In Pietroski ( 2018 ) a simple representation language called SMPL is introduced, construed as a hypothesis about core conceptual structure. The present work is a study of this system from a logical perspective. In addition to establishing a completeness result and a complexity characterization for reasoning in the system, we also pinpoint its expressive limits, in particular showing that the fourth corner in the square of opposition (“ Some_not ”) eludes expression. We then study a seemingly small extension, called (...) SMPL +, which allows for a minimal predicate-binding operator. Perhaps surprisingly, the resulting system is shown to encode precisely the concepts expressible in first-order logic. However, unlike the latter class, the class of SMPL + expressions admits a simple procedural (context-free) characterization. Our contribution brings together research strands in logic—including natural logic, modal logic, description logic, and hybrid logic—with recent advances in semantics and philosophy of language. (shrink)

Abstract Impossible fictions have lessons to teach us about linguistic representation, about mental content and concepts, and about uses of conceivability in epistemology. An adequate theory of impossible fictions may require theories of meaning that can distinguish between different impossibilities; a theory of conceptual truth that allows us to make useful sense of a variety of conceptual falsehoods; and a theory of our understanding of necessity and possibility that permits impossibilities to be conceived. After discussing these questions, strategies for resisting (...) the picture of impossible fictions presented here and in Part I are discussed. Perhaps apparently impossible fictions describe possibilities after all; or perhaps impossible fictions are all trivial; or perhaps some apparently intelligible impossible fictions are unintelligible after all. (shrink)

Abstract The purpose of this paper is twofold: (i) we will argue that formal semantics might have faltered due to its failure in distinguishing between two fundamentally very different types of concepts, namely ontological concepts, that should be types in a strongly-typed ontology, and logical concepts, that are predicates corresponding to properties of, and relations between, objects of various ontological types; and (ii) we show that accounting for these differences amounts to a new formal semantics; one that integrates lexical and (...) compositional semantics in one coherent framework and one where formal semantics is embedded with a strongly typed ontology; an ontology that reflects our commonsense knowledge of the world and the way we talk about it in ordinary language. We will show how in such a framework a number of challenges in the semantics of natural language are adequately and systematically treated. (shrink)

This paper contains an argument to the effect that possible worlds semantics renders semantic knowledge impossible, no matter what ontological interpretation is given to possible worlds. The essential contention made is that possible worlds semantic knowledge is unsafe and this is shown by a parallel with the preface paradox.

In truth theory one aims at general formal laws governing the attribution of truth to statements. Gupta’s and Belnap’s revision-theoretic approach provides various well-motivated theories of truth, in particular T* and T#, which tame the Liar and related paradoxes without a Tarskian hierarchy of languages. In property theory, one similarly aims at general formal laws governing the predication of properties. To avoid Russell’s paradox in this area a recourse to type theory is still popular, as testified by recent work in (...) formal metaphysics by Williamson and Hale. There is a contingent Liar that has been taken to be a problem for type theory. But this is because this Liar has been presented without an explicit recourse to a truth predicate. Thus, type theory could avoid this paradox by incorporating such a predicate and accepting an appropriate theory of truth. There is however a contingent paradox of predication that more clearly undermines the viability of type theory. It is then suggested that a type-free property theory is a better option. One can pursue it, by generalizing the revision-theoretic approach to predication, as it has been done by Orilia with his system P*, based on T*. Although Gupta and Belnap do not explicitly declare a preference for T# over T*, they show that the latter has some advantages, such as the recovery of intuitively acceptable principles concerning truth and a better reconstruction of informal arguments involving this notion. A type-free system based on T# rather than T* extends these advantages to predication and thus fares better than P* in the intended applications of property theory. (shrink)

Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

Since the pioneering work by Kripke and Montague, the term possible world has appeared in most theories of formal semantics for modal logics, natural languages, and knowledge-based systems. Yet that term obscures many questions about the relationships between the real world, various models of the world, and descriptions of those models in either formal languages or natural languages. Each step in that progression is an abstraction from the overwhelming complexity of the world. At the end, nothing is left but a (...) colorful metaphor for an undefined element of a set W called worlds, which are related by an undefined and undefinable primitive relation R called accessibility. For some purposes, the resulting abstraction has proved to be useful, but as a general theory of meaning, the abstraction omits too many significant features. So much information has been lost at each step that many philosophers, linguists, and psychologists have dismissed model-theoretic semantics as irrelevant to the study of meaning. This article examines the steps in the process of extractingthe pair (W,R) from the world and the way people talk about the world. It shows that the Kripke worlds can be reinterpreted as part of a Peircean semiotic theory, which can also include contributions from many other studies in cognitive science. Among them are Dunn’s semantics based on laws and facts, the lexical semantics preferred by manylinguists, psychological models of how the world is perceived, and philosophies of science that relate theories to the world. A full integration of all those sources is far beyond the scope of this article, but an outline of the approach suggests that Peirce’s vision is capable of relating and reconciling the competing sources. (shrink)

In celebrating Arthur Prior we celebrate what he gave to the world. Much of this is measured by what others have made of his ideas after his death. The focus of this paper is a little different. It looks at what Prior himself thought he was accomplishing. In particular it considers Prior’s attitude to the semantic metatheory of the logics that he was interested in. The paper sets out some characteristics of the metalogical study of intensional languages in terms of (...) an indexical theory of truth conditions stated in the language of set theory. In examining Prior’s work using these characteristics, it emerges that Prior had serious reservations about this way of studying modal and tense logics. (shrink)

This paper aims to clarify the connection between the logic of temporal distinctions and the temporal features of propositions. Contra Prior, it argues that the adoption of tense operators does not commit one to the view that propositions can change their truth value over time.

‘The following sentence is true only if numbers exist: The number of planets is eight. It is true; hence, numbers exist.’ So runs a familiar argument for realism about mathematical objects. But this argument relies on a controversial semantic thesis: that ‘The number of planets’ and ‘eight’ are singular terms standing for the number eight, and the copula expresses identity. This is the ‘Fregean analysis’.I show that the Fregean analysis is false by providing an analysis of sentences such as that (...) best explains the available linguistic data, and according to which no terms in purport to stand for numbers. (shrink)

The book presents the case that cognitive science should turn its attention to developing theories of human cognition that cover the full range of human perceptual, cognitive, and action phenomena. Cognitive science has now produced a massive number of high-quality regularities with many microtheories that reveal important mechanisms. The need for integration is pressing and will continue to increase. Equally important, cognitive science now has the theoretical concepts and tools to support serious attempts at unified theories. The argument is made (...) entirely by presenting an exemplar unified theory of cognition both to show what a real unified theory would be like and to provide convincing evidence that such theories are feasible. The exemplar is SOAR, a cognitive architecture, which is realized as a software system. After a detailed discussion of the architecture and its properties, with its relation to the constraints on cognition in the real world and to existing ideas in cognitive science, SOAR is used as theory for a wide range of cognitive phenomena: immediate responses ; discrete motor skills ; memory and learning ; problem solving ; language ; and development. The treatments vary in depth and adequacy, but they clearly reveal a single, highly specific, operational theory that works over the entire range of human cognition, SOAR is presented as an exemplar unified theory, not as the sole candidate. Cognitive science is not ready yet for a single theory – there must be multiple attempts. But cognitive science must begin to work toward such unified theories. (shrink)

The common account of the analog vs digital distinction is based on features of physical systems, being related to the usage of continuous vs discrete supports respectively. It is proposed here to alternatively characterize the concepts of analog and digital as related to coding systems, of which a formal definition is given, by suggesting that the distinction refers to the strategy adopted to define the coding function: extensional in digital systems, isomorphic intensional in analog systems. This thesis is supported by (...) examples, in particular of analog systems exploiting discrete supports, and is discussed to explain why digital coding is currently so widespread in technological and social practice. (shrink)

My point in this paper is to focus on some details of Alfred Tarski’s writing that in my opinion have not been aptly represented — or aptly rejected — in Richard Montague’s grammar and to agree with those who share Tarski’s view that human language is something uncapturable. The paper consists of two parts, concerning 1) some attempts to formalize the non-declarative utterances, and 2) the limitations of T-scheme and of Montague grammar.

Three misrepresentations of informal and formal logic by two feminist writers are discussed. Andrea Nye's criticism that the semantics for formal logic abstracts from context is a misrepresentation of formal logic because Nye ignores the development of intensional logics. Second, Nye's criticism that informaIlogicians ignore the origins of arguments is a misrepresentation of fallacy theory. Prominent writers in the field specifiy numerous cases where the origins of an argument are relevant to its evaluation. Third, Valerie Plumwood's criticism that negation in (...) classical logic rests on an exclusivistic dualism that encourages the exclusion of women is shown to be false. (shrink)

This article presents a detailed formal approach to concepts and concept combination. Sense generation is a competence‐level theory that attempts to respect constraints from the various cognitive sciences, and postulates “quasi‐classical” conceptual structures where attributes receive only one value (but are defeasible and so do not represent necessary and sufficient conditions on category membership) and where classification is binary (but explicitly context‐sensitive). It is also argued that any general theory of concepts must account for “privative” combinations (e.g., stone lion, fake (...) gun, apparent friend) as extreme test‐cases of representational and classificatory flexibility. The approach presented therefore provides a treatment of these combinations. The approach differentiates between the “lexical concept” (the stable information represented in a mental lexicon) which acts as a base from which the various “senses” (flexible contents associated with words and phrases in context, and used in classification) are “generated.” Generation allows nonmonotonicity, so that in different circumstances, different attributes may be defeated or modified. Classification is treated as relative to the perspective adopted, so that a classification acceptable from one perspective may be unacceptable from another, without contradiction. The result is a view that assumes bottom‐up priority in concept combination, where the range of senses generated by bottom‐up rules of combination is tempered by pragmatic‐communicative constraints on classification. An account of the representational and classification behavior of privative combinations is outlined, and the article concludes with a discussion of some of the implications of the approach. (shrink)

Sometimes two expressions in a discourse can be about the same thing in a way that makes that very fact evident to the participants. Consider, for example, 'he' and 'John' in 'John went to the store and he bought some milk'. Let us call this 'de jure' coreference. Other times, coreference is 'de facto' as with 'Mark Twain' and 'Samuel Clemens' in a sincere use of 'Mark Twain is not Samuel Clemens'. Here, agents can understand the speech without knowing that (...) the names refer to the same person. After surveying many available linguistic and pragmatic tools (intentions to corefer, presuppositions, meanings, indexing, discourse referents, binding etc.) I conclude that we must posit a new semantic primitive to account for de jure coreference. (shrink)

In the present piece we defend predicate approaches to modality, that is approaches that conceive of modal notions as predicates applicable to names of sentences or propositions, against the challenges raised by Montague’s theorem. Montague’s theorem is often taken to show that the most intuitive modal principles lead to paradox if we conceive of the modal notion as a predicate. Following Schweizer (J Philos Logic 21:1–31, 1992) and others we show this interpretation of Montague’s theorem to be unwarranted unless a (...) further non trivial assumption is made—an assumption which should not be taken as a given. We then move on to showing, elaborating on work of Gupta (J Philos Logic 11:1–60, 1982), Asher and Kamp (Properties, types, and meaning. Vol. I: foundational issues, Kluwer, Dordrecht, pp 85−158, 1989), and Schweizer (J Philos Logic 21:1–31, 1992), that the unrestricted modal principles can be upheld within the predicate approach and that the predicate approach is an adequate approach to modality from the perspective of modal operator logic. To this end we develop a possible world semantics for multiple modal predicates and show that for a wide class of multimodal operator logics we may find a suitable class of models of the predicate approach which satisfies, modulo translation, precisely the theorems of the modal operator logic at stake. (shrink)

It is commonly argued that natural language has the expressive power of quantifying over intensional entities, such as times, worlds, or situations. A standard way of modelling this assumes that there are unpronounced but syntactically represented variables of the corresponding type. Not all that much as has been said, however, about the exact syntactic location of these variables. Meanwhile, recent work has highlighted a number of problems that arise because the interpretive options for situation pronouns seem to be subject to (...) various restrictions. This paper is primarily concerned with situation pronouns inside of determiner phrases, arguing that they are introduced as arguments of (certain) determiners. Verbal predicates, on the other hand, are assumed to not combine with a situation pronoun. The various restrictions on their interpretation are shown to fall out from the semantic system that is developed based on that view. Further support for such an account comes from situation semantic analyses of donkey sentences as well as data on the temporal interpretation of nominal predicates. Its ability to account for this full range of data in a unified manner is shown to set it apart from previous proposals. The paper closes with an outlook on further extensions, including an account of quantifier domain restriction based on situation pronouns. (shrink)

The authors provide an object-theoretic analysis of two paradoxes in the theory of possible worlds and propositions stemming from Russell and Kaplan. After laying out the paradoxes, the authors provide a brief overview of object theory and point out how syntactic restrictions that prevent object-theoretic versions of the classical paradoxes are justified philosophically. The authors then trace the origins of the Russell paradox to a problematic application of set theory in the definition of worlds. Next the authors show that an (...) object-theoretic analysis of the Kaplan paradox reveals that there is no genuine paradox at all, as the central premise of the paradox is simply a logical falsehood and hence can be rejected on the strongest possible grounds—not only in object theory but for the very framework of propositional modal logic in which Kaplan frames his argument. The authors close by fending off a possible objection that object theory avoids the Russell paradox only by refusing to incorporate set theory and, hence, that the object-theoretic solution is only a consequence of the theory’s weakness. (shrink)

Current theories of grammar handle both extraction and anaphorization by introducing variables into syntactic representations. Combinatory categorial grammar eliminates variables corresponding to gaps. Using the combinator W, the paper extends this approach to anaphors, which appear to act as overt bound variables. [Slightly extended version in Bartsch et al 1989.].

This paper discusses empty quotation (‘’ is an empty string) and lexical quotation (his praise was, quote, fulsome, unquote), it challenges the minimal theory of quotation (‘ “x” ’ quotes ‘x’) and it defends the identity theory of quotation. In the process it illuminates disciplinary differences between the science of language and the philosophy of language. First, most philosophers assume, without argument, that language includes writing, whereas linguists have reason to identify language with speech (plus sign language). Second, philosophers tend (...) to think of languages as abstract objects whereas linguists tend to think of them as natural objects. These foundational differences help to explain disagreements in grammaticality judgments and consequent disagreements in semantic theory. (shrink)

This paper explores the relationship between Hume's Prinicple and Basic Law V, investigating the question whether we really do need to suppose that, already in Die Grundlagen, Frege intended that HP should be justified by its derivation from Law V.

This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church's Logic of Sense and Denotation. Church understands such senses themselves to be "sense-functions," functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain undesirable results given certain unusual or "deviant" sense-functions. Certain absurdities result, e.g., an argument can be found for equating any two (...) senses of the same type. An alternative treatment of the senses of functions is discussed, and is thought to do better justice to Frege's original theory. (shrink)

This article introduces three arguments that share a single conclusion: that a comprehensive science of language cannot describe relations of semantic reference, i.e. word–world relations. Spelling this out, if there is to be a genuine science of linguistic meaning, then a theory of meaning cannot involve assigning external, real-world, objects to names, nor sets of external objects to predicates, nor truth values to sentences. Most of the article tries to explain and defend this broad conclusion. The article also presents, in (...) a very limited way, a positive alternative to external-referent semantics for expressions. This alternative has two parts: first, that the meanings of words and sentences are mental instructions, not external things; second, that it is people who refer by using words and sentences, and word/sentence meanings play but a partial role in allowing speakers to talk about the world. (shrink)

This paper describes a prototype implementation of a Labelled Deduction System for natural language interpretation, where interpretation is taken to be the process of understanding a natural language utterance. The implementation models the process of understanding wh-gap dependencies in questions and relative clauses for a fragment of English. The paper is divided in three main sections. In Section 1, we introduce the basic architecture of the system. Section 2 outlines a prototype implementation of wh-binding and indicates its potential for explanation (...) of linguistic phenomena, and in Section 3 we briefly set the model within a large theoretical perspective, comparing it to other type-logical approaches to natural language analysis. (shrink)

I argue that linguistic meanings are instructions to build monadic concepts that lie between lexicalizable concepts and truth-evaluable judgments. In acquiring words, humans use concepts of various adicities to introduce concepts that can be fetched and systematically combined via certain conjunctive operations, which require monadic inputs. These concepts do not have Tarskian satisfaction conditions. But they provide bases for refinements and elaborations that can yield truth-evaluable judgments. Constructing mental sentences that are true or false requires cognitive work, not just an (...) exercise of basic linguistic capacities. (shrink)

The development of possible worlds semantics for modal claims has led to a more general application of that theory as a complete semantics for various formal and natural languages, and this view is widely held to be an adequate (philosophical) interpretation of the model theory for such languages. We argue here that this view generates a self-referential inconsistency that indicates either the falsity or the incompleteness of PWS.

From the Editor’s Introduction: "The Internal Limitations of Human Understanding." We carry, unavoidably, the limits of our understanding with us. We are perpetually confined within the horizons of our conceptual structure. When this structure grows or expands, the breadth of our comprehensions enlarges, but we are forever barred from the wished-for glimpse beyond its boundaries, no matter how hard we try, no matter how much credence we invest in the substance of our learning and mist of speculation. -/- The limitations (...) in view here are not due to the mere finitude of our understanding of ourselves and of the world in which we live. They are limitations that come automatically and necessarily with any form of understanding. They are, as we shall see, part and parcel of any organization or ordering of data that we call information. -/- The consequences of these limitations are varied: As a result of them, hermeneutics cannot help but be hermetic; scientific theories of necessity are circumscribed by the boundaries of the ideas that define them; formal systems must choose between consistency and comprehensiveness; philosophical study, because it includes itself within its own proper subject matter, is forced to be reflexive in its self-enclosure. The fundamental dynamic shared by all forms of understanding testifies to an internal limitative keystone. (shrink)

Measures of theory-Distance are defined for theories formalizable within first-Order predicate logic by using distributive normal forms. The account is applied to give measures of verisimilitude.

Gilbert Harman, in Logic and Reasoning (Synthese 60 (1984), 107–127) describes an unsuccessful attempt ... to develop a theory which would give logic a special role in reasoning. Here reasoning is psychological, a procedure for revising one''s beliefs. In the present paper, I construe reasoning sociologically, as a process of linguistic interaction; and show how both reasoning in the psychologistic sense and logic are related to that process.

In this paper, we address several puzzles concerning speech acts, particularly indirect speech acts. We show how a formal semantictheory of discourse interpretation can be used to define speech acts and to avoid murky issues concerning the metaphysics of action. We provide a formally precise definition of indirect speech acts, including the subclass of so-called conventionalized indirect speech acts. This analysis draws heavily on parallels between phenomena at the speech act level and the lexical level. First, we argue that, just (...) as co-predication shows that some words can behave linguistically as if they're `simultaneously' of incompatible semantic types, certain speech acts behave this way too. Secondly, as Horn and Bayer (1984) and others have suggested, both the lexicon and speech acts are subject to a principle of blocking or "preemption by synonymy": Conventionalized indirect speech acts can block their `paraphrases' from being interpreted as indirect speech acts, even if this interpretation is calculable from Gricean-style principles. We provide a formal model of this blocking, and compare it with existing accounts of lexical blocking. (shrink)

This paper has two goals. The first is to formulate an adequate account of the semantics of the progressive aspect in English: the semantics of Agatha is making a cake, as opposed to Agatha makes a cake. This account presupposes a version of the so-called Aristotelian classification of verbs in English into EVENT, PROCESS and STATE verbs. The second goal of this paper is to refine this classification so as to account for the infamous category switch problem, the problem of (...) how it is that modification of a verb like run by an adverbial like to the store can turn a PROCESS phrase (run) into an EVENT phrase (run to the store). Views discussed include those of Aqvist, Bach, Bennett, Bennett and Partee, Dowry, Montague and Scott, and Vendler. (shrink)

Our purpose is to formulate a complete logic of propositions that takes into account the fact that propositions are both senses provided with truth values and contents of conceptual thoughts. In our formalization, propositions are more complex entities than simple functions from possible worlds into truth values. They have a structure of constituents (a content) in addition to truth conditions. The formalization is adequate for the purposes of the logic of speech acts. It imposes a stronger criterion of propositional identity (...) than strict equivalence. Two propositions P and Q are identical if and only if, for any illocutionary force F, it is not possible to perform with success a speech act of the form F(P) without also performing with success a speech act of the form F(Q). Unlike hyperintensional logic, our logic of propositions is compatible with the classical Boolean laws of propositional identity such as the symmetry and the associativity of conjunction and the reduction of double negation. (shrink)

This paper embeds the core part of Discourse Representation Theory in the classical theory of types plus a few simple axioms that allow the theory to express key facts about variables and assignments on the object level of the logic. It is shown how the embedding can be used to combine core analyses of natural language phenomena in Discourse Representation Theory with analyses that can be obtained in Montague Semantics.

This paper argues against relativism, focusing on relativism based on the semantics of predicates of personal taste. It presents and defends a contextualist semantics for these predicates, derived from current work on gradable adjectives. It then considers metasemantic questions about the kinds of contextual parameters this semantics requires. It argues they are not metasemantically different from those in other gradable adjectives, and that contextual parameters of this sort are widespread in natural language. Furthermore, this paper shows that if such parameters (...) are rejected, it leads to an unacceptably rampant form of relativism, that relativizes truth to an open-ended list of parameters. (shrink)

The aim of this paper is to consider some logical aspects of the debate between the view that the present is the only 'real' time, and the view that the present is not in any way metaphysically privileged. In particular I shall set out a language of first-order predicate tense logic with a now predicate, and a first order (extensional) language with an abstraction operator, in such a way that each language can be shewn to be exactly translatable into the (...) other. I shew that this translation is preserved at the metalinguistic level, so that equivalent truth conditions can be defined in a tensed metalanguage or an indexical metalanguage. I then make some remarks about the connection between proofs of relative consistency and metaphysical truth; and some historical remarks about Arthur Prior's use of formal logic in expressing his presentist views. (shrink)

This paper concerns the semantics of belief-sentences. I pass over ontologically lavish theories which appeal to impossible worlds, or other points of reference which contain more than possible worlds. I then refute ontologically stingy, quotational theories. My own theory employs the techniques of possible worlds semantics to elaborate a Fregean analysis of belief-sentences. In a belief-sentence, the embedded clause does not have its usual reference, but refers rather to its own semantic structure. I show how this theory can accommodate quantification (...) into belief-contexts. I close with skirmishes against the threat posed by the Liar Paradox. (shrink)