Syntactic Theories, Misc

Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning (...) of true that attribution of being true to a given thing presupposes the thing is a sentence. Beta’s importance is further highlighted by the fact that alpha can be satisfied using the recursively definable concept of being satisfied by every infinite sequence, which Tarski explicitly rejects. Moreover, in Definition 23, the famous truth-definition, Tarski supplements “being satisfied by every infinite sequence” by adding the condition “being a sentence”. Even where truth is undefinable and treated by Tarski axiomatically, he adds as an explicit axiom a sentence to the effect that every truth is a sentence. Surprisingly, the sentence just before the presentation of Convention T seems to imply that alpha alone might be sufficient. Even more surprising is the sentence just after Convention T saying beta “is not essential”. Why include a condition if it is not essential? Tarski says nothing about this dissonance. Considering the broader context, the Polish original, the German translation from which the English was derived, and other sources, we attempt to determine what Tarski might have intended by the two troubling sentences which, as they stand, are contrary to the spirit, if not the letter, of several other passages in Tarski’s corpus. (shrink)

In recent years, dependency grammars have established themselves as valuable tools in theoretical and computational linguistics. To many linguists, dependency grammars and the more standard constituency-based formalisms are notational variants. We argue that, beyond considerations of formal equivalence, cognition may also serve as a background for a genuine comparison between these different views of syntax. In this paper, we review and evaluate some of the most common arguments and evidence employed to advocate for the cognitive or neural reality of dependency (...) grammars in linguistics, psycholinguistics, or neurolinguistics. We then raise the possibility that the abilities to represent and track, alternatively or in parallel, constituency and dependency structures co-exist in human cognition and are constitutive of syntactic competence. (shrink)

A 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. (shrink)

Deontic necessity modals (e.g. 'have to', 'ought to', 'must', 'need to', 'should', etc.) seem to vary in how they interact with negation. According to some accounts, what forces modals like 'ought' and 'should' to outscope negation is their polarity sensitivity -- modals that scope over negation do so because they are positive polarity items. But there is a conflict between this account and a widely assumed theory of if-clauses, namely the restrictor analysis. In particular, the conflict arises for constructions containing (...) a bound pronoun in the if-clause. This note spells out the core conflict. (shrink)

In the paper, various notions of the logical semiotic sense of linguistic expressions – namely, syntactic and semantic, intensional and extensional – are considered and formalised on the basis of a formal-logical conception of any language L characterised categorially in the spirit of certain Husserl's ideas of pure grammar, Leśniewski-Ajdukiewicz's theory of syntactic/semantic categories and, in accordance with Frege's ontological canons, Bocheński's and some of Suszko's ideas of language adequacy of expressions of L. The adequacy ensures their unambiguous syntactic and (...) semantic senses and mutual, syntactic and semantic correspondence guaranteed by the acceptance of a postulate of categorial compatibility of syntactic and semantic (extensional and intensional) categories of expressions of L. This postulate defines the unification of these three logical senses. There are three principles of compositionality which follow from this postulate: one syntactic and two semantic ones already known to Frege. They are treated as conditions of homomorphism of partial algebra of L into algebraic models of L: syntactic, intensional and extensional. In the paper, they are applied to some expressions with quantifiers. Language adequacy connected with the logical senses described in the logical conception of language L is, obviously, an idealisation. The syntactic and semantic unambiguity of its expressions is not, of course, a feature of natural languages, but every syntactically and semantically ambiguous expression of such languages may be treated as a schema representing all of its interpretations that are unambiguous expressions. (shrink)

This chapter presents a thorough analysis of Neurath’s physicalist syntacticism. It explores connections between syntacticism and other elements of Neurath’s philosophy such as the unity of science and the sociological imperative of empiricism. It also defends the intelligibility of syntacticism. Finally, the case is made that Neurath’s fear of semantics was warranted: logical empiricism was undermined to a large extent by the widespread acceptance of semantics.

Semantics in the Montagovian tradition combines two basic tenets. One tenet is that the semantic value of a sentence is an intension, a function from points of evaluations into truth-values. The other tenet is that the semantic value of a composite expression is the result of applying the function denoted by one component to arguments denoted by the other components. Many philosophers object to intensional semantics on the grounds that intensionally equivalent sentences do not substitute salva veritate into attitude ascriptions. (...) They propose instead that the semantic values of sentences must be structured propositions. In rejecting intensional semantics, philosophers who endorse structured propositions also usually reject functional compositionality, undermining both tenets of the Montagovian programme. I defend a semantic theory that incorporates both structured propositions and functional compositionality. I argue that this semantic theory can preserve many explanatory benefits of Montague semantics. Finally, I show how treating composition functional application can resolve core problems internal to a theory of structured propositions. (shrink)

The main purpose of the paper is to outline the formal-logical, general theory of language treated as a particular ontological being. The theory itself is called the ontology of language, because it is motivated by the fact that the language plays a special role: it reflects ontology and ontology reflects the world. Language expressions are considered to have a dual ontological status. They are understood as either concretes, that is tokens – material, physical objects, or types – classes of tokens, (...) which are abstract objects. Such a duality is taken into account in the presented logical theory of syntax, semantics and pragmatics. We point to the possibility of building it on two different levels; one which stems from concretes, language tokens of expressions, whereas the other one – from their classes, types conceived as abstract, ideal beings. The aim of this work is not only to outline this theory as taking into account the functional approach to language, with respect to the dual ontological nature of its expressions, but also to show that the logic based on it is ontologically neutral in the sense that it abstracts from accepting some existential assumptions, related with the ontological nature of these linguistic expressions and their extra-linguistic ontological counterparts (objects). (shrink)

Logical form has always been a prime concern for philosophers belonging to the analytic tradition. For at least one century, the study of logical form has been widely adopted as a method of investigation, relying on its capacity to reveal the structure of thoughts or the constitution of facts. This book focuses on the very idea of logical form, which is directly relevant to any principled reflection on that method. Its central thesis is that there is no such thing as (...) a correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfil two major theoretical roles that pertain respectively to logic and to semantics. This thesis has a negative and a positive side. The negative side is that a deeply rooted presumption about logical form turns out to be overly optimistic: there is no unique notion of logical form that can play both roles. The positive side is that the distinction between two notions of logical form, once properly spelled out, sheds light on some fundamental issues concerning the relation between logic and language. (shrink)

Lecture notes from Husserl's logic lectures published during the last 20 years offer a much better insight into his doctrine of the forms of meaning than does the fourth Logical Investigation or any other work published during Husserl's lifetime. This paper provides a detailed reconstruction, based on all the sources now available, of Husserl's system of logical grammar. After having explained the notion of meaning that Husserl assumes in his later logic lectures as well as the notion of form of (...) meaning as it features in ‘doctrine of the forms of meaning’, I present a system of rules that describes all the various forms of meaning that Husserl singles out in his lectures. (shrink)

I review and challenge the views on simplicity and its role in linguistics put forward by Ludlow. In particular, I criticize the claim that simplicity—in the sense pertinent to science—is nothing more than ease of use or “user-friendliness”, motivated by economy of labor. I argue that Ludlow’s discussion fails to do justice to the diversity of factors that are relevant to simplicity considerations. This, in turn, leads to the neglect of crucial cases in which the rationale for simplification is unmistakably (...) epistemic, as well as instances where simplicity is part of the content of substantive, empirical hypotheses. I illustrate these points with examples from the history of generative linguistics, such as: the shaping influence exerted by simplicity, via its involvement in the notion of “linguistically significant generalization”, its methodological and substantive contribution to the goal of explanatory adequacy, and its central role in the Minimalist Program’s search “beyond explanatory adequacy”. (shrink)

This paper argues that the theory of phrase structure a certain linguistic approach assumes implies taking a stance on the formal nature of the computational procedures that generate that phrase structure. We will proceed by critically evaluating theories of phrase structure and labeling -which implies taking a structure as a unit for the purposes of further computations-, and building on and opposing to the proposals we review, we will claim that syntactic objects are not computationally uniform, and therefore the computational (...) system in charge of establishing dependencies between symbolic objects within the mind is not uniform as well. We argue in favor of a linguistic-cognitive model which dynamically chooses different grammars based on the complexity of the input, and is capable of assigning a mixed phrase marker to an object that presents more than one computational pattern. Empirical evidence is provided in favor of our approach to phrase structure building, and further implications for a theory of labeling and predication are discussed as prolegomena to further research. (shrink)

In this paper we will analyze the conceptual and computational motivations of the property of displacement in natural languages from a revisited perspective. We will account for displacement phenomena proposing our own version of displacement-as-external token Merge, as opposed to the traditional displacement-as-literal movement or, more recently, displacement-as-copy and Merge (Chomsky 1995; Kitahara 1997; Nunes 2004). As far as empirical data is concerned, we will provide a brief analysis of parasitic gaps and their derivation, comparing our proposal with previous accounts (...) making particular stress on the idea that operations are not feature-driven in a highly constrained syntactic component, but interface-driven, syntax being free and unbounded. (shrink)

Category mistakes are sentences such as 'Green ideas sleep furiously' or 'Saturday is in bed'. They strike us as highly infelicitous but it is hard to explain precisely why this is so. Ofra Magidor explores four approaches to category mistakes in philosophy of language and linguistics, and develops and defends an original, presuppositional account.

This paper is an attempt at exploring the possibility of reconciling the two interpretations of biolinguistics which have been recently projected by Koster(Biolinguistics 3(1):61–92, 2009). The two interpretations—trivial and nontrivial—can be roughly construed as non-internalist and internalist conceptions of biolinguistics respectively. The internalist approach boils down to a conception of language where language as a mental grammar in the form of I-language grows and functions like a biological organ. On the other hand, under such a construal consistent with Koster’s (Biolinguistics (...) 3(1):61-92, 2009), the non-internalist version does not necessarily have to be externalist in nature; rather it is a matter of mutual reinforcement of biology and culture under the rubric of a co-evolutionary dynamics. Here it will be argued that the apparent dichotomy between these two conceptions of biolinguistics can perhaps be resolved if we have a richer synthesis that accounts for both internalism and non-internalism. (shrink)

We study the process of interpretation of a text written in some unspecified natural language, say in English, considered as a means of communication. Our analysis concerns the only texts written “with good grace” and intended for human understanding; we call them 'admissible'. Whether a part of an admissible text is meaningful or not depends on some accepted 'criterion of meaningfulness'. We argue that the criterion of meaningfulness conveying an idealized reader's linguistic competence meant as ability to grasp a communicative (...) content gives rise to a genuine topology on an admissible text, which we call 'phonocentric'. We argue that the following properties of phonocentric topology are 'linguistic universals' of topological nature: (i) T0-separability, (ii) topological connectedness, (iii) acyclicity of corresponding Hasse diagram. This way, we interpret linguistic notions in terms of topology and specialization order; their geometric studies is a kind of 'Topological Formal Syntax'. For an admissible text X, we define the Schleiermacher category Schl(X) of sheaves of fragmentary meanings, and we define the category Context(X) of étale bundles of contextual meanings. Their geometric studies is a kind of 'Sheaf-Theoretic Formal Semantics' that allows us to generalize Frege's compositionality and contextuality principles related by 'Frege Duality' defined in categorical terms. It reveals that the acceptance of one of these principles implies the acceptance of the other, and it gives rise to a functional representation of fragmentary meanings that allows us to develop a kind of 'Dynamic Semantics' describing how the interpretation of a given text proceeds by induction over the discrete time as a successive extension of a continuous function, which represents a meaning, to the whole finite topological space naturally attached to interpreted text. (shrink)

A familiar dialogue is taking place in the professional literature of records and information management. Since the early 1990s, the theoretical foundation of a records management theory has been constructed on convergence (Pemberton & Nugent, 1995; Walters, 1995; Zawiyah M Yusof & Robert W Chell, 2002). While certain concepts are shared across disciplines, arguably the most foundational definition is the most divergent: a record. Each discipline (Archival Science, Library Science, Computer Science) defines the term record in its own way. Records (...) managers at all levels have difficulty espousing a universal definition of the term, while claiming sole responsibility for the authority, organization, authenticity, and sustainability of records. (shrink)

In this article I present the conception of syntax emerging from the “dynamic approach” to syntax and semantics, developed in the last few decades, moving from the critic to the static theories of language, either those developed in the Chomskian framework or those based on Montague’s grammar. I will suggest that this view can be fruitfully compared with Saussure’s position on syntax.

The logos question, one of the most important among the subjects that traverse the Plato's Sophist, has in fact some different aspects: the criticism of father Parmenides' logos, that is unable to speak about the not-being, but also about the being; the relations between logos and its cognates, phantasia, doxa and dianoia; the logos’ complex structure, that is a compound with onoma and rema; the difference between naming and saying, two distinct but inseparable actions; the logical and ontological conditions that (...) make possible to say the truth, or to lie or simply to joke; the necessity of a most flexible logos that allows us to speak about the not-being, and about the being, but at the same time is a logos dangerously similar to the sophist’ one; finally, the identity between the power to produce “spoken images” and the very power to speak. The aim of the present article is giving a systematical view of the matter that grasps all these faces. (shrink)

In Languages of Art, Nelson Goodman presents a general theory of symbolic notation. However, I show that his theory could not adequately explain possible cases of natural language notational uses, and argue that this outcome undermines, not only Goodman's own theory, but any broadly type versus token based account of notational structure.Given this failure, an alternative representational theory is proposed, in which different visual or perceptual aspects of a given physical inscription each represent a different letter, word, or other notational (...) item. Such a view is strongly supported by the completely conventional relation between inscriptions and notation, as shown by encryption techniques etc. (shrink)

The paper develops Lambda Grammars, a form of categorial grammar that, unlike other categorial formalisms, is non-directional. Linguistic signs are represented as sequences of lambda terms and are combined with the help of linear combinators.

This paper sketches or signals some ideas, results, and proposals connected with the theoretical issues related to the categorial approach to language which originated from the first author and which form the basis for further research by the second author. The main aims are the following: 1) to bring into common use some Polish ideas concerned with classical categorial grammar; 2) to take into consideration a universal and simultaneously formal-logical perspective; 3) to consider Peirce's well-known differentiation of linguistic objects, i.e. (...) their twofold ontological status as tokens and types and, according to this, to consider the biaspectual formalization of language dealing with the two main orientations in the controversy between nominalism and Platonism; 4) to characterize language according to Frege's ontological canons, according to which each expression of language corresponds to its denotation. All of these factors make possible not only the syntactic characterization of language but also the introduction of syntactic and semantic definitions of a true expression and its denotation. These notions correspond here to the old classical, but not necessarily standard, understanding of semantic concepts. The paper is divided into four sections: the first contains a brief characterization of the categorial approach to syntax; the second presents two strains of this approach; the third touches on certain general semantic issues connected with the notion of truth; and the last gives some final remarks. (shrink)

The paper contains an overview of the most important results presented in the monograph of the author "Teorie Językow Syntaktycznie-Kategorialnych" ("Theories of Syntactically-Categorial Languages" (in Polish), PWN, Warszawa-Wrocław 1985. In the monograph four axiomatic systems of syntactically-categorial languages are presented. The first two refer to languages of expression-tokens. The others also takes into consideration languages of expression-types. Generally, syntactically-categorial languages are languages built in accordance with principles of the theory of syntactic categories introduced by S. Leśniewski [1929,1930]; they are connected (...) with- the Ajdukiewicz’s work [1935] which was a continuation of Leśniewski’s idea and further developed and popularized in the research on categorial grammars, by Y. Bar-Hillel [1950,1953,1964]. To assign a suitable syntactic category to each word of the vocabulary is the main idea of syntactically-categorial approach to language. Compound expressions are built from the words of the vocabulary and then a suitable syntactic-category is assigned to each of them. A language built in this way should be decidable, which means that there should exist an algorithm for deciding about each expression of it, whether it is well-formed or is syntactically connected . The traditional, originating from Husserl, understanding of the syntactic category confronts some difficulties. This notion is defined by abstraction using the concept of affiliation of two expressions to the same syntactic category. (shrink)

This note is based on a lecture delivered at the Conference on the Scien- tic Research of the Mathematical Center of Opole, Turawa, May 10-11th, 1980. A somewhat extended version will be published in the Proceedings of the Conference. At the same time it is an abstract of a part of a planned larger paper, which will involve the theory of label-tokens. The theory is included into the author's monograph in Polish "Teorie Językow Syntaktycznie Kategorialnych", PWN, Warszawa-Wrocław 1985 and into (...) its English version: Theory of Language Syntax. Categorial Approach, Kluwer Academic Publishers, Boston-London-Dordrecht 1991. (shrink)

Since the early 1980s, there has been a debate in the semantics literature pertaining to whether wh-interrogatives can be directly disjoined, as main clauses and as complements. Those who held that the direct disjunction of wh-interrogatives was in conflict with certain theoretical considerations proposed that they could be disjoined indirectly. Indirect disjunction proceeds by first lifting both wh-interrogatives and then disjoining them; it assigns matrix-level scope to OR. As we will see, the notorious theoretical need for indirect disjunction has disappeared (...) by today. But the factual question remains. Are wh-complements disjoined directly or indirectly? What is the fact of the matter? This paper argues that the case for indirect disjunction remains reasonably strong. (shrink)