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)

J.L. Austin is regarded as having an especially acute ear for fine distinctions of meaning overlooked by other philosophers. Austin employs an informal experimental approach to gathering evidence in support of these fine distinctions in meaning, an approach that has become a standard technique for investigating meaning in both philosophy and linguistics. In this paper, we subject Austin's methods to formal experimental investigation. His methods produce mixed results: We find support for his most famous distinction, drawn on the (...) basis of his `donkey stories', that `mistake' and `accident' apply to different cases, but not for some of his other attempts to distinguish the meaning of philosophically significant terms (such as `intentionally' and `deliberately'). We critically examine the methodology of informal experiments employed in ordinary language philosophy and much of contemporary philosophy of language and linguistics, and discuss the role that experimenter bias can play in influencing judgments about informal and formal linguistic experiments. (shrink)

A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a wave function in Hilbert space. The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered. A series of formal definitions is deduced from this for: “representation”, “reality”, “language”, “ontology”, etc. All are based on Hilbert space. A few statements (...) about a quantum computer are implied: The sodefined reality is inherent and internal to it. It can report a result only “metaphorically”. It will demolish transmitting the result “literally”, i.e. absolutely exactly. A new and different formal definition of metaphor is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above. The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought. Four areas of cognition are unified as different but isomorphic interpretations of the mathematical model based on Hilbert space. These are: quantum mechanics, frame semantics, formal semantics by means of quantum computer, and the theory of metaphor in linguistics. (shrink)

Formal thought disorder (FTD) is a clinical mental condition that is typically diagnosable by the speech productions of patients. However, this has been a vexing condition for the clinical community, as it is not at all easy to determine what “formal” means in the plethora of symptoms exhibited. We present a logic-based model for the syntax–semantics interface in semantic networking that can not only explain, but also diagnose, FTD. Our model is based on description logic (DL), which is (...) well known for its adequacy to model terminological knowledge. More specifically, we show how faulty logical form as defined in DL-based Conception Language (CL) impacts the semantic content of linguistic productions that are characteristic of FTD. We accordingly call this the dyssyntax model. (shrink)

In the era of “big data,” science is increasingly information driven, and the potential for computers to store, manage, and integrate massive amounts of data has given rise to such new disciplinary fields as biomedical informatics. Applied ontology offers a strategy for the organization of scientific information in computer-tractable form, drawing on concepts not only from computer and information science but also from linguistics, logic, and philosophy. This book provides an introduction to the field of applied ontology that is (...) of particular relevance to biomedicine, covering theoretical components of ontologies, best practices for ontology design, and examples of biomedical ontologies in use. After defining an ontology as a representation of the types of entities in a given domain, the book distinguishes between different kinds of ontologies and taxonomies, and shows how applied ontology draws on more traditional ideas from metaphysics. It presents the core features of the Basic Formal Ontology (BFO), now used by over one hundred ontology projects around the world, and offers examples of domain ontologies that utilize BFO. The book also describes Web Ontology Language (OWL), a common framework for Semantic Web technologies. Throughout, the book provides concrete recommendations for the design and construction of domain ontologies. (shrink)

Viewed in the light of the remarkable performance of ‘Watson’ - IBMs proprietary artificial intelligence computer system capable of answering questions posed in natural language - on the US general knowledge quiz show ‘Jeopardy’, we review two experiments on formal systems - one in the domain of quantum physics, the other involving a pictographic languaging game - whereby behaviour seemingly characteristic of domain understanding is generated by the mere mechanical application of simple rules. By re-examining both experiments in the (...) context of Searle’s Chinese Room Argument, we suggest their results merely endorse Searle’s core intuition: that ‘syntactical manipulation of symbols is not sufficient for semantics’. Although, pace Watson, some artificial intelligence practitioners have suggested that more complex, higher-level operations on formal symbols are required to instantiate understanding in computational systems, we show that even high-level calls to Google translate would not enable a computer qua ‘formal symbol processor’ to understand the language it processes. We thus conclude that even the most recent developments in ‘quantum linguistics’ will not enable computational systems to genuinely understand natural language. (shrink)

Recent advances in the Super Linguistics of pictures have laid the Super Semantic foundation for modelling the phenomena of narrative sequencing and co-reference in pictorial and mixed linguistic-pictorial discourses. We take up the question of how one arrives at the pragmatic interpretations of such discourses. In particular, we offer an analysis of: (i) the discourse composition problem: how to represent the joint meaning of a multi-picture discourse, (ii) observed differences in narrative sequencing in prima facie equivalent linguistic vs pictorial (...) discourses, and (iii) the phenomenon of co-referencing across pictures. We extend Segmented Discourse Representation Theory to spell out a formal Super Pragmatics that applies to linguistic, pictorial and mixed discourses, while respecting the particular ‘genius’ of either medium and computing their distinctive pragmatic interpretations. (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)

dolce, the first top-level ontology to be axiomatized, has remained stable for twenty years and today is broadly used in a variety of domains. dolce is inspired by cognitive and linguistic considerations and aims to model a commonsense view of reality, like the one human beings exploit in everyday life in areas as diverse as socio-technical systems, manufacturing, financial transactions and cultural heritage. dolce clearly lists the ontological choices it is based upon, relies on philosophical principles, is richly formalized, and (...) is built according to well-established ontological methodologies, e.g. OntoClean. Because of these features, it has inspired most of the existing top-level ontologies and has been used to develop or improve standards and public domain resources. Being a foundational ontology, dolce is not directly concerned with domain knowledge. Its purpose is to provide the general categories and relations needed to give a coherent view of reality, to integrate domain knowledge, and to mediate across domains. In these 20 years dolce has shown that applied ontologies can be stable and that interoperability across reference and domain ontologies is a reality. This paper briefly introduces the ontology and shows how to use it on a few modeling cases. (shrink)

What are the prospects for a linguistic approach to ontology? Given that it seems that there are true subject-predicate sentences containing empty names, traditional linguistic approaches to ontology appear to be flawed. I argue that in order to determine what there is, we need to determine which sentences ascribe properties (and relations) to objects, and that there does not appear to be any formal criterion for this. This view is then committed to giving an account of what predicates do (...) in sentences when they do not ascribe properties. I sketch an approach to the varieties of predication. (shrink)

A common framing has it that any adequate treatment of quotation has to abandon one of the following three principles: (i) The quoted expression is a syntactic constituent of the quote phrase; (ii) If two expressions are derived by applying the same syntactic rule to a sequence of synonymous expressions, then they are synonymous; (iii) The language contains synonymous but distinct expressions. In the following, a formal syntax and semantics will be provided for a quotational language which adheres to (...) all three principles. The point here is not merely to provide a “possibility proof”, but to reveal the hard constraints on the theory of quotation, and to highlight certain assumptions at the syntax/semantics/post-semantics interfaces. (shrink)

This paper develops an account of the meaning of `ought', and the distinction between weak necessity modals (`ought', `should') and strong necessity modals (`must', `have to'). I argue that there is nothing specially ``strong'' about strong necessity modals per se: uses of `Must p' predicate the (deontic/epistemic/etc.) necessity of the prejacent p of the actual world (evaluation world). The apparent ``weakness'' of weak necessity modals derives from their bracketing whether the necessity of the prejacent is verified in the actual world. (...) `Ought p' can be accepted without needing to settle that the relevant considerations (norms, expectations, etc.) that actually apply verify the necessity of p. I call the basic account a modal-past approach to the weak/strong necessity modal distinction (for reasons that become evident). Several ways of implementing the approach in the formal semantics/pragmatics are critically examined. The account systematizes a wide range of linguistic phenomena: it generalizes across flavors of modality; it elucidates a special role that weak necessity modals play in discourse and planning; it captures contrasting logical, expressive, and illocutionary properties of weak and strong necessity modals; and it sheds light on how a notion of `ought' is often expressed in other languages. These phenomena have resisted systematic explanation. In closing I briefly consider how linguistic inquiry into differences among necessity modals may improve theorizing on broader philosophical issues. (shrink)

I argue that what determines whether a science is ‘formal’ or ‘empirical’ is not the ontological status of its objects of study, but, rather, its methodology. Since all sciences aim at generalizations, and generalizations concern types, if types are abstract (non-spatiotemporal) objects, then all sciences are concerned to discover the nature of certain abstract objects. What distinguishes empirical from formal sciences is how they study such things. If the types of a science have observable instances (‘tokens’), then the (...) nature of the types may be determined empirically. If they types have either abstract tokens, or no tokens at all, their nature must be determined by non-empirical methods involving intuition, reasoning and proof. I conclude that the status of (theoretical) linguistics depends on the methodologies of syntax, semantics, phonology, morphology and orthography (and any other subdiscipline that is concerned with the study of the structure of language). (shrink)

The current resurgence of interest in cognition and in the nature of cognitive processing has brought with it also a renewed interest in the early work of Husserl, which contains one of the most sustained attempts to come to grips with the problems of logic from a cognitive point of view. Logic, for Husserl, is a theory of science; but it is a theory which takes seriously the idea that scientific theories are constituted by the mental acts of cognitive subjects. (...) The present essay begins with an exposition of Husserl's act-based conception of what a science is, and goes on to consider his account of the role of linguistic meanings, of the ontology of scientific objects, and of evidence and truth. The essay concentrates almost exclusively on the Logical Investigations of 1900/01. This is not only because this work, which is surely Husserl's single most important masterpiece, has been overshadowed first of all by his Ideas I and then later by the Crisis. It is also because the Investigations contain, in a peculiarly clear and pregnant form, a whole panoply of ideas on logic and cognitive theory which either simply disappeared in Husserl's own later writings or became obfuscated by an admixture of that great mystery which is 'transcendental phenomenology'. (shrink)

Hilbert arithmetic in a wide sense, including Hilbert arithmetic in a narrow sense consisting by two dual and anti-isometric Peano arithmetics, on the one hand, and the qubit Hilbert space (originating for the standard separable complex Hilbert space of quantum mechanics), on the other hand, allows for an arithmetic version of Gentzen’s cut elimination and quantum measurement to be described uniformy as two processes occurring accordingly in those two branches. A philosophical reflection also justifying that unity by quantum neo-Pythagoreanism links (...) it to the opposition of propositional logic, to which Gentzen’s cut rule refers immediately, on the one hand, and the linguistic and mathematical theory of metaphor therefore sharing the same structure borrowed from Hilbert arithmetic in a wide sense. An example by hermeneutical circle modeled as a dual pair of a syllogism (accomplishable also by a Turing machine) and a relevant metaphor (being a formal and logical mistake and thus fundamentally inaccessible to any Turing machine) visualizes human understanding corresponding also to Gentzen’s cut elimination and the Gödel dichotomy about the relation of arithmetic to set theory: either incompleteness or contradiction. The metaphor as the complementing “half” of any understanding of hermeneutical circle is what allows for that Gödel-like incompleteness to be overcome in human thought. (shrink)

Logic is about reasoning, or so the story goes. This thesis looks at the concept of logic, what it is, and what claims of correctness of logics amount to. The concept of logic is not a settled matter, and has not been throughout the history of it as a notion. Tools from conceptual analysis aid in this historical venture. Once the unsettledness of logic is established we see the repercussions in current debates in the philosophy of logic. Much of the (...) battle over the ‘one true logic’ is conceptually talking past each other. The theory of logics-as-formalizations is presented as a conceptually open theory of logic which is Carnapian in flavour and grounding. Rudolf Carnap’s notions surrounding ‘external’ and ‘pseudo-questions’ about linguistic frameworks apply to formalizations, thus logics, as well. An account of what formalizations are, a more structured sub-set of modelling, is given to ground the claim that logics are formalizations. Finally, a novel account of correctness, the COFE framework, is developed which allows the notions of logical monism, pluralism and nihilism to be more precisely formulated than they currently are in the discourse. (shrink)

With reference to Polish logical-philosophical tradition two formal theories of language syntax have been sketched and then compared with each other. The first theory is based on the assumption that the basic linguistic stratum is constituted by object-tokens (concrete objects perceived through the senses) and that the types of such objects (ideal objects) are derivative constructs. The other is founded on an opposite philosophical orientation. The two theories are equivalent. The main conclusion is that in syntactic researches it is (...) redundant to postulate the existence of abstract linguistic entities. Earlier, in a slightly different form, the idea was presented in paper "Logiczne podstawy ontologii składni języka" (1988). (shrink)

Ontology has been proposed as a solution to the 'Tower of Babel' problem that threatens the semantic interoperability of information systems constructed independently for the same domain. In information systems research and applications, ontologies are often implemented by formalizing the meanings of words from natural languages. However, words in different natural languages sometimes subdivide the same domain of reality in terms of different conceptual categories. If the words and their associated concepts in two natural languages, or even in two terminological (...) traditions within the same language, do not have common referents in the real world, an ontology based on word meanings will inherit the 'Tower of Babel' problem from the languages involved, rather than solve it. In this paper we present evidence from a preliminary comparison of landscape terms in English with those in the Yindjibarndi language of northwestern Australia demonstrating that this problem is not just hypothetical. Some possible solutions are suggested. (shrink)

As formal theoretical linguistic methodology has matured, recent years have seen the advent of applying it to objects of study that transcend language, e.g., to the syntax and semantics of music (Lerdahl & Jackendoff 1983, Schlenker 2017a; see also Rebuschat et al. 2011). One of the aims of such extensions is to shed new light on how meaning is construed in a range of communicative systems. In this paper, we approach this goal by looking at narrative dance in the (...) form of Bharatanatyam. We argue that a semantic approach to dance can be modeled closely after the formal semantics of visual narrative proposed by Abusch (2013, 2014, 2021). A central conclusion is that dance not only shares properties of other fundamentally human means of expression, such as visual narrative and music, but that it also exhibits similarities to sign languages and the gestures of non-signers (see, e.g., Schlenker 2020) in that it uses space to track individuals in a narrative and performatively portray the actions of those individuals. From the perspective of general human cognition, these conclusions corroborate the idea that linguistic investigations beyond language (see Patel-Grosz et al. forthcoming) can yield insights into the very nature of the human mind and of the communicative devices that it avails. (shrink)

Language, science and politics go together and learning these genres is to learn a language created for codifying, extending and conveying scientific and political knowledge. Grammatical metaphor is divided into two broad areas: ideational and interpersonal. This article focuses on the first type of grammatical metaphor, i.e. the ideational one, which includes process types and nominalization. The principal objective of the current work is to analyze a corpus comprising 10 scientific and 10 political texts. The Ideational Grammatical Metaphor framework was (...) used to carry out an analysis on these texts to pinpoint their similarities and dissimilarities. The analysis indicates that Ideational Grammatical Metaphor has dominated political and scientific texts and is used approximately with the same frequency in both genres and the prevailing process types in both are material and relational types. Consequently, the tone of the writing is more abstract, pretentious and formal. In science, instances of IGM enable technicalizing and rationalizing; and in politics they deal with dominance, provocation, persuasion toward an intended objective. Based on the findings of this study, some implications can be drawn for academic writing and reading as well as translators and teachers involved in writing and reading pedagogy. (shrink)

This is a review of From Discourse to Logic: Introduction to Modeltheoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory, written by Hans Kamp and Uwe Reyle and published by Kluwer Academic Publishers in 1993.

By logical foundations of language syntax ontology we understand here the construction of formalized linguistic theories based on widely conceived mathematical logic and dependent on two trends in language ontology. The formalization includes exclusively the syntactic aspect of logical analysis of language characterized categorially according to Ajdukiewicz's approach [1935, 1960]. Any categorial language L is characterized formally on two levels: on one of them it concerns the language of expression-tokens, on the other one - that of expression-types. Accepting the view (...) that expression-concretes, that is expression-tokens - thus, physical objects are fundamental language layer, whereas the secondary layer for L are expression-abstracts, that is expression-types - thus, ideal objects, it is the nominalistic, concretistic philosophical view on the ontological nature of language entities that is adhered to. Supporting the view that expression-types are the basic language layer, while expression-concretes are the secondary one, we take the opposite standpoint - platonizing one. We prove that the two dual approaches towards the two-level syntax theory of language are logically eqivalent. In the scope of language syntax, both conceptions deriving from two different existential assumption are equivalent. This statement is philosophical significance, since it proves that in syntactical studies on language the assumption of the existence of abstract language beings (interpreted as classes equiform tokens) can be neglected. The idea was signalized by author in ealier paper "On the type-token relationships'' [1986) and than, in a slighly diffrent form in English "On the eliminatibility of ideal linguistic entities, Studia Logica 48,no 4 (1989), pp. 587-615. (shrink)

Post-Fregean theorists use 'quotation' to denote indifferently both colloquially called quotations (repetitions of prior utterances) and what I call 'displays': 'Rot' means red. Colloquially, quotation is a strictly historical property, not semantic or syntactic. Displays are semantically and syntactically distinctive sentential elements. Most displays are not quotations. Pure echo quotations (Cosmological arguments involve "an unnecessary shuffle") aren't displays. Frege-inspired formal languages stipulate that enquotation forms a singular term referring to the enquoted expression (type). Formalist enquotations differ semantically and syntactically (...) from natural language displays. Call them autonomes, and mark them with stars: *Rot* means red. In formal languages, an unenstarred expression has only one meaning, and an autonome has only one meaning viz., a name (or indexical) designating the unenstarred expression (type). Stars have semantic content and can’t disambiguate. Display punctuation only disambiguates; it says only: This material is displayed. Displays have a semantic function; their marks don't. Displays are not terms or lexical items. Displays are objects incorporable into utterances. Such incorporation enables them to be linguistically appropriated much as we appropriate speech-external objects by extrasentential supplementation (e.g., gesturing) to identify the extension of a term by ostending the object -- but now without any extrasentential supplement. Displays are always adjunctive to an (implicit or explicit) ostensionable term, a term whose extension is identifiable by ostending an object. The display-ostensionable term-extension relations are various. A display may (1) be the term's referent, or (2) represent the term's extension by (a) replicating or (b) instantiating or (c) expressing the term's referent, or (e) instantiating the property the term predicates. (shrink)

In this essay, our goal is to discover science in Martin Heidegger's Introduction to Metaphysics, lecture notes for his 1935 summer semester course, because, after all, his subject is metaphysica generalis, or ontology, and this could be construed as a theory of the human brain. Here, by means of verbatim quotes from his text, we attempt to show that indeed these lectures can be viewed as suggestion for an objective scientific theory of human perception, the human capacity for deciphering phenomena, (...) ie. hermeneutics in its broadest sense. His added notes from the 1953 edition, all of which are comments, not corrections, imply that he never abandoned these thoughts on metaphysics, despite all of his utterances about a need to overcome it, and their popular interpretations to that effect. In his presentation, he further develops the colorful and intuitive style, an hermeneutic language, that he had created in his earlier work Being and Time. Of human existence he speaks in such expressions as being-there -- ``Dasein" -- and being-in-the-world, the latter term no longer explicit in the 1935 lectures. The lectures can be read as a pre-scientific analysis of how man, being-there, perceives his environment, artfully managing to deal with the manifold challenges posed by the phenomenal structures of the universe. Man attentively recognizes and deciphers their pre-linguistic contents and, while trying to make sense of it all, puts into words his awareness. There are numerous passages in Heidegger's work where he in fairly concrete terms provides us with hints for a perceptive science that, as it turns out and is demonstrated below in this essay, can be explained in terms of recent advances in neuroscience. It would be implausible, even unthinkable, unimaginable, for there not to be found essential agreement between on one hand his philosophical insights gained by hermeneutics of Dasein, into how our brain functions to let us know what's happening & on the other hand, scientific discoveries obtained through anatomy, EEG, fMRI, TMS, electrode implants, etc, of brain structures & functions employed in perception of the momentary scene. A nexus between science and philosophy is provided in Heidegger's definitive treatment of the Logos, here interpreted as a structural version of Platonic forms (Burchard, 2014). This allows for neurolinguistic brain functions to serve as meta-context for Heidegger's being-in-the-world. The logical functions of Dasein's anatomical brain are performed by the logos machine, formerly the human soul, using top-down processing based on a global context, the noumenal cosmos which humans maintain internally. Heidegger's 1942/43 winter semester lectures Parmenides extend in unbroken fashion his 1935 work, proving that he never abandoned, as is widely claimed, his metaphysical avenue of thought. (shrink)

The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of Language Signs and the Problem of (...) Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)

The two-fold ontological character of linguistic objects revealed due to the distinction between “type” and “token” introduced by Ch. S. Peirce can be a base of the two-fold, both theoretical and axiomatic, approach to the language. Referring to some ideas included in A. A. Markov’s work [1954] (in Russian) on Theory of Algorithms and in some earlier papers of the author, the problem of formalization of the concrete and abstract words theories raised by J. Słupecki was solved. The construction of (...) the theories presented here has two levels. The axiomatic theory of label-tokens: material, physical linguistic objects, constitutes the first one. Label-types, according to the literature of the subject, are defined on the other level as equivalence classes of equiform label-tokens. Assuming the opposite point of view, one can accept that theory of label-types: abstract labels, formalized on the first level, in which it is possible to define the notion of label-token as well as the derivative notions on the second level, should become the basis of formalization of the theory of linguistic expressions and the theory of language in general. The axioms and definitions of both theories of labels: T k and T p representing the other approach to the ontology of language are included in the sequel of the abstract. The foundations of the theory of labels T k in which the primary assumption as to the label-types existence is superfluous have been referred on the basis of the author's monography "Teorie Języków Syntaktycznie Kategorialnych" ( "The Theories of Syntactically Categorial Languages"), PWN, Warszawa-Wrocław 1985. The basis of the theory of labels T p which takes into account the other position has to be presented here for the first time. Some extended ideas of the paper will also be presented in author's paper "Logiczne podstawy ontologii składni Języka" ("Logical foundations of language syntax ontology), Studia Filozoficzne 6-7 (271-272), (1988), pp. 263-284. (shrink)

The Unified Foundational Ontology (UFO) was developed over the last two decades by consistently putting together theories from areas such as formal ontology in philosophy, cognitive science, linguistics, and philosophical logics. It comprises a number of micro-theories addressing fundamental conceptual modeling notions, including entity types and relationship types. The aim of this paper is to summarize the current state of UFO, presenting a formalization of the ontology, along with the analysis of a number of cases to illustrate the (...) application of UFO and facilitate its comparison with other foundational ontologies in this special issue. (The cases originate from the First FOUST Workshop – the Foundational Stance, an international forum dedicated to Foundational Ontology research.). (shrink)

Ways of Scope Taking is concerned with syntactic, semantic and computational aspects of scope. Its starting point is the well-known but often neglected fact that different types of quantifiers interact differently with each other and other operators. The theoretical examination of significant bodies of data, both old and novel, leads to two central claims. (1) Scope is a by-product of a set of distinct Logical Form processes; each quantifier participates in those that suit its particular features. (2) Scope interaction is (...) further constrained by the semantics of the interacting operators. The arguments are developed using Minimalist syntax, Generalized Quantify theory, Discourse Representation Theory, and algebraic semantics. The contributors (Beghelli, Ben-Shalom, Doetjes, Farkas, Gutiérrez Rexach, Honcoop, Stabler, Stowell, Szabolcsi and Zwarts) make tightly related theoretical assumptions and focus on related empirical phenomena, which include the direct and inverse scope of quantifiers, distributivity, negation, modal and intensional contexts, weak islands, event-related readings, interrogatives, wh/quantifier interactions, and Hungarian syntax. An introduction to the formal semantics background is provided. Audience: Linguists, philosophers, computational and psycholinguists; advanced undergraduates, graduate students and researchers in these fields. (shrink)

In the era of “big data,” science is increasingly information driven, and the potential for computers to store, manage, and integrate massive amounts of data has given rise to such new disciplinary fields as biomedical informatics. Applied ontology offers a strategy for the organization of scientific information in computer-tractable form, drawing on concepts not only from computer and information science but also from linguistics, logic, and philosophy. This book provides an introduction to the field of applied ontology that is (...) of particular relevance to biomedicine, covering theoretical components of ontologies, best practices for ontology design, and examples of biomedical ontologies in use. After defining an ontology as a representation of the types of entities in a given domain, the book distinguishes between different kinds of ontologies and taxonomies, and shows how applied ontology draws on more traditional ideas from metaphysics. It presents the core features of the Basic Formal Ontology (BFO), now used by over one hundred ontology projects around the world, and offers examples of domain ontologies that utilize BFO. The book also describes Web Ontology Language (OWL), a common framework for Semantic Web technologies. Throughout, the book provides concrete recommendations for the design and construction of domain ontologies. (shrink)

Swear words are highly colloquial expressions that have the capacity to signal the speaker's affective states, i.e., to display the speaker's feelings with respect to a certain stimulus. For this reason, swear words are often called 'expressives'. Which linguistic mechanisms allow swear words display affective states, and, more importantly, how can such 'affective content' be characterized in a theory of meaning? Even though research on expressive meaning has produced models that integrate the affective aspects of swear words in a compositional (...) framework, there is extensive evidence that swear words cannot be assigned a single or stable affective interpretation across contexts. For example, even though expletive adjectives (e.g., 'damn'), particularistic insults (e.g., 'bastard') and slurs (e.g., 'wop') typically express (and elicit) negatively valenced affective states, they can also be interpreted positively in some contexts. Thus, inspired in recent developments in formal sociolinguistics, I propose an 'indexical' approach to affective meaning. Under this approach, an affective expression is associated with a set of affective qualities, anyone of which may emerge at a given context depending on the interpreter's prior assumptions about the speaker's affective states and/or relation with the target of the swear word. To define this set, also called 'indexical field', I will use the dimensions pleasure, arousal and dominance, standardly employed in cognitive psychology to characterize and measure affective episodes. In this dissertation, thus, the affective meaning of an expression is given by the set of affective states it typically conveys within a linguistic community, but its interpretation at a given context is established by taking into account the interpreter's prior assumptions about the speaker's affective states and/or attitudes with respect to the target of the affective expression. (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)

This paper applies homotopy type theory to formal semantics of natural languages and proposes a new model for the linguistic phenomenon of copredication. Copredication refers to sentences where two predicates which assume different requirements for their arguments are asserted for one single entity, e.g., "the lunch was delicious but took forever". This paper is particularly concerned with copredication sentences with quantification, i.e., cases where the two predicates impose distinct criteria of quantification and individuation, e.g., "Fred picked up and mastered (...) three books." In our solution developed in homotopy type theory and using the rule of existential closure following Heim analysis of indefinites, common nouns are modeled as identifications of their aspects using HoTT identity types, e.g., the common noun book is modeled as identifications of its physical and informational aspects. The previous treatments of copredication in systems of semantics which are based on simple type theory and dependent type theories make the correct predictions but at the expense of ad hoc extensions (e.g., partial functions, dot types and coercive subtyping). The model proposed here, also predicts the correct results but using a conceptually simpler foundation and no ad hoc extensions. (shrink)

Linguistic intervention in rational decision making is standardly captured in terms of information change. But the standard view gives us no way to model interventions involving expressions that only have an attentional effects on conversational contexts. How are expressions with non‐informational content – like epistemic modals – used to intervene in rational decision making? We show how to model rational decision change without information change: replace a standard conception of value (on which the value of a set of worlds reduces (...) to values of individual worlds in the set) with one on which the value of a set of worlds is determined by a selection function that picks out a generic member world. We discuss some upshots of this view for theorizing in philosophy and formal semantics. (shrink)

When one looks into the role of artificial languages in philosophy of language it seems appropriate to start with making a distinction between philosophy of language proper and formal semantics of natural language. Although the distinction between the two disciplines may not always be easy to make since there arguably exist substantial historical and systematic relationships between the two, it nevertheless pays to keep the two apart, at least initially, since the motivation commonly given for the use of artificial (...) languages in philosophy of language is often rather different from the one that drives the use of such languages in semantics. Of course, this difference in motivation should not blind us for the commonalities that exists between the two disciplines. Philosophy of language and formal semantics have a common history, and arguably also share some of their substance. Philosophy of language is by and large an outgrowth of work in the analytical tradition in philosophy in the first half of the twentieth century. Both ordinary language philosophy, with its emphasis on the description of actual language use, as well as the more logic-oriented and formally inclined school of logical positivism contributed to the definition of philosophy of language as a separate philosophical discipline, with its own set of problems and methods to solve them. Another major contributor to the establishment of philosophy of language as a distinct discipline has been modern linguistics, in particular generative grammar in the tradition of Chomsky that became the dominant paradigm in linguisticsin the fifties and sixties of the previous century. And as it happens, both the generative tradition of Chomsky and analytic philosophy in its formal and less formal guises have been important factors in the development of formal semantics as well. Thus, it should come as no surprise that the two have something in common. That the communalities go beyond a common ancestry, but are reflected in substance and methods as well, will be argued later on. However, be that as it may, it is still a good idea to keep philosophy of language and formal semantics separate, at least initially, since the role that is assigned to artificial languages and the ways in which these languages are employed in both does differ in a number of respects that are worth keeping in mind.. (shrink)

I present a formal theory of the logic and aboutness of imagination. Aboutness is understood as the relation between meaningful items and what they concern, as per Yablo and Fine’s works on the notion. Imagination is understood as per Chalmers’ positive conceivability: the intentional state of a subject who conceives that p by imagining a situation—a configuration of objects and properties—verifying p. So far aboutness theory has been developed mainly for linguistic representation, but it is natural to extend it (...) to intentional states. The proposed framework combines a modal semantics with a mereology of contents: imagination operators are understood as variably strict quantifiers over worlds with a content-preservation constraint. (shrink)

In the paper, original formal-logical conception of syntactic and semantic: intensional and extensional senses of expressions of any language L is outlined. Syntax and bi-level intensional and extensional semantics of language L are characterized categorically: in the spirit of some Husserl’s ideas of pure grammar, Leśniewski-Ajukiewicz’s theory syntactic/semantic categories and in accordance with Frege’s ontological canons, Bocheński’s famous motto—syntax mirrors ontology and some ideas of Suszko: language should be a linguistic scheme of ontological reality and simultaneously a tool of (...) its cognition. In the logical conception of language L, its expressions should satisfy some general conditions of language adequacy. The adequacy ensures their unambiguous syntactic and semantic senses and mutual, syntactic, and semantic compatibility, correspondence guaranteed by the acceptance of a postulate of categorial compatibility syntactic and semantic categories of expressions of L. From this postulate, three principles of compositionality follow: one syntactic and two semantic already known to Frege. They are treated as conditions of homomorphism 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, of course, an idealization, but only expressions with high degrees of precision of their senses, after due justification, may become theorems of science. (shrink)

According to the analysis of concessive conditionals suggested by Crupi and Iacona, a concessive conditional $$p{{\,\mathrm{\hookrightarrow }\,}}q$$ p ↪ q is adequately formalized as a conjunction of conditionals. This paper presents a sound and complete axiomatic system for concessive conditionals so understood. The soundness and completeness proofs that will be provided rely on a method that has been employed by Raidl, Iacona, and Crupi to prove the soundness and completeness of an analogous system for evidential conditionals.

This paper defends a view of the Gene Ontology (GO) and of Basic Formal Ontology (BFO) as examples of what the manufacturing industry calls product-service systems. This means that they are products (the ontologies) bundled with a range of ontology services such as updates, training, help desk, and permanent identifiers. The paper argues that GO and BFO are contrasted in this respect with DOLCE, which approximates more closely to a scientific theory or a scientific publication. The paper provides a (...) detailed overview of ontology services and concludes with a discussion of some implications of the product-service system approach for the understanding of the nature of applied ontology. Ontology developer communities are compared in this respect with developers of scientific theories and of standards (such as W3C). For each of these we can ask: what kinds of products do they develop and what kinds of services do they provide for the users of these products? (shrink)

The main objective of the paper is to provide a conceptual apparatus of a general logical theory of language communication. The aim of the paper is to outline a formal-logical theory of language in which the concepts of the phenomenon of language communication and language communication in general are defined and some conditions for their adequacy are formulated. The theory explicates the key notions of contemporary syntax, semantics, and pragmatics. The theory is formalized on two levels: token-level and type-level. (...) As such, it takes into account the dual – token and type – ontological character of linguistic entities. The basic notions of the theory: language communication, meaning and interpretation are introduced on the second, type-level of formalization, and their required prior formalization of some of the notions introduced on the first, token-level; among others, the notion of an act of communication. Owing to the theory, it is possible to address the problems of adequacy of both empirical acts of communication and of language communication in general. All the conditions of adequacy of communication discussed in the presented paper, are valid for one-way communication (sender-recipient); nevertheless, they can also apply to the reverse direction of language communication (recipient-sender). Therefore, they concern the problem of two-way understanding in language communication. (shrink)

The Generalized Quantifiers Theory, I will argue, in the second half of last Century has led to an important rapprochement, relevant both in logic and in linguistics, between logical quantification theories and the semantic analysis of quantification in natural languages. In this paper I concisely illustrate the formal aspects and the theoretical implications of this rapprochement.

The linguistic turn provided philosophers with a range of reasons for engaging in careful investigation into the nature and structure of language. However, the linguistic turn is dead. The arguments for it have been abandoned. This raises the question: why should philosophers take an interest in the minutiae of natural language semantics? I’ll argue that there isn’t much of a reason - philosophy of language has lost its way. Then I provide a suggestion for how it can find its way (...) again. (shrink)

Imperatives are linguistic devices used by an authority (speaker) to express wishes, requests, commands, orders, instructions, and suggestions to a subject (addressee). This essay's goal is to tentatively address some of the following questions about the imperative. -/- METASEMANTIC. What is the menu of options for understanding fundamental semantic notions like satisfaction, truth-conditions, validity, and entailment in the context of imperatives? Are there good imperative arguments, and, if so, how are they to be characterized? What are the options for understanding (...) the property that an account of good imperative arguments is supposed to track? What constraints on a semantic analysis of the imperative do different positions on the metasemantic issues impose? -/- SEMANTIC. How might we implement metasemantic postures in a rigorous formal system? How much can we do using familiar tools from deontic modal logic? How much leverage over semantic questions can we gain by introducing tools from natural language semantics—ordering sources, dyadic modal operators, salient alternatives, and the like—into a formal semantics for an imperative object language? How much leverage can we gain by introducing tools from rather less-utilized areas of modal logic—devices for representing actions and planning in time, modal operators constructed from action-terms, and the like—into the analysis? -/- DYNAMIC. How do imperatives succeed in performing the speech acts they are used to perform? How do imperatives update discourses? How can we leverage an account of imperative discourse update in giving a dynamic semantics for the imperative? Is there anything about the imperative that demands a dynamic semantic treatment? (shrink)

Initiatory symbology collects various forms of symbols: those that belong to an ancient tradition and that present themselves as a normalization of the past in a modernized key; those that derive from a pact between the members of the initiatory community and that guarantee the unity of the group, which are synchronized within the group itself; those that have the sense of projection to overcome the gnoseological limits of the group and its members, are traditional but through their character of (...) semantic multiplicity offer new gnoseological opportunities. Silence is not part of the first category, because not all ancient or traditional initiatory groups used it ritually or considered it as a symbol and therefore could not have a normative function susceptible to modernization. It can be a crucial moment of the second when it is ritualized in the different phases of learning on the basis of an agreement connected to the creation of the ritual and forming itself as one of the synchronic fulcrums of the group, ensuring its unity. It can also belong to the third case when it takes on a traditional guise but having its own multidimensional semantics, in the communion of saying and silent pulses of new opportunities for initiatory growth. Silence in the initiatory context is a specific linguistic form that characterizes the entire path of the initiates. Within the group, they elaborate the syntax of silence, the morphology of tacitly expressed symbols, without fully explaining their meanings. Each symbol, or sign in the semiotic sense, has different meanings for the different phases of the initiation process. Each one belongs to a different type of relationship with what it refers to: it has a relationship of "similarity" such as the design of a team and compass that illustrates operational objects, of "proximity" when it manifests the operation of measuring and relating the relationships for which the object is intended, of "concordance" if it refers to the object within the knowledge of an architectural rule. The symbol as a special form of sign manifests itself (first phase of learning), as in the example, in iconographic-descriptive mode containing a meaning "dictated". It is an initiatory dictatio to be kept in silence in front of the essoteric world, of which the initiating is still permeated, the symbolism must be evoked without making explicit its intimate meanings, it is described but not fully exposed. It is the evocative, indeterminate and silent value that must stimulate the initiating in the search for meanings. The indetermination of silence destructures the essoteric, its thought its categories, criteria and values, leads to the desert of essoteric meanings as a way to the ontology of initiatory language. It is a stage of waiting, of referral to another world. We suspect meanings that in the next phase begin to manifest themselves in a more precise dictatio, a functional dictamen to represent the concept of measurement in its multiple meanings where the measure is assumed as symbolic-conceptual abstraction. Continuing, the sign in the form of an object strips itself of any factual and existential reference, of the communication of an abstraction or conceptual ideation and unmasks itself in its being an initiatory "rule". It is assumed, therefore, that initiatory improvement passes through the understanding of the signs, an understanding that is increasingly deeper and more comprehensive and that is autonomous and independent of the signs of the exoteric world. With regard to the symbolic-initiatic language, learning, from the apprenticeship phase to the following phases, focuses on the study of the formal relationships of symbols within initiatory gnoseology, on the meanings inherent in symbols and on their relationship with the initiatory community. (shrink)

In traditional formal semantics the notions of reference, truth and satisfaction are basic and that of representation is derivative and dispensable. If a level of representation is included in the formal presentation of the theory, it is included as a heuristic. Semantics in the traditional sense has no bearing on any form of mental processing. When reference is understood within this framework, cognitive neuroscience cannot possibly provide any insights into the nature of reference. Traditional semantics, however, has numerous (...) shortcomings that render it inadequate as an account of natural language. Dynamic semantic theories, such as discourse representation theory (DRT), treat ever­growing, revisable mental representations as the basic semantic entities. Within this framework, there are two central notions of reference. New information may refer back to previously introduced discourse referents and discourse referents may refer to worldly entities. Because DRT treats mental representations as indispensable elements of the theory, evidence from neuroscience, particularly the recording of electroencephalograms (EEG) and its derivative event-­related potentials (ERPs), can reasonably be thought to shed light on meaning and reference within this framework. In this chapter I first review the advantages of DRT in accommodating linguistic data and then review data from neuroscience that seem to support it. Finally, I consider some methodological concerns that have been raised about the neuroscientific approach to semantics. (shrink)

Conversational exculpature is a pragmatic process whereby information is subtracted from, rather than added to, what the speaker literally says. This pragmatic content subtraction explains why we can say “Rob is six feet tall” without implying that Rob is between 5'0.99" and 6'0.01" tall, and why we can say “Ellen has a hat like the one Sherlock Holmes always wears” without implying Holmes exists or has a hat. This article presents a simple formalism for understanding this pragmatic mechanism, specifying how, (...) in context, the result of such subtractions is determined. And it shows how the resulting theory of conversational exculpature accounts for a varied range of linguistic phenomena. A distinctive feature of the approach is the crucial role played by the question under discussion in determining the result of a given exculpature. (shrink)

Homo deceptus is a book that brings together new ideas on language, consciousness and physics into a comprehensive theory that unifies science and philosophy in a different kind of Theory of Everything. The subject of how we are to make sense of the world is addressed in a structured and ordered manner, which starts with a recognition that scientific truths are constructed within a linguistic framework. The author argues that an epistemic foundation of natural language must be understood before laying (...) claim to any notion of reality. This foundation begins with Ludwig Wittgenstein’s Tractatus Logico-Philosophicus and the relationship of language to formal logic. Ultimately, we arrive at an answer to the question of why people believe the things they do. This is effectively a modification of Alfred Tarski’s semantic theory of truth. The second major issue addressed is the ‘dreaded’ Hard Problem of Consciousness as first stated by David Chalmers in 1995. The solution is found in the unification of consciousness, information theory and notions of physicalism. The physical world is shown to be an isomorphic representation of the phenomenological conscious experience. New concepts in understanding how language operates help to explain why this relationship has been so difficult to appreciate. The inclusion of concepts from information theory shows how a digital mechanics resolves heretofore conflicting theories in physics, cognitive science and linguistics. Scientific orthodoxy is supported, but viewed in a different light. Mainstream science is not challenged, but findings are interpreted in a manner that unifies consciousness without contradiction. Digital mechanics and formal systems of logic play central roles in combining language, consciousness and the physical world into a unified theory where all can be understood within a single consistent framework. (shrink)

Quality assurance in large terminologies is a difficult issue. We present two algorithms that can help terminology developers and users to identify potential mistakes. We demon­strate the methodology by outlining the different types of mistakes that are found when the algorithms are applied to SNOMED-CT. On the basis of the results, we argue that both formal logical and linguistic tools should be used in the development and quality-assurance process of large terminologies.

It is common to distinguish two great families of representation. Symbolic representations include logical and mathematical symbols, words, and complex linguistic expressions. Iconic representations include dials, diagrams, maps, pictures, 3-dimensional models, and depictive gestures. This essay describes and motivates a new way of distinguishing iconic from symbolic representation. It locates the difference not in the signs themselves, nor in the contents they express, but in the semantic rules by which signs are associated with contents. The two kinds of rule have (...) divergent forms, occupying opposite poles on a spectrum of naturalness. Symbolic rules are composed entirely of primitive juxtapositions of sign types with contents, while iconic rules determine contents entirely by uniform natural relations with sign types. This distinction is marked explicitly in the formal semantics of familiar sign systems, both for atomic first-order representations, like words, pixel colors, and dials, and for complex second-order representations, like sentences, diagrams, and pictures. (shrink)

The verb to legitimate is often used in political discourse in a way that is prima facie perplexing. To wit, it is often said that an actor legitimates a practice which is officially prohibited in the relevant context – for example, that a worker telling sexist jokes legitimates sex discrimination in the workplace. In order to clarify the meaning of statements like this, and show how they can sometimes be true and informative, we need an explanation of how something that (...) is officially illegitimate can have a kind of ersatz legitimacy conferred on it, and how this can occur even when the actor ‘doing the legitimating’ lacks formal authority. I examine one putative explanation centred around the phenomenon of normalization, and I highlight some advantages that this account has in comparison to an alternative explanation, one that makes reference to the phenomenon of licensed authority. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)