The paper concentrates on the problem of adequate reflection of fragments of reality via expressions of language and inter-subjective knowledge about these fragments, called here, in brief, language adequacy. This problem is formulated in several aspects, the most being: the compatibility of language syntax with its bi-level semantics: intensional and extensional. In this paper, various aspects of language adequacy find their logical explication on the ground of the formal-logical theory T of any categorial language L generated by the so-called classical (...) categorial grammar, and also on the ground of its extension to the bi-level, intensional and extensional semantic-pragmatic theory ST for L. In T, according to the token-type distinction of Ch.S. Peirce, L is characterized first as a language of well-formed expression-tokens (wfe-tokens) - material, concrete objects - and then as a language of wfe-types - abstract objects, classes of wfe-tokens. In ST the semantic-pragmatic notions of meaning and interpretation for wfe-types of L of intensional semantics and the notion of denotation of extensional semanics for wfe-types and constituents of knowledge are formalized. These notions allow formulating a postulate (an axiom of categorial adequacy) from which follow all the most important conditions of the language adequacy, including the above, and a structural one connected with three principles of compositionality. (shrink)

In demonstration, speakers use real-world activity both for its practical effects and to help make their points. The demonstrations of origami mathematics, for example, reconfigure pieces of paper by folding, while simultaneously allowing their author to signal geometric inferences. Demonstration challenges us to explain how practical actions can get such precise significance and how this meaning compares with that of other representations. In this paper, we propose an explanation inspired by David Lewis’s characterizations of coordination and scorekeeping in conversation. In (...) particular, we argue that words, gestures, diagrams and demonstrations can function together as integrated ensembles that contribute to conversation, because interlocutors use them in parallel ways to coordinate updates to the conversational record. (shrink)

We can distinguish two non-equivalent ways in which a natural language argument can be valid: it can be interpretationally or representationally valid. However, there is just one notion of classical first-order validity for formal languages: truth-preservation in all classical first-order models. To ease the tension, Baumgartner suggests that we should understand interpretational and representational validity as imposing different adequacy conditions on formalizations of natural language arguments. I argue against this proposal. To that end, I first show that Baumgartner’s definition of (...) representational validity is extensionally inadequate. I present a number of natural language arguments that we pre-theoretically hold to be representationally valid, but are not representationally valid according to Baumgartner’s definition. I then point to two further untenable features of Baumgartner’s definitions: according to Baumgartner’s definition of a representationally correct formalization, we cannot arrive at formalizations in a recursive way, and Baumgartner’s definition of representational validity is non-monotonic. I conclude that interpretational and representational validity cannot be understood as merely imposing different adequacy conditions on formalizations. If we want to capture our interpretational and representational intuitions, we need two different formal definitions of validity. (shrink)

According to the contemporary consensus, when reaching in the lexicon grammar looks for items like nouns, verbs, and prepositions while logic sees items like predicates, connectives, and quantifiers. In fact, there doesn’t seem to be a single lexical category contemporary grammar and logic both make use of. I hope to show that while a perfect match between the lexical categories of grammar and logic is impossible there can be a substantial overlap. I propose semantic definitions for all the major parts (...) of speech . I argue that the differences among these categories can be captured in terms of distinctions recognized in logic. (shrink)

Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that are simple enough. This contradiction points to the fruitlessness of trying to solve the Logical Omniscience Problem qualitatively if the rationality of agents is to be maintained. We provide a (...) quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness. More precisely, we provide a test for the logical omniscience problem in a given formal theory of knowledge. The quantitative measures we use are inspired by the complexity theory. We illustrate our framework with a number of examples ranging from the traditional implicit representation of knowledge in modal logic to the language of justification logic, which is capable of spelling out the internal inference process. We use these examples to divide representations of knowledge into logically omniscient and not logically omniscient, thus trying to determine how much information about the reasoning process needs to be present in a theory to avoid logical omniscience. (shrink)

In questa comunicazione, non intendo contribuire all’analisi di questa o quella classe di espressioni linguistiche. Vorrei invece dare un contributo alla nostra consapevolezza (chiamiamola pure “filosofica”) della funzione che il concetto di forma logica svolge nelle nostre analisi. Più in particolare, vorrei mettere in guardia contro certe possibili conseguenze di quello che a me pare un uso “metafisico” dell’idea di forma logica. Vorrei dimostrare che una certa eredità filosofica, per lo pi...

Tema je ovoga teksta u širem smislu osvrt na odnos logike i lingvistike. U užem smislu tekst će se u prvome dijelu osvrnuti na teme i instrumentarij, a u drugom na povijest formalne semantike. Recepcija formalnosemantičkih radova na našim područjima nema čvršću tradiciju, kao ni primjena formalnih metoda na proučavanje jezika, pa se i stoga čini korisnim ukazati na njezine dosege. Formalna semantika inspirativno je i plodonosno interdisciplinarno polje istraživanja koje je od 70-tih godina 20. stoljeća iznimno uspješno povezivalo istraživanja (...) lingvista, logičara i filozofa.Broadly, the subject of this paper is the relation between logic and linguistics. More narrowly, it concentrates on formal semantics. The first part of the text discusses the topics and methods of formal semantics, and the second part the history of formal semantics. Formal semantic analysis has not been widely known and applied in our research community, and formal methods have been applied extremely rarely in linguistic analyses. This is why it is useful to point out the significant achievements of formal semantics. This inspiring interdisciplinary field of research has been successfully connecting research in linguistics, logic and philosophy since the early 1970s. (shrink)

A generative grammar for a language L generates one or more syntactic structures for each sentence of L and interprets those structures both phonologically and semantically. A widely accepted assumption in generative linguistics dating from the mid-60s, the Generative Grammar Hypothesis , is that the ability of a speaker to understand sentences of her language requires her to have tacit knowledge of a generative grammar of it, and the task of linguistic semantics in those early days was taken to be (...) that of specifying the form that the semantic component of a generative grammar must take. Then in the 70s linguistic semantics took a curious turn. Without rejecting GGH, linguists turned away from the task of characterizing the semantic component of a generative grammar to pursue instead the Montague-inspired project of providing for natural languages the same kind of model-theoretic semantics that logicians devise for the artificial languages of formal systems of logic, and “formal semantics” continues to dominate semantics in linguistics. This essay argues that the sort of compositional meaning theory that would verify GGH would not only be quite different from the theories formal semanticists construct, but would be a more fundamental theory that supersedes those theories in that it would explain why they are true when they are true, but their truth wouldn’t explain its truth. Formal semantics has undoubtedly made important contributions to our understanding of such phenomena as anaphora and quantification, but semantics in linguistics is supposed to be the study of meaning. This means that the formal semanticist can’t be unconcerned that the kind of semantic theory for a natural language that interests her has no place in a theory of linguistic competence; for if GGH is correct, then the more fundamental semantic theory is the compositional meaning theory that is the semantic component of the internally represented generative grammar, and if that is so, then linguistic semantics has so far ignored what really ought to be its primary concern. (shrink)

Testimony, the transmission of knowledge through communication, requires a shared understanding of linguistic expressions and utterances of them. Is this understanding itself a kind of knowledge, knowledge of meaning? The intuitive answer is ‘yes’, but the nature of such knowledge is controversial, as is the assumption that understanding is a kind of knowledge at all. This article is a critical examination of recent work on the nature and role of semantic knowledge in the generation of the linguistic understanding needed for (...) testimony. After describing a default view – that linguistic understanding partially consists in the possession and application of knowledge of a compositional theory of truth conditions – it scrutinizes two recent charges against this view: that linguistic understanding and knowledge of meaning are conceptually distinct, and that semantic ‘knowledge’ is knowledge without an object. (shrink)

Linguistic expressions frequently make reference to the situation in which they are uttered. In fact, there are expressions whose whole point of use is to relate to their context of utterance. It is such expressions that this article is primarily about. However, rather than presenting the richness of pertinent phenomena (cf. Anderson & Keenan 1985), it concentrates on the theoretical tools provided by the (standard) two-dimensional analysis of context dependence, essentially originating with Kaplan (1989)--with a little help from Stalnaker (1978) (...) and Lewis (1979a, 1980), and various predecessors including Kamp (1971) and Vlach (1973). The current article overlaps in content with the account in Zimmermann (1991), which is however much broader (and at times deeper).. (shrink)

I argue that compositionality (in the sense of homomorphic interpretation) is compatible with radical and pervasive contextual effects on interpretation. Apparent problems with this claim lose their force if we are careful in distinguishing the question of how a grammar assigns interpretations from the question of how people figure out which interpretations the grammar assigns. I demonstrate, using a simple example, that this latter task must sometimes be done not by computing a derivation defined directly by the grammar, but through (...) the use of pragmatic background knowledge and extragrammatical reasoning, even when the grammar is designed to be fully compositional. The fact that people must sometimes use global pragmatic mechanisms to identify truth conditions therefore tells us nothing about whether the grammar assigns truth conditions compositionally. Compositional interpretation (or the lack thereof) is identifiable not by the mechanisms necessary to calculating truth conditions, but by the structural relation between the interpretation of a phrase in context and the interpretations of its parts in that same context. Even if this relation varies by context, an invariant grammar is possible if grammars can “invoke” pragmatic concepts; but this does not imply that grammatical theory must explain these concepts or incorporate a theory of pragmatics. (shrink)

Theories of collective intentions must distinguish genuinely collective intentions from coincidentally harmonized ones. Two apparently equally apt ways of doing so are the ‘neo-reductionism’ of Bacharach (2006) and Gold and Sugden (2007a) and the ‘non-reductionism’ of Searle (1990, 1995). Here, we present findings from theoretical linguistics that show that we is not a cognitive primitive, but is composed of notions of I and grouphood. The ramifications of this finding on the structure both of grammatical and lexical systems suggests that an (...) understanding of collective intentionality does not require a primitive we-intention, but the notion of grouphood implicit in team reasoning, coupled with the individual concept I. This, we argue, supports neo-reductionism but poses difficulties for non-reductionism. (shrink)

Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I also describe (...) some properties of the logic that are interesting from a philosophical perspective, and apply it to the so-called nesting problem. (shrink)

In fact, Godel gave an important model of pure predication, where he showed that restricted comprehension without parameters is valid, but where restricted comprehension with parameters is not (although this invalidity was not established until Cohen). This is the model based on ordinal definability in set theory.

Inferentialism is the conviction that to be meaningful in the distinctively human way, or to have a 'conceptual content', is to be governed by a certain kind of inferential rules. The term was coined by Robert Brandom as a label for his theory of language; however, it is also naturally applicable (and is growing increasingly common) within the philosophy of logic.

Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical forms (...) of ordinary language sentences consequently may be taken to be much less misleading than logicians in the first half of the 20th century often thought them to be. This was realized by Richard Montague, who used the theory of types to translate fragments of ordinary language into a logical language. Semantics is commonly divided into lexical semantics, which studies the meaning of words, and compositional semantics, which studies the way in which complex phrases obtain a meaning from their constituents. The strength of type-logical semantics lies with the latter, but type-logical theories can be combined with many competing hypotheses about lexical meaning, provided these hypotheses are expressed using the language of type theory. (shrink)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 BASIC MODAL LOGIC . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.

This paper does not deal with the topic of ‘the generosity of artificial languages from an Asian or a comparative perspective’. Rather, it is concerned with a particular case taken from a development in the Western tradition, when in the wake of the rise of formal logic at the end of the nineteenth and the beginning of the twentieth century people in philosophy and later in linguistics started to use formal languages in the study of the semantics of natural languages. (...) This undertaking rests on certain philosophical assumptions and instantiates a particular methodology, that we want to examine critically. However, that in itself is still too broad a topic for a single paper, so we will focus on a particular aspect, viz., the distinction between grammatical form and logical form and the crucial role it plays in how the relationship between natural languages and formal languages is understood in this tradition. We will uncover two basic assumptions that underlie the standard view on the distinction between grammatical form and logical form, and discuss how they have contributed to the shaping of a particular methodology and a particular view on the status of semantics as a discipline. But before we turn to the topic at hand, a few more words on the general nature of the investigation are in order. Its general aim is to find out how semantics constructs its object, i.e., we are interested in what semanticists view as the proper object of study, how they think this object can best be approached, and how they view the relations between their own undertaking and neighbouring disciplines that deal with related, or even the same kind of phenomena, such as cognitive psychology, cognitive neuroscience, philosophy, anthropology. The background assumption is that, much like in other disciplines, semantics, too, does not have its object of investigation cut out for itself by nature, but constructs it in a complex process that involves empirical elements (‘facts’ being already too dangerous a term), philosophical assumptions, and borrowings.... (shrink)

The paper identifies some background assumptions of compositionality in formal semantics and investigates how they shape formal semantics as a scientific discipline.

Recently, von Fintel (2001) and Gillies (2007) have argued that certain sequences of counterfactuals, namely reverse Sobel sequences, should motivate us to abandon standard truth conditional theories of counterfactuals for dynamic semantic theories. I argue that we can give a pragmatic account of our judgments about counterfactuals without giving up the standard semantics. In particular, I introduce a pragmatic principle governing assertability, and I use this principle to explain a variety of subtle data concerning reverse Sobel sequences.

Variabilism is the view that proper names (like pronouns) are semantically represented as variables. Referential names, like referential pronouns, are assigned their referents by a contextual variable assignment (Kaplan 1989). The reference parameter (like the world of evaluation) may also be shifted by operators in the representation language. Indeed verbs that create hyperintensional contexts, like ‘think’, are treated as operators that simultaneously shift the world and assignment parameters. By contrast, metaphysical modal operators shift the world of assessment only. Names, being (...) variables, refer rigidly in the latter merely intensional contexts, but may vary their reference in hyperintensional contexts. This conforms to the intuition that the content of attitude ascriptions encapsulates referential uncertainty. Furthermore, names in hyperintensional contexts are ambiguous between de re* and de dicto* interpretations. This fact is used to account for asymmetric mistaken identity attributions (for example, Biron thinks Katherine is Rosaline, but he doesn’t think Rosaline is Katherine). -/- The variable theory compares favourably with its alternatives, including Millianism and descriptivism. Millians cannot account for the behaviour of names in hyperintensional contexts, while descriptivists cannot generate a necessary contrast between intensional and hyperintensional contexts. No other theory can capture the facts pertaining to the existentially bound use of names. (shrink)

Italian translation of "On Logical Relativity" (2002), by Luca Morena.

When reasons are given for compositionality, the arguments usually purport to establish compositionality in an almost a priori manner. I will rehearse these arguments why one could think that compositionality is a priori true, or almost a priori true, and will find all of them inconclusive. This, in itself, is no reason against compositionality, but a reason to try to establish or defend the principle on other than quasi-a priori grounds.

Vagueness as Indeterminacy. I defend the traditional view that a vague term is one with an indeterminate denotation from a bevy of recent challenges.

This work gives an extended presentation of the treatment of variable-binding operators adumbrated in [3:1993d]. Illustrative examples include elementary languages with quantifiers and lambda-equipped categorial languages. Some remarks are also offered to illustrate the philosophical import of the resulting picture. Particularly, a certain conception of logic emerges from the account: the view that logics are true theories in the model-theoretic sense, i.e. the result of selecting a certain class of models as the only “admissible” interpretation structures (for a given language).

It is argued that a number of important, and seemingly disparate, types of representation are species of a single relation, here called structural representation, that can be described in detail and studied in a way that is of considerable philosophical interest. A structural representation depends on the existence of a common structure between a representation and that which it represents, and it is important because it allows us to reason directly about the representation in order to draw conclusions about the (...) phenomenon that it depicts. The present goal is to give a general and precise account of structural representation, then to use that account to illuminate several problems of current philosophical interest — including some that do not initially seem to involve representation at all. In particular, it is argued that ontological reductions (like that of the natural numbers to sets), compositional accounts of semantics, several important sorts of mental representation, and (perhaps) possible worlds semantics for intensional logics are all species of structural representation and are fruitfully studied in the framework developed here. (shrink)

Gareth Evans proposes that there are semantic natural kinds of words. In his development of this theory,he argues for two constraints on the identification of these kinds. I argue that neither of these constraints are justified. Furthermore,my argument against Evans' second constraint constitutes a direct argument for the existence of semantic natural kinds,something Evans himself never offers. I conclude by sketching some positive details of a more plausible theory of semantic natural kinds.

In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it (...) is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up. (shrink)

Inscrutability arguments threaten to reduce interpretationist metasemantic theories to absurdity. Can we find some way to block the arguments? A highly influential proposal in this regard is David Lewis’ ‘ eligibility ’ response: some theories are better than others, not because they fit the data better, but because they are framed in terms of more natural properties. The purposes of this paper are to outline the nature of the eligibility proposal, making the case that it is not ad hoc, but (...) instead flows naturally from three independently motivated elements; and to show that severe limitations afflict the proposal. In conclusion, I pick out the element of the eligibility response that is responsible for the limitations: future work in this area should therefore concentrate on amending this aspect of the overall theory. (shrink)

In this paper we discuss the treatment of variables in dynamic semantics. Referent systems are introduced as a flexible mechanism for working with variables. In a referent system we carefully distinguish the variables themselves both from the machinery by which we manipulate them - their names - and from the information that we store in them - their values. It is shown that the referent systems provide a natural basis for dynamic semantics. The semantics with referent systems is compared with (...) the familiar formalisms in dynamic semantics, DRT and DPL. (shrink)

The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends propositions to truth values or sets of possible worlds in Thomason (1980) must be replaced by a relation and the meaning postulates governing the behaviour of (...) this relation must be given in the form of a logic program. The resulting system does not only throw light on the properties of sense and their relation to computation, but also shows circular behaviour if some ingredients of the Liar Paradox are added. The connection is natural, as algorithms can be inherently circular and the Liar is explained as expressing one of those. Many ideas in the present paper are closely related to those in Moschovakis (1994), but receive a considerably lighter formalization. (shrink)

This paper argues that truth values of sentences containing predicates of “personal taste” such as fun or tasty must be relativized to individuals. This relativization is of truth value only, and does not involve a relativization of semantic content: If you say roller coasters are fun, and I say they are not, I am negating the same content which you assert, and directly contradicting you. Nonetheless, both our utterances can be true (relative to their separate contexts). A formal semantic theory (...) is presented which gives this result by introducing an individual index, analogous to the world and time indices commonly used, and by treating the pragmatic context as supplying a particular value for this index. The context supplies this value in the derivation of truth values from content, not in the derivation of content from character. Predicates of personal taste therefore display a kind of contextual variation in interpretation which is unlike the familiar variation exhibited by pronouns and other indexicals. (shrink)

There are two principles which bear the name Frege''sprinciple: the principle of compositionality, and the contextprinciple. The aim of this contribution is to investigate whether thisis justified: did Frege accept both principles at the same time, did hehold the one principle but not the other, or did he, at some moment,change his opinion? The conclusion is as follows. There is a developmentin Frege''s position. In the period of Grundlagen he followed to a strict form of contextuality. He repeatedcontextuality in later (...) writings, but became less strict. From 1914 on,pushed by the needs of research, he comes close to compositionality. Buthe could never make the final step toward compositionality forprincipled reasons, therefore he always would reject compositionality. (shrink)

This paper argues for a distinction between fictional characters, as parts of intentionally created abstract artifacts, and intentional objects, as nonexistent objects generated by referential acts that fail to refer. It argues that intentional objects as the nonexistent objects of imagination and other objectual attitudes are well-reflected in natural language, though in a highly restricted way, reflecting their ontological dependence on referential acts. The paper elaborates how that ontological dependence can be understood.

We investigate whether ordinary quantification over objects is an extensional phenomenon, or rather creates non-extensional contexts; each claim having been propounded by prominent philosophers. It turns out that the question only makes sense relative to a background theory of syntax and semantics (here called a grammar) that goes well beyond the inductive definition of formulas and the recursive definition of satisfaction. Two schemas for building quantificational grammars are developed, one that invariably constructs extensional grammars (in which quantification, in particular, thus (...) behaves extensionally) and another that only generates non-extensional grammars (and in which quantification is responsible for the failure of extensionality). We then ask whether there are reasons to favor one of these grammar schemas over the other, and examine an argument according to which the proper formalization of deictic utterances requires adoption of non-extensional grammars. (shrink)

This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the verdicts, hypotheses, or conjectures of any science. In work currently in progress, we argue for the unique suitability of LF for the formalization of logic, mathematics, syntax, and semantics. The present document specifies the language and rules of (...) LF, lays out some notational conventions, and states some basic technical facts about the system. (shrink)

The topic of this dissertation is the nature of linguistic competence, the capacity to understand and produce sentences of natural language. I defend the empiricist account of linguistic competence embedded in the connectionist cognitive science. This strand of cognitive science has been opposed to the traditional symbolic cognitive science, coupled with transformational-generative grammar, which was committed to nativism due to the view that human cognition, including language capacity, should be construed in terms of symbolic representations and hardwired rules. Similarly, linguistic (...) competence in this framework was regarded as being innate, rule-governed, domain-specific, and fundamentally different from performance, i.e., idiosyncrasies and factors governing linguistic behavior. I analyze state-of-the-art connectionist, deep learning models of natural language processing, most notably large language models, to see what they can tell us about linguistic competence. Deep learning is a statistical technique for the classification of patterns through which artificial intelligence researchers train artificial neural networks containing multiple layers that crunch a gargantuan amount of textual and/or visual data. I argue that these models suggest that linguistic competence should be construed as stochastic, pattern-based, and stemming from domain-general mechanisms. Moreover, I distinguish syntactic from semantic competence, and I show for each the ramifications of the endorsement of a connectionist research program as opposed to the traditional symbolic cognitive science and transformational-generative grammar. I provide a unifying front, consisting of usage-based theories, a construction grammar approach, and an embodied approach to cognition to show that the more multimodal and diverse models are in terms of architectural features and training data, the stronger the case is for the connectionist linguistic competence. I also propose to discard the competence vs. performance distinction as theoretically inferior so that a novel and integrative account of linguistic competence originating in connectionism and empiricism that I propose and defend in the dissertation could be put forward in scientific and philosophical literature. (shrink)

Two opposed movements of thought threaten philosophy as an autonomous practice from the inside: scientific naturalism and quietism. Naturalism (qua methodological thesis) threatens to turn philosophy into a mere ancilla of the sciences, quietism understood as the prescription to remain silent in philosophy would not countenance any more "positive" philosophy. This book reconstructs naturalism and quietism such that it becomes clear naturalism does have the potential to end philosophy as an autonomous practice and that quietism, correctly understood, does not. To (...) this end, this book provides arguments against the prevailing orthodox status of naturalism and a heterogenous reading of Wittgenstein's metaphilosophical quietism as the rejection of a certain kind of theories in philosophy, namely quasi-scientific theories. (shrink)

We argue that formal linguistic theory, properly extended, can provide a unifying framework for diverse phenomena beyond traditional linguistic objects. We display applications to pictorial meanings, visual narratives, music, dance, animal communication, and, more abstractly, to logical and non-logical concepts in the ‘language of thought’ and reasoning. In many of these cases, a careful analysis reveals that classic linguistic notions are pervasive across these domains, such as for instance the constituency (or grouping) core principle of syntax, the use of logical (...) variables (for object tracking), or the variety of inference types investigated in semantics/pragmatics. The aim of this overview is to show how the application of formal linguistic concepts and methodology to non-linguistic objects yields non-trivial insights, thus opening the possibility of a general, precise theory of signs. (An appendix, found in the online supplements to this article, surveys applications of Super Linguistics to animal communication.). (shrink)

There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. (...) We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege's distinction between sense and reference. (shrink)

CAT4 is proposed as a general method for representing information, enabling a powerful programming method for large-scale information systems. It enables generalised machine learning, software automation and novel AI capabilities. It is based on a special type of relation called CAT4, which is interpreted to provide a semantic representation. This is Part 1 of a five-part introduction. The focus here is on defining the key mathematical structures first, and presenting the semantic-database application in subsequent Parts. We focus in Part 1 (...) on general axioms for the structures, and introduce key concepts. Part 2 analyses the CAT2 sub-relation of CAT4 in more detail. The interpretation of fact networks is introduced in Part 3, where we turn to interpreting semantics. We start with examples of relational and graph databases, with methods to translate them into CAT3 networks, with the aim of retaining the meaning of information. The full application to semantic theory comes in Part 4, where we introduce general functions, including the language interpretation or linguistic functions. The representation of linear symbolic languages, including natural languages and formal symbolic languages, is a function that CAT4 is uniquely suited to. In Part 5, we turn to software design considerations, to show how files, indexes, functions and screens can be defined to implement a CAT4 system efficiently. (shrink)