scholarly journals Why is Generative Grammar Recursive?

Erkenntnis ◽  
2021 ◽  
Author(s):  
Fintan Mallory
Keyword(s):  
Generative Grammar ◽  
Linguistic Competence ◽  
Adequate Account ◽  
Natural Languages ◽  
Finite Representation ◽  
The Real ◽  
Generative Linguistics ◽  
Infinite Sets

AbstractA familiar argument goes as follows: natural languages have infinitely many sentences, finite representation of infinite sets requires recursion; therefore any adequate account of linguistic competence will require some kind of recursive device. The first part of this paper argues that this argument is not convincing. The second part argues that it was not the original reason recursive devices were introduced into generative linguistics. The real basis for the use of recursive devices stems from a deeper philosophical concern; a grammar that functions merely as a metalanguage would not be explanatorily adequate as it would merely push the problem of explaining linguistic competence back to another level. The paper traces this concern from Zellig Harris and Chomsky’s early work in generative linguistics and presents some implications.

On phonotactically motivated rules

1974 ◽  
Vol 10 (1) ◽  
pp. 71-94 ◽  
Author(s):  
Alan H. Sommerstein
Keyword(s):  
Generative Grammar ◽  
Linguistic Competence ◽  
Consonant Clusters ◽  
Natural Languages ◽  
Main Thesis ◽  
Phonological Rules

The main thesis of this paper is that the grammars of natural languages contain an exhaustive set of conditions on the output of the phonological rules – in fact, a surface phonotactics. I shall show that, contrary to what is usually assumed in generative phonology, a surface phonotactics is not redundant in a generative grammar if the grammar is indeed intended as ‘a theory of linguistic competence’ (Chomsky, 1965: 3), and that if any set of rules in the phonological section of the grammar is redundant it is the morphophonotactic rules, better known as morpheme structure conditions. I shall propose a format for the statement of rules (including so-called ‘conspiracies’) which are ‘motivated’ by the phonotactics in the sense of Matthews (1972: 219–220). Finally, I shall present a set of phonotactic rules for consonant clusters in Latin, and show how the statement of certain rules of Latin phonology can be simplified by taking their phonotactic motivation into account.

A question of relevance

2004 ◽  
Vol 28 (3) ◽  
pp. 648-674 ◽  
Author(s):  
Helmut Weiß
Keyword(s):  
Native Speakers ◽  
Natural Languages ◽  
Underlying Assumption ◽  
Generative Linguistics ◽  
First Languages

Data from natural languages (in contrast to, say, the results of psycholinguistic experiments) are still a major source of evidence used in linguistics, whether they are elicited through grammatical judgments, as in generative linguistics, or by collecting samples, as preferred in typology. The underlying assumption is that data are alike in their value as evidence if they occur in natural languages. The present paper questions this assumption in showing that there is a difference in the naturalness of languages because languages like German or English have originally emerged as secondarily learned written languages, that is they once were languages without native speakers. Although they are nowadays acquired as first languages, their grammars still contain inconsistent properties which partly disqualify standard languages as a source of evidence.

Generative Grammar and Linguistic Competence.

1980 ◽  
Vol 30 (118) ◽  
pp. 90
Author(s):  
David E. Cooper ◽  
P. H. Matthews
Keyword(s):  
Generative Grammar ◽  
Linguistic Competence

Newmeyer's cyclic view of the history of generative grammar

1999 ◽  
Vol 35 (1) ◽  
pp. 151-166 ◽  
Author(s):  
JAMES D. McCAWLEY
Keyword(s):  
Historical Perspective ◽  
Generative Grammar ◽  
Generative Linguistics ◽  
History Of

Frederick J. Newmeyer, Generative linguistics: a historical perspective. London: Routledge, 1996. Pp. x+218.In this book (henceforth, GL), Newmeyer has collected 11 of his articles (including two co-authored ones), two of them previously unpublished, on the history of generative grammar, supplemented by reprints of two sections of Newmeyer 1986.

scholarly journals On Arbitrary sets andZFC

2011 ◽  
Vol 17 (3) ◽  
pp. 361-393 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Set Theory ◽  
Axiom Of Choice ◽  
Real Numbers ◽  
The Real ◽  
Formal Systems ◽  
Infinite Sets ◽  
The Axiom Of Choice ◽  
The Continuum

AbstractSet theory deals with the most fundamental existence questions in mathematics-questions which affect other areas of mathematics, from the real numbers to structures of all kinds, but which are posed as dealing with the existence of sets. Especially noteworthy are principles establishing the existence of some infinite sets, the so-called “arbitrary sets.” This paper is devoted to an analysis of the motivating goal of studying arbitrary sets, usually referred to under the labels ofquasi-combinatorialismorcombinatorial maximality. After explaining what is meant by definability and by “arbitrariness,” a first historical part discusses the strong motives why set theory was conceived as a theory of arbitrary sets, emphasizing connections with analysis and particularly with the continuum of real numbers. Judged from this perspective, the axiom of choice stands out as a most central and natural set-theoretic principle (in the sense of quasi-combinatorialism). A second part starts by considering the potential mismatch between the formal systems of mathematics and their motivating conceptions, and proceeds to offer an elementary discussion of how far the Zermelo–Fraenkel system goes in laying out principles that capture the idea of “arbitrary sets”. We argue that the theory is rather poor in this respect.

Procedural theories of linguistic performance

1981 ◽  
Vol 295 (1077) ◽  
pp. 297-304 ◽  
Keyword(s):  
Generative Grammar ◽  
Computer Programs ◽  
Modern Theory ◽  
Natural Languages ◽  
Adequate Model ◽  
Linguistic Performance ◽  
Numeral Systems ◽  
Theory Of Language ◽  
Effective Procedures ◽  
The Ideal

In the modern theory of language it has been found useful to distinguish between questions of ‘competence’ and questions of ‘performance’. The distinction has at least two aspects. First, it recognizes that the description of a language as such is logically distinct from an account of the way in which particular people use that language, but, secondly, it separates questions of grammaticality from questions about naturalness or intelligibility. It is argued that, while the former distinction is valuable, the latter has now outlived its usefulness. A generative grammar can be regarded as an adequate model of the ideal speaker’s competence only if it is accompanied by a specification of processes by which ideas could be encoded in words, and these words subsequently decoded by the hearer. Examples are given of effective procedures, implemented as computer programs, for the performance of specific linguistic tasks; one of these, due to A. C. Davey, is a model of the production of connected English discourse; another, due to R. J. D. Power and myself, is a device that learns, from representative number—numeral pairs, the numeral systems of a variety of natural languages.

scholarly journals : Generative Grammar and Linguistic Competence . P. H. Matthews.

1981 ◽  
Vol 83 (1) ◽  
pp. 211-212
Author(s):  
H. Stephen Straight
Keyword(s):  
Generative Grammar ◽  
Linguistic Competence

Open induction and the true theory of rationals

1987 ◽  
Vol 52 (3) ◽  
pp. 793-801
Author(s):  
Zofia Adamowicz
Keyword(s):  
Linear Space ◽  
Usual Sense ◽  
Saturated Model ◽  
The Real ◽  
Maximal Subset ◽  
True Theory ◽  
Real Closure ◽  
Open Induction ◽  
Infinite Sets ◽  
Image Position

In the paper we prove the following theorem:Theorem. There is a model N of open induction in which the set of primes is bounded and N is such that its field of fractions 〈N*, +, ·, <〉 is elementarily equivalent to 〈Q, +, ·, <〉 (the standard rationals).We fix an ω1-saturated model 〈M, +, ·, <〉 of PA. Let 〈M*, +, ·, <〉 denote the field of fractions of M. The model N that we are looking for will be a substructure of 〈M*, +, ·, <〉.If A ⊆ M* then let Ā denote the ring generated by A within M*, Ậ the real closure of A, and A* the field of fractions generated by A. We haveLet J ⊆ M. Then 〈M*, +, ·〉 is a linear space over J*. If x1,…,xk ∈ M*, we shall say that x1,…,xk are J-independent if 〈1, x1,…, xk〉 are J*-independent in the usual sense. As usual, we extend the notion of J-independence to the case of infinite sets.If A ⊆ M* and X ⊆ A, then we say that X is a J-basis of A if X is a maximal subset of A which is J-independent.Definition 1.1. By a J-form ρ we mean a function from (M*)k into M*, of the formwhere q0,…, qk ∈ J*If υ ∈ M, we say that ρ is a υ-form if the numerators and denominators of the qi's have absolute values ≤ υ.

On generativity

1993 ◽  
Vol 20 (2-3) ◽  
pp. 341-454
Author(s):  
James W. Ney
Keyword(s):  
Generative Grammar ◽  
Linguistic Theory ◽  
Recent History ◽  
Modus Operandi ◽  
Generative Linguistics ◽  
History Of ◽  
Explicit Grammar ◽  
Infinite Set

Summary Chomsky insists that he has always understood a generative grammar to be “nothing more than an explicit grammar”. Other commentators have understood that ‘generate’ means ‘specify an infinite set’ and that a ‘generative’ grammar is a grammar which specifies an infinite set of sentences. This understanding of the term ‘generative’ has had a long and interesting history within the confines of linguistic theory starting in the writings of Chomsky’s intellectual predecessors and continuing through the writings of Chomsky himself. In some cases, it even seems that ‘to generate’ is a near synonym for ‘to produce’ both in the writings of Chomsky and of other early transformationalists. In other instances, it is difficult to see how ‘explicit’, an adjective, can serve as a synonym for ‘generate’, a verb as this verb has been used throughout the history of transformational generative linguistics. Furthermore, it would appear that a rule like move-α has little or no meaning in a non-generative grammar, i.e., one that is merely ‘explicit’, one that does not rely on process type statements as its modus operandi. Nevertheless, in the recent history of transformationalism, Chomsky insists that ‘generative’ means nothing more than ‘explicit’ and nothing less. To him, the notion that ‘generative’ has something to do with specifying or characterizing a set of sentences is a notion that never was.

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