This volume seeks to further the use of formal methods in clarifying one of the central problems of philosophy: that of our free human agency and its place in our indeterministic world. It celebrates the important contributions made in this area by Nuel Belnap, American logician and philosopher. Philosophically, indeterminism and free action can seem far apart, but in Belnap’s work, they are intimately linked. This book explores their philosophical interconnectedness through a selection of original research papers that build forth (...) on Belnap’s logical and philosophical work. Some contributions take the form of critical discussions of Belnap's published work, some develop points made in his publications in new directions, and others provide additional insights on the topics of indeterminism and free action. In Nuel Belnap’s work on indeterminism and free action, three formal frameworks figure prominently: the simple branching histories framework known as "branching time;" its relativistic spatio-temporal extension, branching space-times; and the “seeing to it that” logic of agency. As those frameworks provide the formal background for the contributed papers, the volume introduction gives an overview of the current state of their development. It also introduces case-intensional first order logic, a general intensional logic offering resources for a first-order extension of the mentioned frameworks and a recent research focus of Belnap’s. The volume also contains an extended biographical interview with Nuel Belnap. (shrink)

Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in related (...) fields get up to speed on open research-level problems. (shrink)

I discuss two competing theories of the progressive: the theory proposed in Parsons (1980, 1985, 1989, 1990) and the theory proposed in Landman (1992). These theories differ in more than one way. Landman regards the progressive as an intentional operator, while Parsons doesn't. Moreover, Landman and Parsons disagree on what uninflected predicates denote. For Landman, cross the street has in its denotation complete events of crossing the street; the aspectual contribution of English simple past (perfective aspect) is the identity function. (...) For Parsons, both complete and incomplete events of crossing the street can be in the denotation of the base VP; perfective aspect restricts its denotation to the events that culminate. I present a version of ParsonÕs theory that avoids the problems raised by Landman, in particular the problem posed for Parsons by creation verbs. The repaired version and Landman's theory still differ in the way they analyze uninflected verbs. The repaired version and Landman's theory still differ in the way they analyze uninflected predicates. I present evidence from Slavic languages that both theories are needed. Finally, I discuss some evidence that may favor one or the other approach to the semantics of the English progressive. (shrink)

This paper is based on Tarski’s theory of truth. The purpose of this paper is to solve the liar paradox (and its cousins) and keep both of the deductive power of classical logic and the expressive power of the word “true” in natural language. The key of this paper lies in the distinction between the predicate usage and the operator usage of the word “true”. The truth operator is primarily used for characterizing the semantics of the language. Then, we do (...) not need the hierarchy of languages. The truth predicate is mainly used for grammatical function. Tarski’s schema of the truth predicate is not necessary in this proposal. The schema of the word "true" is the schema of the truth operator. The liar paradox (and its cousins) can be solved in this way. In the appendix, I show a consistent model for both of the truth predicate and the truth operator. (shrink)

In formal semantics based on modern type theories, some sentences may be interpreted as judgements and some as logical propositions. When interpreting composite sentences, one may want to turn a judgemental interpretation or an ill-typed semantic interpretation into a proposition in order to obtain an intended semantics. For instance, an incorrect judgement $$a:A$$ may be turned into its propositional form $$\textsc {is}(A,a)$$ and an ill-typed application p(a) into $$\textsc {do}(p,a)$$, so that the propositional forms can take part in logical compositions (...) that interpret composite sentences, especially those that involve negations and conditionals.In this paper, we propose an operator not that facilitates such a transformation. Introducing not axiomatically, with five axiomatic laws to govern its behaviour, we shall use it to define $$\textsc {is}$$ and $$\textsc {do}$$ and give examples to illustrate its use in semantic interpretation. The introduction of not into type theories is logically consistent – this is justified by showing that not can be defined by means of the heterogeneous equality $$\textrm{JMeq}$$ so that all of the axiomatic laws for not become provable. Therefore, since the extension with $$\textrm{JMeq}$$ preserves logical consistency, so does the extension with not. We shall also study conditions under which $$\textsc {is}$$ and $$\textsc {do}$$ operators can be used safely without the risk of over-generation. (shrink)

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

This paper continues a strain of intellectual complaint against the presumptions of certain kinds of formal semantics (the qualification is important) and their bad effects on those areas of artificial intelligence concerned with machine understanding of human language. After some discussion of the use of the term epistemology in artificial intelligence, the paper takes as a case study the various positions held by McDermott on these issues and concludes, reluctantly, that, although he has reversed himself on the issue, there was (...) no time at which he was right. (shrink)

Michael Dummett famously maintained that analytic philosophy was simply philosophy that followed Frege in treating the philosophy of language as the basis for all other philosophy (1978, 441). But one important insight to emerge from computer science is how difficult it is to animate the linguistic artifacts that the analysis of thought produces. Yet, modeling the effects of thought requires a new skill that goes beyond analysis: procedural literacy. Some of the most promising research in philosophy makes use of a (...) variety of modeling techniques that go beyond basic logic and elementary probability theory. What unifies this approach is a focus on what Alan Perlis called procedural literacy. This essay argues that the future spoils in philosophical research will disproportionally go to those who are procedurally literate. (shrink)

We investigate axiomatizations of Kripke's theory of truth based on the Strong Kleene evaluation scheme for treating sentences lacking a truth value. Feferman's axiomatization KF formulated in classical logic is an indirect approach, because it is not sound with respect to Kripke's semantics in the straightforward sense: only the sentences that can be proved to be true in KF are valid in Kripke's partial models. Reinhardt proposed to focus just on the sentences that can be proved to be true in (...) KF and conjectured that the detour through classical logic in KF is dispensable. We refute Reinhardt's Conjecture, and provide a direct axiomatization PKF of Kripke's theory in partial logic. We argue that any natural axiomatization of Kripke's theory in Strong Kleene logic has the same proof-theoretic strength as PKF, namely the strength of the system RA< ωω ramified analysis or a system of Tarskian ramified truth up to ωω. Thus any such axiomatization is much weaker than Feferman's axiomatization KF in classical logic, which is equivalent to the system RA<ε₀ of ramified analysis up to ε₀. (shrink)

This light piece reflects on analogies between two often disjoint streams of research: the logical semantics and pragmatics of natural language and dynamic logics of general information-driven agency. The two areas show significant overlap in themes and tools, and yet, the focus seems subtly different in each, defying a simple comparison. We discuss some unusual questions that emerge when the two are put side by side, without any pretense at covering the whole literature or at reaching definitive conclusions.

The psychological orientation treats semantics as a matter of idealized computation over symbolic structures, and semantic relations like denotation as relations between linguistic expressions and these structures. I argue that results similar to Gödel's incompleteness theorems and Tarski's theorem on truth create foundational difficulties for this view of semantics.

A number of authors have argued that the fact that certain indexicals depend for their reference-determination on the speaker’s referential intentions demonstrates the inadequacy of associating such expressions with functions from contexts to referents (characters). By distinguishing between different uses to which the notion of context is put in these argument, I show that this line of argument fails. In the course of doing so, I develop a way of incorporating the role played by intentions into a character-based semantics for (...) indexicals and I argue that the framework I prefer is superior to an alternative which has been proposed by others. (shrink)

It is suggested that taking into account considerations that traditionally fall within the scope of computer science in general, and artificial intelligence in particular, sheds new light on the subject of causation. It is argued that adopting causal notions con be viewed as filling a computational need: They allow reasoning with incomplete information, facilitate economical representations, and afford relatively efficient methods for reasoning about those representations. Specifically, it is proposed that causal reasoning is intimately bound to nonmonotonic reasoning. An account (...) of causation is offered that relies upon this connection, and compares this proposal to previous accounts within philosophy and artificial intelligence. (shrink)

In this paper we show that the membership problem for second order non-linear Abstract Categorial Grammars is decidable. A consequence of that result is that Montague-like semantics yield to a decidable text generation problem. Furthermore the proof we propose is based on a new tool, Higher Order Intersection Signatures, which grasps statically dynamic properties of λ-terms and presents an interest in its own.

In this paper we defend structural representations, more specifically neural structural representation. We are not alone in this, many are currently engaged in this endeavor. The direction we take, however, diverges from the main road, a road paved by the mathematical theory of measure that, in the 1970s, established homomorphism as the way to map empirical domains of things in the world to the codomain of numbers. By adopting the mind as codomain, this mapping became a boon for all those (...) convinced that a representation system should bear similarities with what was being represented, but struggled to find a precise account of what such similarities mean. The euforia was brief, however, and soon homomorphism revealed itself to be affected by serious weaknesses, the primary one being that it included systems embarrassingly alien to representations. We find that the defense attempts that have followed, adopt strategies that share a common format: valid structural representations come as “homomorphism plus X”, with various “X”, provided in descriptive format only. Our alternative direction stems from the observation of the overlooked departure from homomorphism as used in the theory of measure and its later use in mental representations. In the former case, the codomain or the realm of numbers, is the most suited for developing theorems detailing the existence and uniqueness of homomorphism for a wide range of empirical domains. In the latter case, the codomain is the realm of the mind, possibly more vague and more ill-defined than the empirical domain itself. The time is ripe for articulating the mapping between represented domains and the mind in formal terms, by exploiting what is currently known about coding mechanisms in the brain. We provide a sketch of a possible development in this direction, one that adopts the theory of neural population coding as codomain. We will show that our framework is not only not in disagreement with the “plus X” proposals, but can lead to natural derivation of several of the “X”. (shrink)

This is the introductory essay to a collection commemorating the 100th anniversary of the publication in Mind of Bertrand Russell’s paper ‘On Denoting’.

This paper argues for the idea that in describing language we should follow Haskell Curry in distinguishing between the structure of an expression and its appearance or manifestation . It is explained how making this distinction obviates the need for directed types in type-theoretic grammars and a simple grammatical formalism is sketched in which representations at all levels are lambda terms. The lambda term representing the abstract structure of an expression is homomorphically translated to a lambda term representing its manifestation, (...) but also to a lambda term representing its semantics. (shrink)

This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis, in the context for type-logical grammars, of the logical models and algorithms currently used in natural language semantics, defined as a function from a grammatical sentence to a set of logical formulas—because a statement can be ambiguous, it can correspond to multiple formulas, one for each (...) reading. We argue that as long as we do not explicitly compute the interpretation in terms of possible world models, one can compute the semantic representation of a given statement, including aspects of lexical meaning. This is a very generic process, so the results are, at least in principle, widely applicable. We also discuss the algorithmic complexity of this process. (shrink)

'Propositionalism' is the widely held view that all intentional mental relations-all intentional attitudes-are relations to propositions or something proposition-like. Paradigmatically, to think about the mountain is ipso facto to think that it is F, for some predicate 'F'. It seems, however, many intentional attitudes are not relations to propositions at all: Mary contemplates Jonah, adores New York, misses Athens, mourns her brother. I argue, following Brentano, Husserl, Church and Montague among others, that the way things seem is the way they (...) are, and that propositionalism must be abandoned. (shrink)

This paper gives an overview of logico-philosophical issues of time and determinism. After a brief review of historical roots and 20th century developments, three current research areas are discussed: the definition of determinism, space-time indeterminism, and the temporality of individual things and their possibilities.

Different notions of analysis have been both theorized and put to use in early analytic philosophy. Two of them stand out: connective analysis and analysis as paraphrase. The latter played a central role in the development of analytic philosophy from Frege to Quine and beyond. With the advent of formal semantics of natural language in the 1970s, paraphrase came to be characterizable as translation into a formal “target language”. While I claim that the method cannot achieve its original philosophical aims, (...) I insist that, in spite of them, it is far from being a theoretically empty operation and that it lives on in some contemporary philosophical enterprises. (shrink)

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. This paper presents a case study of a new type of intertheoretic relation that is inspired by Montague’s analysis of the linguistic syntax-semantics relation. The paper develops a simple model of this relation. To motivate the adoption of our new model, we show that this model (...) extends the scope of application of the Nagelian models and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework. (shrink)

Foundations of Illocutionary Logic de John Searle et Daniel Vanderveken constitue, à ma connaissance, la première suggestion sérieuse d'un cadre formel destiné à l'élaboration d'une logique de l'illocutoire. Les phénomènes illocutoires sont en effet d'une telle com-plexité que, souvent, les schèmes explicatifs proposés n'ont qu'une valeur très locale et ne constituent une explication que pour quelques exemples bien précis, ceux qui justement ont servi de base empirique sur laquelle ces schèmes se sont élaborés. La prévention de FIL est tout autre. (...) On ne saurait en aucun cas faire un reproche de provincialisme aux auteurs dont le but explicite est d'élaborer un véritable cadre théorique général à l'intérieur duquel tous les phénomènes illocutoires pourront trouver une explication. (shrink)

In philosophical contexts, logical formalisms are often resorted to as a means to render the validity and invalidity of informal arguments formally transparent. Since Oliver and Massey , however, it has been recognized in the literature that identifying valid arguments is easier than identifying invalid ones. Still, any viable theory of adequate logical formalization should at least reliably identify valid arguments. This paper argues that accounts of logical formalization as developed by Blau and Brun do not meet that benchmark. The (...) paper ends by suggesting different strategies to remedy the problem. (shrink)

As an undergraduate I was taught to multiply two numbers with the help of log tables, using the formulaHaving graduated to teach calculus to Engineers, I learned that log tables were to be replaced by slide rules. It was then that Imade the fateful decision that there was no need for me to learn how to use this tedious device, as I could always rely on the students to perform the necessary computations. In the course of time, slide rules were (...) replaced by pocket calculators and personal computers, but I stuck to my original decision.My computer phobia did not prevent me from taking an interest in the theoretical question: what is a computation? This question goes back to Hilbert's 10th problem, which asks for an algorithm, or computational procedure, to decide whether any given polynomial equation is solvable in integers. It quickly leads to the related question: which numerical functionsf: ℕn→ ℕ are computable?While Hilbert's 10th problem was only resolved in 1970, this related question had some earlier answers, of which I shall single out the following three:f is recursive,f is computable on an abstract machine,f is definable in the untyped λ-calculus.These tentative answers were shown to be equivalent by Church [1936] and Turing [1936–7].I shall discuss here some of the more recent developments of these notions of computability and their relevance to linguistics and logic. I hope to be forgiven for dwelling on some of the work I have been involved with personally, with greater emphasis than is justified by its historical significance. (shrink)

Quantifiers in Language and Logic (QLL) is a major contribution to natural language semantics, specifically to quantification. It integrates the extensive recent work on quantifiers in logic and linguistics. It also presents new observations and results. QLL should help linguists understand the mathematical generalizations we can make about natural language quantification, and it should interest logicians by presenting an extensive array of quantifiers that lie beyond the pale of classical logic. Here we focus on those aspects of QLL we judge (...) to be of specific interest to linguists, and we contribute a few musings of our own, as one mark of a worthy publication is whether it stimulates the reader to seek out new observations, and QLL does. QLL is long and fairly dense, so we make no attempt to cover all the points it makes. But QLL has a topic index, a special symbols index and two tables of contents, a detailed one and an overview one, all of which help make it user friendly. QLL is presented in four parts: I, The Logical Conception of Quantifiers and Quantification with an introductory section Quantification . II, Quantifiers of Natural Language , the most extensive section in the book and of the most direct interest to linguists. III, Beginnings of a Theory of Expressiveness, Translation, and Formalization introduces notions of expressive power and definability, and IV, presents recent work and techniques concerning quantifier definability over finite domains, making accessible to linguists recent work in finite model theory. (shrink)

The unwinding that Cook, 767–774 2004) proposed is a simple but powerful method of generating new paradoxes from known ones. This paper extends Cook’s unwinding to a larger class of paradoxes and studies further the basic properties of the unwinding. The unwinding we study is a procedure, by which when inputting a Boolean modal net together with a definable digraph, we get a set of sentences in which we have a ‘counterpart’ for each sentence of the Boolean modal net and (...) each point of the digraph. What is more, whenever a sentence of the Boolean modal net says another sentence is necessary, then the counterpart of the first sentence at a point correspondingly says the counterparts of the second one at all accessible points of that point are all true. The output of the procedure is called ‘the unwinding of a Boolean modal net on a definable digraph’. We prove that the unwinding procedure preserves paradoxicality: a Boolean modal net is paradoxical on a definable digraph, iff the unwinding of it on this digraph is also paradoxical. Besides, the dependence digraph for the unwinding of a Boolean modal net on a definable digraph is proved to be isomorphic to the unwinding of the dependence digraph for the Boolean modal net on the previous definable digraph. So the unwinding of a Boolean modal net on a digraph is self-referential, iff the Boolean modal net is self-referential and the digraph is cyclic. Thus, on the one hand, the unwinding of any Boolean modal net on an acyclic digraph is non-self-referential. In particular, the unwinding of any Boolean modal net on \ is non-self-referential. On the other hand, if a Boolean modal net is paradoxical on a locally finite digraph, the unwinding of it on that digraph must be self-referential. Hence, starting from a Boolean modal paradox, the unwinding can output a non-self-referential paradox only if the digraph is not locally finite. (shrink)

This paper propounds a systematic examination of the link between the Knower Paradox and provability interpretations of modal logic. The aim of the paper is threefold: to give a streamlined presentation of the Knower Paradox and related results; to clarify the notion of a syntactical treatment of modalities; finally, to discuss the kind of solution that modal provability logic provides to the Paradox. I discuss the respective strength of different versions of the Knower Paradox, both in the framework of first-order (...) arithmetic and in that of modal logic with fixed point operators. It is shown that the notion of a syntactical treatment of modalities is ambiguous between a self-referential treatment and a metalinguistic treatment of modalities, and that these two notions are independent. I survey and compare the provability interpretations of modality respectively given by Skyrms, B. (1978, The Journal of Philosophy 75: 368–387) Anderson, C.A. (1983, The Journal of Philosophy 80: 338–355) and Solovay, R. (1976, Israel Journal of Mathematics 25: 287–304). I examine how these interpretations enable us to bypass the limitations imposed by the Knower Paradox while preserving the laws of classical logic, each time by appeal to a distinct form of hierarchy. (shrink)

The Idea behind Tarski's Definition of Truth. In Tarski's presentations of his truth-definition, the steps of the construction are not sufficiently explained. It is not clear, on what general strategy the construction is based, what the fundamental ideas are, how some crucial steps work, and especially how the transition from the definition of satisfaction to the definition of truth should be understood. The paper shows that the account given in the model-theoretic literature, which is supported by Tarski's lemmata A and (...) B, is unsatisfactory, because Tarski's notion of truth can't be interpreted as ‘truth independent of the assignment of values to the variables’. Moreover, a satisfactory account of all the crucial steps is given. (shrink)

This paper is a demonstration of an application of Semiotic Textology to a limited case study. The main aspects of Semiotic Textology, the theory elaborated by Petöfi, are presented; secondly the linguistic aspects of the interpretation of lines 133–134 of the Theognis of Megara’s poem, analysed in the framework of said theory, are presented. All the relevant syntactic, semantic, pragmatic information involved in text processing have been considered. Through fixed steps, it is shown that text processing is not exclusively a (...) grammatical activity, because within a theoretical interpretation an Interpreter needs a number of contextual hypotheses, in order to understand the author’s ontology. (shrink)

Quotation has been much studied in philosophy. Given that quotation allows one to diagonalize out of any grammar, there have been comparatively few attempts within the linguistic literature to develop an account within a formal linguistic theory. Nonetheless, given the ubiquity of quotation in natural language, linguists need to explicate the formal mechanisms it employs. The central claim of this paper is that once one assumes a dialogical perspective on language such as provided by the KoS (KoS is not an (...) acronym, despite emphasizing a Konversationally Oriented Semantics) framework, formalized in a rich type theory like Type Theory with Records, much of the mystery evaporates. In particular, one can utilize as denotations for quotative constructions entities that are independently motivated for dialogue processing—utterance types and locutionary propositions, Austinian propositions about speech events. (shrink)

According to the structured theory of propositions, if two sentences express the same proposition, then they have the same syntactic structure, with corresponding syntactic constituents expressing the same entities. A number of philosophers have recently focused attention on a powerful argument against this theory, based on a result by Bertrand Russell, which shows that the theory of structured propositions is inconsistent in higher order-logic. This paper explores a response to this argument, which involves restricting the scope of the claim that (...) propositions are structured, so that it does not hold for all propositions whatsoever, but only for those which are expressible using closed sentences of a given formal language. We call this restricted principle Closed Structure, and show that it is consistent in classical higher-order logic. As a schematic principle, the strength of Closed Structure is dependent on the chosen language. For its consistency to be philosophically significant, it also needs to be consistent in every extension of the language which the theorist of structured propositions is apt to accept. But, we go on to show, Closed Structure is in fact inconsistent in a very natural extension of the standard language of higher-order logic, which adds resources for plural talk of propositions. We conclude that this particular strategy of restricting the scope of the claim that propositions are structured is not a compelling response to the argument based on Russell’s result, though we note that for some applications, for instance to propositional attitudes, a restricted thesis in the vicinity may hold some promise. (shrink)

We defend the thesis that every necessarily true proposition is always true. Since not every proposition that is always true is necessarily true, our thesis is at odds with theories of modality and time, such as those of Kit Fine and David Kaplan, which posit a fundamental symmetry between modal and tense operators. According to such theories, just as it is a contingent matter what is true at a given time, it is likewise a temporary matter what is true at (...) a given possible world; so a proposition that is now true at all worlds, and thus necessarily true, may yet at some past or future time be false in the actual world, and thus not always true. We reconstruct and criticize several lines of argument in favor of this picture, and then argue against the picture on the grounds that it is inconsistent with certain sorts of contingency in the structure of time. (shrink)

Prior’s puzzle is standardly taken to be the puzzle of why, given the assumption that that-clauses denote propositions, substitution of “the proposition that P” for “that P” within the complements of many propositional attitude verbs is invalid. I show that Prior’s puzzle is much more general than is ordinarily supposed. There are two variants on the substitutional form of the puzzle—a quantificational variant and a pronominal variant—and all three forms of the puzzle arise in a wide range of grammatical positions, (...) rather than merely in the complements of propositional attitude verbs. The generalized puzzle shows that a range of proposed solutions to the original puzzle fail, or are radically incomplete, and also reveals the connections between Prior’s puzzle and debates over the nature of semantic types and higher-order quantification. I go on to develop a novel, higher-order solution to the generalized form of the puzzle, and I argue that this higher-approach is superior to its first-order alternatives. (shrink)

This paper charts some early history of the possible worlds semantics for modal logic, starting with the pioneering work of Prior and Meredith. The contributions of Geach, Hintikka, Kanger, Kripke, Montague, and Smiley are also discussed.

One of the claims of Type Theory with Records is that it can be used to model types learned by agents in order to classify objects and events in the world, including speech events. That is, the types can be represented by patterns of neural activation in the brain. This claim would be empty if it turns out that the types are in principle impossible to represent on a finite network of neurons. We will discuss how to represent types in (...) terms of neural events on a network and present a preliminary computational implementation that maps types to events on a network. The kind of networks we will use are closely related to the transparent neural networks discussed by Strannegård. (shrink)

Conceptual realism begins with a conceptualist theory of the nexus of predication in our speech and mental acts, a theory that explains the unity of those acts in terms of their referential and predicable aspects. This theory also contains as an integral part an intensional realism based on predicate nominalization and a reflexive abstraction in which the intensional contents of our concepts are “object”-ified, and by which an analysis of predication with intensional verbs can be given. Through a second nominalization (...) of the common names that are part of conceptual realism’s theory of reference (via quantifier phrases), the theory also accounts for both plural reference and predication and mass noun reference and predication. Finally, a separate nexus of predication based on natural kinds and the natural properties and relations nomologically related to those natural kinds, is also an integral part of the framework of conceptual realism. (shrink)

Linguists often sharply distinguish the different modules that support linguistics competence, e.g., syntax, semantics, pragmatics. However, recent work has identified phenomena in syntax (polarity sensitivity) and pragmatics (implicatures), which seem to rely on semantic properties (monotonicity). We propose to investigate these phenomena and their connections as a window into the modularity of our linguistic knowledge. We conducted a series of experiments to gather the relevant syntactic, semantic and pragmatic judgments within a single paradigm. The comparison between these quantitative data leads (...) us to four main results, (i) Our results support a departure from one element of the classical Gricean approach, thus helping to clarify and settle an empirical debate. This first outcome also confirms the soundness of the methodology, as the results align with standard contemporary accounts of scalar implicature (SI), (ii) We confirm that the formal semantic notion of monotonicity underlies negative polarity item (NPI) syntactic acceptability, but (iii) our results indicate that the notion needed is perceived monotonicity. We see results (ii) and (iii) as the main contribution of this study: (ii) provides an empirical interpretation and confirmation of one of the insights of the model-theoretic approach to semantics, while (iii) calls for an incremental, cognitive implementation of the current generalizations, (iv) Finally, our results do not indicate that the relationship between NPI acceptability and monotonicity is mediated by pragmatic features related to Sis: this tells against elegant attempts to unify polarity sensitivity and Sis (pioneered by Krifka and Chierchia). These results illustrate a new methodology for integrating theoretically rigorous work in formal semantics with an experimentally-grounded cognitively-oriented view of linguistic competence. (shrink)

Thanks to David Kaplan (1989a, 1989b), we all know how to handle indexicals like ‘I’. ‘I’ doesn’t refer to an object simpliciter; rather, it refers to an object only relative to a context. In particular, relative to a context C, ‘I’ refers to the agent of C. Since different contexts can have different agents, ‘I’ can refer to different objects relative to different contexts. For example, relative to a context cwhose agent is Gottlob Frege, ‘I’ refers to Frege; relative to (...) a context 0* whose agent is Alexius.. (shrink)

Khemlani et al. (2018) mischaracterize logic in the course of seeking to show that mental model theory (MMT) can accommodate a form of inference (, let us label it) they find in a high percentage of their subjects. We reveal their mischaracterization and, in so doing, lay a landscape for future modeling by cognitive scientists who may wonder whether human reasoning is consistent with, or perhaps even capturable by, reasoning in a logic or family thereof. Along the way, we note (...) that the properties touted by Khemlani et al. as innovative aspects of MMT‐based modeling (e.g., nonmonotonicity) have for decades been, in logic, acknowledged and rigorously specified by families of (implemented) logics. Khemlani et al. (2018) further declare that is “invalid in any modal logic.” We demonstrate this to be false by our introduction (Appendix A) of a new propositional modal logic (within a family of such logics) in which is provably valid, and by the implementation of this logic. A second appendix, B, partially answers the two‐part question, “What is a formal logic, and what is it for one to capture empirical phenomena?”. (shrink)