategaonkar-Roseblade theorem, the Artin-Rees property, and residual finiteness. It also talks about the Frattini subgroup.
Colin McLarty
Apostolos Doxiadis and Barry Mazur (eds)
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691149042
- eISBN:
- 9781400842681
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149042.003.0004
- Subject:
- Mathematics, History of Mathematics
This chapter examines the myth surrounding Paul Gordan's response to David Hilbert's finiteness theorems. A proof introduced by Hilbert in 1888 became the paradigm of modern axiomatic mathematics. In ...
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This chapter examines the myth surrounding Paul Gordan's response to David Hilbert's finiteness theorems. A proof introduced by Hilbert in 1888 became the paradigm of modern axiomatic mathematics. In the myth, Gordan denounced Hilbert's proof, and his anathema rebounded against himself when he said, “This is not Mathematics, it is Theology!” After providing the background to the various interpretations that Gordan's comment has generated, the chapter considers the so-called “Gordan's problem”—to find finite complete systems of invariants for forms. It then discusses Hilbert's theorem and Gordan's reaction to Hilbert's fuller version of the invariant theorem, as well as Gordan's mythic quotation. It also explores the role played by Gordan's one and only doctoral student, Emmy Noether, in the Gordan–Hilbert controversy and concludes by emphasizing Gordan's story as an example of the deliberate use of narrative in mathematics.Less
This chapter examines the myth surrounding Paul Gordan's response to David Hilbert's finiteness theorems. A proof introduced by Hilbert in 1888 became the paradigm of modern axiomatic mathematics. In the myth, Gordan denounced Hilbert's proof, and his anathema rebounded against himself when he said, “This is not Mathematics, it is Theology!” After providing the background to the various interpretations that Gordan's comment has generated, the chapter considers the so-called “Gordan's problem”—to find finite complete systems of invariants for forms. It then discusses Hilbert's theorem and Gordan's reaction to Hilbert's fuller version of the invariant theorem, as well as Gordan's mythic quotation. It also explores the role played by Gordan's one and only doctoral student, Emmy Noether, in the Gordan–Hilbert controversy and concludes by emphasizing Gordan's story as an example of the deliberate use of narrative in mathematics.
Donald Davidson
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199246298
- eISBN:
- 9780191715181
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199246297.003.0002
- Subject:
- Philosophy, Philosophy of Language
Develops the criterion of learnability proposed in Essay 1 into a constraint for a satisfactory theory of meaning: such a theory must show how, on the basis of a finite stock of semantic primitives, ...
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Develops the criterion of learnability proposed in Essay 1 into a constraint for a satisfactory theory of meaning: such a theory must show how, on the basis of a finite stock of semantic primitives, speakers come to understand a potentially infinite number of sentences; more precisely, how the meaning of each and every sentence in the language is owed to the sentence's structural composition. Davidson notes that introducing distinct entities as meanings for each expression (‘intensions’, ‘senses’) does not illuminate these structural workings of the language (this complaint, he says, operates quite independently of ontological reservations about intensions being ‘abstract’ or lacking clear individuation conditions). If, on the other hand, we dispense with intensions, we must define ‘meaning’ by mere appeal to reference; but this clearly won’t work since, if we concede that sentences ‘refer’ to their truth‐values, all sentences alike in truth value would be alike in meaning. Davidson therefore individuates a sentence's meaning by its ‘logical place’ in the language to which it belongs, i.e. by its entailment relations to other sentences in the language; the meaning of a subsentential expression is likewise individuated holistically, namely in terms of the systematic effect the expression has on the entailment relations of the sentence in which it occurs. Since a Tarskian truth theory captures these entailment relations for each sentence (in a specified language) by associating it with its ‘truth‐condition’, the truth theory can be said to give the ‘meaning’ thus construed for each sentence (a fortiori for their subsentential expressions), while meeting both the constraint for finiteness and the restriction to purely referential means. Davidson discusses various objections to this proposal (since called ‘Davidson's programme’), e.g. that it cannot accomodate sentences containing indexicals or contexts in which extensionality breaks down; and he shows its merit in its varied applicability to questions of logical form, the success of which is evaluated by whether the aforementioned entailments are preserved and explained for a variety of sentences (see Essays 6–8, and Essays 6–10 of the companion volume Essays on Actions and Events).Less
Develops the criterion of learnability proposed in Essay 1 into a constraint for a satisfactory theory of meaning: such a theory must show how, on the basis of a finite stock of semantic primitives, speakers come to understand a potentially infinite number of sentences; more precisely, how the meaning of each and every sentence in the language is owed to the sentence's structural composition. Davidson notes that introducing distinct entities as meanings for each expression (‘intensions’, ‘senses’) does not illuminate these structural workings of the language (this complaint, he says, operates quite independently of ontological reservations about intensions being ‘abstract’ or lacking clear individuation conditions). If, on the other hand, we dispense with intensions, we must define ‘meaning’ by mere appeal to reference; but this clearly won’t work since, if we concede that sentences ‘refer’ to their truth‐values, all sentences alike in truth value would be alike in meaning. Davidson therefore individuates a sentence's meaning by its ‘logical place’ in the language to which it belongs, i.e. by its entailment relations to other sentences in the language; the meaning of a subsentential expression is likewise individuated holistically, namely in terms of the systematic effect the expression has on the entailment relations of the sentence in which it occurs. Since a Tarskian truth theory captures these entailment relations for each sentence (in a specified language) by associating it with its ‘truth‐condition’, the truth theory can be said to give the ‘meaning’ thus construed for each sentence (a fortiori for their subsentential expressions), while meeting both the constraint for finiteness and the restriction to purely referential means. Davidson discusses various objections to this proposal (since called ‘Davidson's programme’), e.g. that it cannot accomodate sentences containing indexicals or contexts in which extensionality breaks down; and he shows its merit in its varied applicability to questions of logical form, the success of which is evaluated by whether the aforementioned entailments are preserved and explained for a variety of sentences (see Essays 6–8, and Essays 6–10 of the companion volume Essays on Actions and Events).
Donald Davidson
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199246298
- eISBN:
- 9780191715181
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199246297.003.0004
- Subject:
- Philosophy, Philosophy of Language
Davidson rehearses the demands for an acceptable theory of meaning for a natural language—that it give the meaning for each (actual and potential) utterance in the language, that it do so by finite ...
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Davidson rehearses the demands for an acceptable theory of meaning for a natural language—that it give the meaning for each (actual and potential) utterance in the language, that it do so by finite means and shed light on the structural workings of the language (see Essay 2)—and argues that a theory of truth for that language provides ‘a precise, profound and testable answer’ to these demands. In addition, he demands that the stock of concepts used by metalanguage in which the truth theory is stated (its ‘ideology’) extends minimally beyond, and ideally includes, that of the object language (cf Essay 14); he looks at how alternative semantic programs fare under this constraint (cf Essay 5). He then addresses the more general question of how truth‐theoretic semantics copes with recalcitrant, i.e. non‐extensional, locutions current in natural languages, and addresses Tarski's pessimism of formal frameworks to ‘tame’ them. He concludes by stressing, as he did in Essay 2, that recognizing the role played by logical form (as analysed in truth theories) for the analysis of sentential meaning is all‐important; and questions whether this form or ‘deep structure’ of the sentence can be identified, as Chomsky suggested, with an underlying psychological mechanism in the speaker.Less
Davidson rehearses the demands for an acceptable theory of meaning for a natural language—that it give the meaning for each (actual and potential) utterance in the language, that it do so by finite means and shed light on the structural workings of the language (see Essay 2)—and argues that a theory of truth for that language provides ‘a precise, profound and testable answer’ to these demands. In addition, he demands that the stock of concepts used by metalanguage in which the truth theory is stated (its ‘ideology’) extends minimally beyond, and ideally includes, that of the object language (cf Essay 14); he looks at how alternative semantic programs fare under this constraint (cf Essay 5). He then addresses the more general question of how truth‐theoretic semantics copes with recalcitrant, i.e. non‐extensional, locutions current in natural languages, and addresses Tarski's pessimism of formal frameworks to ‘tame’ them. He concludes by stressing, as he did in Essay 2, that recognizing the role played by logical form (as analysed in truth theories) for the analysis of sentential meaning is all‐important; and questions whether this form or ‘deep structure’ of the sentence can be identified, as Chomsky suggested, with an underlying psychological mechanism in the speaker.
Quentin Smith
- Published in print:
- 1995
- Published Online:
- October 2011
- ISBN:
- 9780198263838
- eISBN:
- 9780191682650
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198263838.003.0002
- Subject:
- Religion, Philosophy of Religion, Theology
This chapter presents an essay which aims to refute the argument that the past is necessarily finite. It considers the arguments offered by William Lane Craig and arguments by other philosophers. It ...
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This chapter presents an essay which aims to refute the argument that the past is necessarily finite. It considers the arguments offered by William Lane Craig and arguments by other philosophers. It agrees that Big Bang cosmology warrants the conclusion that the past is finite but it also argues that the beginning of the universe is not caused by God or anything else. To illustrate the finiteness of the past, this chapter uses the definition of an event as being a maximal complex of whatever occurs during a temporal interval of one second.Less
This chapter presents an essay which aims to refute the argument that the past is necessarily finite. It considers the arguments offered by William Lane Craig and arguments by other philosophers. It agrees that Big Bang cosmology warrants the conclusion that the past is finite but it also argues that the beginning of the universe is not caused by God or anything else. To illustrate the finiteness of the past, this chapter uses the definition of an event as being a maximal complex of whatever occurs during a temporal interval of one second.
Sonia Cristofaro
- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780199282005
- eISBN:
- 9780191719271
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199282005.001.0001
- Subject:
- Linguistics, Syntax and Morphology
This book presents a typology of subordination systems across the world's languages. Traditional definitions of subordination are based on morphosyntactic criteria, such as clausal embedding or ...
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This book presents a typology of subordination systems across the world's languages. Traditional definitions of subordination are based on morphosyntactic criteria, such as clausal embedding or non-finiteness. This book shows that these definitions are untenable in a cross-linguistic perspective, and provides a cognitive-based definition of subordination. The analysis is based on a representative eighty-language sample, and represents the broadest study so far conducted on the cross-linguistic coding of several types of complement, adverbial, and relative sentence. These sentence types display considerable structural variation across languages. However, this variation turns out to be constrained, and appears crucially related to the functional properties of individual sentence types. This book provides a systematic attempt to establish comprehensive implicational hierarchies describing the coding of complement, adverbial, and relative sentences at a single stroke. Concepts from typological theory and cognitive linguistics are integrated to account for these hierarchies.Less
This book presents a typology of subordination systems across the world's languages. Traditional definitions of subordination are based on morphosyntactic criteria, such as clausal embedding or non-finiteness. This book shows that these definitions are untenable in a cross-linguistic perspective, and provides a cognitive-based definition of subordination. The analysis is based on a representative eighty-language sample, and represents the broadest study so far conducted on the cross-linguistic coding of several types of complement, adverbial, and relative sentence. These sentence types display considerable structural variation across languages. However, this variation turns out to be constrained, and appears crucially related to the functional properties of individual sentence types. This book provides a systematic attempt to establish comprehensive implicational hierarchies describing the coding of complement, adverbial, and relative sentences at a single stroke. Concepts from typological theory and cognitive linguistics are integrated to account for these hierarchies.
Hartry Field
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199242894
- eISBN:
- 9780191597381
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199242895.003.0009
- Subject:
- Philosophy, General
Discusses some issues about indeterminacy of reference and truth, from two points of view about reference and truth: that of a correspondence theory and that of a disquotational theory. It is argued ...
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Discusses some issues about indeterminacy of reference and truth, from two points of view about reference and truth: that of a correspondence theory and that of a disquotational theory. It is argued that a correspondence theorist can continue to accept the usual disquotation schemas for reference and truth, despite the indeterminacy. And it is argued that the disquotationalist can accept indeterminacy even in his own conceptual scheme. Together, these claims mean that the two views on truth are much closer in their treatments of indeterminacy than one might have thought. Also discusses indeterminacy in our logical and mathematical vocabulary.Less
Discusses some issues about indeterminacy of reference and truth, from two points of view about reference and truth: that of a correspondence theory and that of a disquotational theory. It is argued that a correspondence theorist can continue to accept the usual disquotation schemas for reference and truth, despite the indeterminacy. And it is argued that the disquotationalist can accept indeterminacy even in his own conceptual scheme. Together, these claims mean that the two views on truth are much closer in their treatments of indeterminacy than one might have thought. Also discusses indeterminacy in our logical and mathematical vocabulary.
Hartry Field
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199242894
- eISBN:
- 9780191597381
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199242895.003.0011
- Subject:
- Philosophy, General
Focuses on an issue about the objectivity of mathematics—the extent to which undecidable sentences have determinate truth‐value—and argues that this issue is more important than the issue of the ...
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Focuses on an issue about the objectivity of mathematics—the extent to which undecidable sentences have determinate truth‐value—and argues that this issue is more important than the issue of the existence of mathematical objects. It argues that certain familiar problems for those who postulate mathematical objects, such as Benacerraf's access argument, are serious for those with highly ‘objectivist’ pictures of mathematics, but dissolve for those who allow for sufficient indeterminacy about undecidable sentences. The nominalist view that does without mathematical entities is simply one among several ways of accomplishing the important task of doing without excess objectivity. There is also a discussion arguing for one kind of structuralism but against another.Less
Focuses on an issue about the objectivity of mathematics—the extent to which undecidable sentences have determinate truth‐value—and argues that this issue is more important than the issue of the existence of mathematical objects. It argues that certain familiar problems for those who postulate mathematical objects, such as Benacerraf's access argument, are serious for those with highly ‘objectivist’ pictures of mathematics, but dissolve for those who allow for sufficient indeterminacy about undecidable sentences. The nominalist view that does without mathematical entities is simply one among several ways of accomplishing the important task of doing without excess objectivity. There is also a discussion arguing for one kind of structuralism but against another.
Hartry Field
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199242894
- eISBN:
- 9780191597381
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199242895.003.0012
- Subject:
- Philosophy, General
Argues that typical undecidable sentences of set theory (e.g. about the size of the continuum) can have no determinate truth‐value, since nothing in our practice can determine which ‘universe of ...
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Argues that typical undecidable sentences of set theory (e.g. about the size of the continuum) can have no determinate truth‐value, since nothing in our practice can determine which ‘universe of sets’ we are talking about. But it gives an account of how typical undecidable number‐theoretic sentences can have determinate truth‐value. The account has it though, that, whether these undecidable number‐theoretic sentences have determinate truth‐value, turns on assumptions about the physical world that could fail, and it explores the consequence of their failure. It concludes with a critique of an argument that at least the Gödel sentence of our fullest mathematical theory must be determinately true: the critique is that the argument depends on the same sort of reasoning that leads to the semantic paradoxes.Less
Argues that typical undecidable sentences of set theory (e.g. about the size of the continuum) can have no determinate truth‐value, since nothing in our practice can determine which ‘universe of sets’ we are talking about. But it gives an account of how typical undecidable number‐theoretic sentences can have determinate truth‐value. The account has it though, that, whether these undecidable number‐theoretic sentences have determinate truth‐value, turns on assumptions about the physical world that could fail, and it explores the consequence of their failure. It concludes with a critique of an argument that at least the Gödel sentence of our fullest mathematical theory must be determinately true: the critique is that the argument depends on the same sort of reasoning that leads to the semantic paradoxes.
Donald Davidson
- Published in print:
- 2001
- Published Online:
- November 2003
- ISBN:
- 9780199246298
- eISBN:
- 9780191715181
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199246297.003.0001
- Subject:
- Philosophy, Philosophy of Language
Davidson asks what properties a language must have to be learnable. He criticizes a (then) popular response that models the order of language acquisition on the epistemological priority of the types ...
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Davidson asks what properties a language must have to be learnable. He criticizes a (then) popular response that models the order of language acquisition on the epistemological priority of the types of expressions learnt; he labels this position the ‘building‐block theory’ (see further Essay 16). He discusses Strawson's critique of Quine's elimination of singular terms and shows how it is likewise premissed on the questionable derivation of claims about language learning from purely a priori considerations. On the positive side, Davidson proposes that a language is learnable by a creature with finite means if the language's number of semantic primitives or undefinables is finite. Using this criterion, he demonstrates that various theories in the philosophy of language introduce an infinite number of semantic primitives into the language and thus make it unlearnable; theories he alleges of this error (1) model quotations on names of expressions (Tarski, Quine; cf Essay 6), (2) analyse belief attributions in terms of linguistic marks (Scheffler, Carnap) or distinct one‐place predicates for each attributed belief (Quine; cf Essay 7), or (3) postulate intensional entities into their overall semantic framework (Frege, Church).Less
Davidson asks what properties a language must have to be learnable. He criticizes a (then) popular response that models the order of language acquisition on the epistemological priority of the types of expressions learnt; he labels this position the ‘building‐block theory’ (see further Essay 16). He discusses Strawson's critique of Quine's elimination of singular terms and shows how it is likewise premissed on the questionable derivation of claims about language learning from purely a priori considerations. On the positive side, Davidson proposes that a language is learnable by a creature with finite means if the language's number of semantic primitives or undefinables is finite. Using this criterion, he demonstrates that various theories in the philosophy of language introduce an infinite number of semantic primitives into the language and thus make it unlearnable; theories he alleges of this error (1) model quotations on names of expressions (Tarski, Quine; cf Essay 6), (2) analyse belief attributions in terms of linguistic marks (Scheffler, Carnap) or distinct one‐place predicates for each attributed belief (Quine; cf Essay 7), or (3) postulate intensional entities into their overall semantic framework (Frege, Church).
John M. Anderson
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199608317
- eISBN:
- 9780191732034
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199608317.001.0001
- Subject:
- Linguistics, Syntax and Morphology, Phonetics / Phonology
This book explores the consequences for syntax of assuming that language is substantively based, or grounded, in extralinguistic cognition and perception. Groundedness does not just apply to the ...
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This book explores the consequences for syntax of assuming that language is substantively based, or grounded, in extralinguistic cognition and perception. Groundedness does not just apply to the categories of syntax, like verb and noun, but also to other aspects of syntactic structure. Thus hierarchization (dependency), linearity, and phonological expression of categories, especially by intonation, are grammaticalizations of, respectively, cognitive salience, our perception of time, and our perception of sound. The major linguistic module of syntax is characterized by a set of categories based on distinctions in the perceived ontological status of what the categories represent, and this basis determines the distribution of categories, defined by category members that are prototypical. This is familiar from the tradition of notional grammar. Submodules in syntax are characterized by the substance they grammaticalize. The first part of the book traces the development in the twentieth century of anti-notionalism, culminating in the autonomy of syntax assumption. Subsequently the book addresses various syntactic phenomena, many of them involving the fundamental notion of finiteness, that illustrate the need to appeal to grounding. Among other things, groundedness permits a lexicalist approach that enables the syntax to dispense with structural mutations such as category change, and the invocation of ‘empty categories’, or of ‘universal grammar’ in general.Less
This book explores the consequences for syntax of assuming that language is substantively based, or grounded, in extralinguistic cognition and perception. Groundedness does not just apply to the categories of syntax, like verb and noun, but also to other aspects of syntactic structure. Thus hierarchization (dependency), linearity, and phonological expression of categories, especially by intonation, are grammaticalizations of, respectively, cognitive salience, our perception of time, and our perception of sound. The major linguistic module of syntax is characterized by a set of categories based on distinctions in the perceived ontological status of what the categories represent, and this basis determines the distribution of categories, defined by category members that are prototypical. This is familiar from the tradition of notional grammar. Submodules in syntax are characterized by the substance they grammaticalize. The first part of the book traces the development in the twentieth century of anti-notionalism, culminating in the autonomy of syntax assumption. Subsequently the book addresses various syntactic phenomena, many of them involving the fundamental notion of finiteness, that illustrate the need to appeal to grounding. Among other things, groundedness permits a lexicalist approach that enables the syntax to dispense with structural mutations such as category change, and the invocation of ‘empty categories’, or of ‘universal grammar’ in general.
John M. Anderson
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199608317
- eISBN:
- 9780191732034
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199608317.003.0005
- Subject:
- Linguistics, Syntax and Morphology, Phonetics / Phonology
Interrogative is a mood, a secondary category of the functional category of finiteness. Different kinds of interrogative structure are described in terms of the framework of Chapter 3. These include ...
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Interrogative is a mood, a secondary category of the functional category of finiteness. Different kinds of interrogative structure are described in terms of the framework of Chapter 3. These include alternative questions, argument questions (wh- in English), re-opened questions, which question an answer or a question, proxy questions, allowing predicators to be questioned, and so-called ‘indirect questions’. The form of these is determined by the meaning of interrogative, so that they involve either a structure whose truth value is open or an argument or predicator that is open. A localist account of truth is offered and its place in relation to finiteness is described. ‘Indirect questions’, whose construction does not appear in main clauses, are regarded as demoted to non-finite. The role of phonology in the expression of interrogatives is described and emphasized. Notionally and lexically based interrogative representations involving argument sharing need not appeal to structural mutation or empty categories.Less
Interrogative is a mood, a secondary category of the functional category of finiteness. Different kinds of interrogative structure are described in terms of the framework of Chapter 3. These include alternative questions, argument questions (wh- in English), re-opened questions, which question an answer or a question, proxy questions, allowing predicators to be questioned, and so-called ‘indirect questions’. The form of these is determined by the meaning of interrogative, so that they involve either a structure whose truth value is open or an argument or predicator that is open. A localist account of truth is offered and its place in relation to finiteness is described. ‘Indirect questions’, whose construction does not appear in main clauses, are regarded as demoted to non-finite. The role of phonology in the expression of interrogatives is described and emphasized. Notionally and lexically based interrogative representations involving argument sharing need not appeal to structural mutation or empty categories.
John M. Anderson
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199608317
- eISBN:
- 9780191732034
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199608317.003.0007
- Subject:
- Linguistics, Syntax and Morphology, Phonetics / Phonology
Finiteness is interpreted here as the category licensing potential independence of a predication, and mood is a secondary category that grammaticalizes speech‐act type. As such it is limited to ...
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Finiteness is interpreted here as the category licensing potential independence of a predication, and mood is a secondary category that grammaticalizes speech‐act type. As such it is limited to main‐clause finites. Declarative is the prototypical mood, and its prototypical interpretation is as a speech act of assertion; and the indicative construction is the prototypical expression of declarative. The indicative varies in its properties from language to language, but it is likely to attract secondary categories associated with the circumstances of utterance, such as tense and person‐number. Most like indicatives are typically expressions of negative and insistent assertion. The expression of non‐declaratives differs more, though interrogatives, in questioning a potential assertion, are less deviant than non‐propositional moods such as imperatives, hortatives, optatives, etc. The structures of a range of types of mood expression are described. This and the two following chapters illustrate the workings of a notional grammar in this fundamental area of the syntax.Less
Finiteness is interpreted here as the category licensing potential independence of a predication, and mood is a secondary category that grammaticalizes speech‐act type. As such it is limited to main‐clause finites. Declarative is the prototypical mood, and its prototypical interpretation is as a speech act of assertion; and the indicative construction is the prototypical expression of declarative. The indicative varies in its properties from language to language, but it is likely to attract secondary categories associated with the circumstances of utterance, such as tense and person‐number. Most like indicatives are typically expressions of negative and insistent assertion. The expression of non‐declaratives differs more, though interrogatives, in questioning a potential assertion, are less deviant than non‐propositional moods such as imperatives, hortatives, optatives, etc. The structures of a range of types of mood expression are described. This and the two following chapters illustrate the workings of a notional grammar in this fundamental area of the syntax.
Dunstan Brown, Marina Chumakina, and Greville G. Corbett (eds)
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199604326
- eISBN:
- 9780191746154
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199604326.001.0001
- Subject:
- Linguistics, Syntax and Morphology, Theoretical Linguistics
This is the first book to present Canonical Typology, a framework for comparing constructions and categories across languages. The canonical method takes the criteria used to define particular ...
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This is the first book to present Canonical Typology, a framework for comparing constructions and categories across languages. The canonical method takes the criteria used to define particular categories or phenomena (e.g. negation, finiteness, possession) to create a multidimensional space in which language-specific instances can be placed. In this way, the issue of fit becomes a matter of greater or lesser proximity to a canonical ideal. Drawing on the expertise of world-class scholars in the field, the book addresses the issue of cross-linguistic comparability, illustrates the wide range of areas—from morphosyntactic features to reported speech—to which linguists are currently applying this methodology.Less
This is the first book to present Canonical Typology, a framework for comparing constructions and categories across languages. The canonical method takes the criteria used to define particular categories or phenomena (e.g. negation, finiteness, possession) to create a multidimensional space in which language-specific instances can be placed. In this way, the issue of fit becomes a matter of greater or lesser proximity to a canonical ideal. Drawing on the expertise of world-class scholars in the field, the book addresses the issue of cross-linguistic comparability, illustrates the wide range of areas—from morphosyntactic features to reported speech—to which linguists are currently applying this methodology.
Irina Nikolaeva
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199604326
- eISBN:
- 9780191746154
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199604326.003.0005
- Subject:
- Linguistics, Syntax and Morphology, Theoretical Linguistics
Since no implicational relations suggested for finiteness parameters so far have been without exceptions, it is argued that finiteness is a clausal notion which is best characterized by independent ...
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Since no implicational relations suggested for finiteness parameters so far have been without exceptions, it is argued that finiteness is a clausal notion which is best characterized by independent criteria belonging to different linguistic components: morphology, syntax, and semantics. There is no uniform dimension called ‘finiteness’. Instead, the relevant category (if it is a category) is sensitive to different kinds of cross-cutting information and each of them can vary independently.Less
Since no implicational relations suggested for finiteness parameters so far have been without exceptions, it is argued that finiteness is a clausal notion which is best characterized by independent criteria belonging to different linguistic components: morphology, syntax, and semantics. There is no uniform dimension called ‘finiteness’. Instead, the relevant category (if it is a category) is sensitive to different kinds of cross-cutting information and each of them can vary independently.
Matt Clay
- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691158662
- eISBN:
- 9781400885398
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691158662.003.0004
- Subject:
- Mathematics, Geometry / Topology
This chapter studies subgroups of free groups using the combinatorics of graphs and a simple operation called folding. It introduces a topological model for free groups and uses this model to show ...
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This chapter studies subgroups of free groups using the combinatorics of graphs and a simple operation called folding. It introduces a topological model for free groups and uses this model to show the rank of the free group H and whether every finitely generated nontrivial normal subgroup of a free group has finite index. The edge paths and the fundamental group of a graph are discussed, along with subgroups via graphs. The chapter also considers five applications of folding: the Nielsen–Schreier Subgroup theorem, the membership problem, index, normality, and residual finiteness. A group G is residually finite if for every nontrivial element g of G there is a normal subgroup N of finite index in G so that g is not in N. Exercises and research projects are included.Less
This chapter studies subgroups of free groups using the combinatorics of graphs and a simple operation called folding. It introduces a topological model for free groups and uses this model to show the rank of the free group H and whether every finitely generated nontrivial normal subgroup of a free group has finite index. The edge paths and the fundamental group of a graph are discussed, along with subgroups via graphs. The chapter also considers five applications of folding: the Nielsen–Schreier Subgroup theorem, the membership problem, index, normality, and residual finiteness. A group G is residually finite if for every nontrivial element g of G there is a normal subgroup N of finite index in G so that g is not in N. Exercises and research projects are included.
Tien-Cuong Dinh, Viet-Anh Nguyen, and Nessim Sibony
Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159294
- eISBN:
- 9781400851317
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159294.003.0020
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter introduces a notion of entropy for possibly singular hyperbolic laminations by Riemann surfaces. It also studies the transverse regularity of the Poincaré metric and the finiteness of ...
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This chapter introduces a notion of entropy for possibly singular hyperbolic laminations by Riemann surfaces. It also studies the transverse regularity of the Poincaré metric and the finiteness of the entropy. The chapter first focuses on compact laminations, which are transversally smooth, before turning to the case of singular foliations, showing how the Poincaré metric on leaves is transversally Hölder continuous. In addition, the chapter considers the problem in the proof that the entropy is finite for singular foliations is quite delicate and requires a careful analysis of the dynamics around the singularities. Finally, the chapter discusses a notion of metric entropy for harmonic probability measures and gives some open questions.Less
This chapter introduces a notion of entropy for possibly singular hyperbolic laminations by Riemann surfaces. It also studies the transverse regularity of the Poincaré metric and the finiteness of the entropy. The chapter first focuses on compact laminations, which are transversally smooth, before turning to the case of singular foliations, showing how the Poincaré metric on leaves is transversally Hölder continuous. In addition, the chapter considers the problem in the proof that the entropy is finite for singular foliations is quite delicate and requires a careful analysis of the dynamics around the singularities. Finally, the chapter discusses a notion of metric entropy for harmonic probability measures and gives some open questions.
Tien-Cuong Dinh, Viet-Anh Nguyen, and Nessim Sibony
Araceli Bonifant, Mikhail Lyubich, and Scott Sutherland (eds)
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691159294
- eISBN:
- 9781400851317
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691159294.003.0021
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter studies Riemann surface foliations with tame singular points. It shows that the hyperbolic entropy of a Brody hyperbolic foliation by Riemann surfaces with linearizable isolated ...
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This chapter studies Riemann surface foliations with tame singular points. It shows that the hyperbolic entropy of a Brody hyperbolic foliation by Riemann surfaces with linearizable isolated singularities on a compact complex surface is finite. The chapter then proves the finiteness of the entropy in the local setting near a singular point in any dimension, using a division of a neighborhood of a singular point into adapted cells. Next, the chapter estimates the modulus of continuity for the Poincaré metric along the leaves of the foliation, using notion of conformally (R,δ)-close maps. The estimate holds for foliations on manifolds of higher dimension.Less
This chapter studies Riemann surface foliations with tame singular points. It shows that the hyperbolic entropy of a Brody hyperbolic foliation by Riemann surfaces with linearizable isolated singularities on a compact complex surface is finite. The chapter then proves the finiteness of the entropy in the local setting near a singular point in any dimension, using a division of a neighborhood of a singular point into adapted cells. Next, the chapter estimates the modulus of continuity for the Poincaré metric along the leaves of the foliation, using notion of conformally (R,δ)-close maps. The estimate holds for foliations on manifolds of higher dimension.
Antonio Fábregas
- Published in print:
- 2018
- Published Online:
- June 2018
- ISBN:
- 9780190876746
- eISBN:
- 9780190876784
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190876746.003.0010
- Subject:
- Linguistics, Syntax and Morphology
This chapter explores how the size of stored exponents can account for word order facts in the nanosyntactic framework. Three Spanish varieties are considered; these varieties differ in the ...
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This chapter explores how the size of stored exponents can account for word order facts in the nanosyntactic framework. Three Spanish varieties are considered; these varieties differ in the availability of preverbal subjects in interrogative sentences. The most restrictive one, European Spanish, disallows them all; Mérida (Venezuela) Spanish allows some under restrictive conditions, whereas Dominican Spanish allows them all. It is argued that the differences follow from the size of the subject agreement exponent and, crucially, whether it is the element that spells out the interrogative force of the sentence: The smaller the stored exponent is, the more available preverbal subjects in interrogative sentences are.Less
This chapter explores how the size of stored exponents can account for word order facts in the nanosyntactic framework. Three Spanish varieties are considered; these varieties differ in the availability of preverbal subjects in interrogative sentences. The most restrictive one, European Spanish, disallows them all; Mérida (Venezuela) Spanish allows some under restrictive conditions, whereas Dominican Spanish allows them all. It is argued that the differences follow from the size of the subject agreement exponent and, crucially, whether it is the element that spells out the interrogative force of the sentence: The smaller the stored exponent is, the more available preverbal subjects in interrogative sentences are.
