Various studies have been made on different aspects of the Turkish and Japanese languages, but comparative studies between the two languages are still limited. The aim of this study is to describe the politeness strategy of these two languages from a cultural perspective within the paradigm of cognitive linguistics. Both Turkish and Japanese are agglutinative languages, and speakers of both languages prefer the subjective construal. So, if the typology of a language might be related to its perception, the conceptualization of (...) ‘polite’ and the perception of politeness in that language may be alike. (shrink)

Various studies have been made on different aspects of the Turkish and Japanese languages, but comparative studies between the two languages are still limited. The aim of this study is to describe the politeness strategy of these two languages from a cultural perspective within the paradigm of cognitive linguistics. Both Turkish and Japanese are agglutinative languages, and speakers of both languages prefer the subjective construal. So, if the typology of a language might be related to its perception, the conceptualization of (...) ‘polite’ and the perception of politeness in that language may be alike. (shrink)

Various studies have been made on different aspects of the Turkish and Japanese languages, but comparative studies between the two languages are still limited. The aim of this study is to describe the politeness strategy of these two languages from a cultural perspective within the paradigm of cognitive linguistics. Both Turkish and Japanese are agglutinative languages, and speakers of both languages prefer the subjective construal. So, if the typology of a language might be related to its perception, the conceptualization of (...) ‘polite’ and the perception of politeness in that language may be alike. (shrink)

Various studies have been made on different aspects of the Turkish and Japanese languages, but comparative studies between the two languages are still limited. The aim of this study is to describe the politeness strategy of these two languages from a cultural perspective within the paradigm of cognitive linguistics. Both Turkish and Japanese are agglutinative languages, and speakers of both languages prefer the subjective construal. So, if the typology of a language might be related to its perception, the conceptualization of (...) ‘polite’ and the perception of politeness in that language may be alike. (shrink)

Quine maintained that philosophical and scientific theorizing should be conducted in an untyped language, which has just one style of variables and quantifiers. By contrast, typed languages, such as those advocated by Frege and Russell, include multiple styles of variables and matching kinds of quantification. Which form should our theories take? In this article, I argue that expressivity does not favour typed languages over untyped ones.

As a new foundational language for mathematics with its very different idea as to the status of logic, we should expect homotopy type theory to shed new light on some of the problems of philosophy which have been treated by logic. In this article, definite description, and in particular its employment within mathematics, is formulated within the type theory. Homotopy type theory has been proposed as an inherently structuralist foundational language for mathematics. Using the new formulation of (...) definite descriptions, opportunities to express ‘the structure of’ within homotopy type theory are explored, and it is shown there is little or no need for this expression. (shrink)

We present Property Theory with Curry Typing (PTCT), an intensional first-order logic for natural language semantics. PTCT permits fine-grained specifications of meaning. It also supports polymorphic types and separation types. We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like “most.” We use the type system and our treatment of generalized quantifiers in natural language to construct a type-theoretic approach to pronominal anaphora that avoids some of the difficulties that undermine previous (...) class='Hi'>type-theoretic analyses of this phenomenon. (shrink)

The original article has been corrected. The article is published with Open Access but was missing Open Access information. This has been added.

I argue that imperatives express contents that are both cognitively and semantically related to, but nevertheless distinct from, modal propositions. Imperatives, on this analysis, semantically encode features of planning that are modally specified. Uttering an imperative amounts to tokening this feature in discourse, and thereby proffering it for adoption by the audience. This analysis deals smoothly with the problems afflicting Portner's Dynamic Pragmatic account and Kaufmann's Modal account. It also suggests an appealing reorientation of clause-type theorizing, in which the (...) cognitive act of updating on a typed sentence plays a central role in theorizing about both its semantics and role in discourse. (shrink)

of type theory has been used successfully to formalize large parts of constructive mathematics, such as the theory of generalized recursive definitions [NPS90, ML79]. Moreover, it is also employed extensively as a framework for the development of high-level programming languages, in virtue of its combination of expressive strength and desirable proof-theoretic properties [NPS90, Str91]. In addition to simple types A, B, . . . and their terms x : A b(x) : B, the theory also has dependent types x (...) : A B(x), which are regarded as indexed families of types. There are simple type forming operations A × B and A → B, as well as operations on dependent types, including in particular the sum x:A B(x) and product x:A B(x) types (see the appendix for details). The Curry-Howard interpretation of the operations A × B and A → B is as propositional conjunction and.. (shrink)

One of the key intentions of fresh expressions of church is to reach the kind of people inherited church find it hard to reach. Psychological type profiling of church congregations has demonstrated that Anglican churches have particular difficulty in reaching those whose Jungian judging preference is for thinking rather than for feeling. Studies that have explored the psychological type profile of participants within fresh expressions suggest that they do not significantly differ from inherited congregations in terms (...) of reaching thinking types. Two previous studies, however, have reported higher proportions of thinking types attending cathedral carol services. The present study among 441 individuals attending the Holly Bough service in Liverpool Cathedral also found a higher proportion of thinking types among the participants. These findings suggest that cathedral carol services may be functioning as fresh expressions of church in a significant way.Contribution: Situated within the science of cathedral studies, rooted in psychological type theory, and drawing on data from 441 attendees at the Holly Bough service, this study demonstrates that cathedral services at Christmas are more successful than either inherited church or fresh expressions of church in reaching thinking types. (shrink)

In part 4 of Meaning, Expression, and Thought, Davis rejects what he calls Fregean ideational theories, according to which the meaning of an expression is an idea; and then presents his own account, which states that, e.g., the meaning of 'Primzahl' in German is the property of meaning prime number. Before casting doubt on the latter ontology of meanings, I come to Frege's defence by pointing out that he was not an advocate of the position Davis named after him because (...) Fregean senses are not lexical meanings and Fregean thoughts are not types of mental events. (shrink)

In the domain of ontology design as well as in Knowledge Representation, modeling universals is a challenging problem.Most approaches that have addressed this problem rely on Description Logics (DLs) but many difficulties remain, due to under-constrained representation which reduces the inferences that can be drawn and further causes problems in expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but, so far they have not been applied in the formalization of ontologies. To bridge this (...) gap, we present in this paper a theory for representing ontologies in a dependently typed framework which relies on strong formal foundations including both a constructive logic and a functional type system. The language of this theory defines in a precise way what ontological primitives such as classes, relations, properties, etc., and thereof roles, are. The first part of the paper details how these primitives are defined and used within the theory. In a second part, we focus on the formalization of the role primitive. A review of significant role properties leads to the specification of a role profile and most of the remaining work details through numerous examples, how the proposed theory is able to fully satisfy this profile. It is demonstrated that dependent types can model several non-trivial aspects of roles including a formal solution for generalization hierarchies, identity criteria for roles and other contributions. A discussion is given on how the theory is able to cope with many of the constraints inherent in a good role representation. (shrink)

Due to extensive product differentiation and the personalized aesthetic needs of consumers, modern enterprises need different expressions of information to attract consumers’ interest and improve their purchase intention. This study draws from the elaboration likelihood model, anchoring theory, and media richness theory to explore how the expression of advertised information can be effectively matched to the product type to enhance consumers’ purchase intention. The mediating effect of information-processing fluency and moderating effect of consumers’ personal involvement on this relationship (...) is also explored. Data from experiments and questionnaires involving 1,292 participants were analyzed. The results show that direct expression of advertised information is more suitable for advertising search products, while metaphorical expressions of advertised information are more suitable for advertising experience products. These combinations of product type and expression of advertised information can effectively improve consumers’ purchase intention. Meanwhile, the main combined effect of the product type and expression of advertised information is mediated by consumers’ information-processing fluency, and moderated by consumers’ personal involvement positively. (shrink)

It is often said that in a purely formal perspective, intuitionistic logic has no obvious advantage to deal with the liar-type paradoxes. In this paper, we will argue that the standard intuitionistic natural deduction systems are vulnerable to the liar-type paradoxes in the sense that the acceptance of the liar-type sentences results in inference to absurdity (⊥). The result shows that the restriction of the Double Negation Elimination (DNE) fails to block the inference to ⊥. It is, (...) however, not the problem of the intuitionistic approaches to the liar-type paradoxes but the lack of expressive power of the standard intuitionistic natural deduction system. We introduce a meta-level negation for a given system and a meta-level absurdity, ⋏, to the intuitionistic system. We shall show that in the system, the inference to ⊥ is not given without the assumption that the system is complete. Moreover, we consider the Double Meta-Level Negation Elimination rules (DMNE) which implicitly assume the completeness of the system. Then, the restriction of DMNE can rule out the inference to ⊥. (shrink)

John Searle's Speech Acts made a highly original contribution to work in the philosophy of language. Expression and Meaning is a direct successor, concerned to develop and refine the account presented in Searle's earlier work, and to extend its application to other modes of discourse such as metaphor, fiction, reference, and indirect speech arts. Searle also presents a rational taxonomy of types of speech acts and explores the relation between the meanings of sentences and the contexts of their utterance. The (...) book points forward to a larger theme implicit in these problems - the basis certain features of speech have in the intentionality of mind, and even more generally, the relation of the philosophy of language to the philosophy of mind. (shrink)

A BSTRACT. We present Property Theory with Curry Typing, an intensional first-order logic for natural language semantics. PTCT permits fine-grained specifications of meaning. It also supports polymorphic types and separation types.1 We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like most. We use the type system and our treatment of generalized quantifiers in natural language to construct a typetheoretic approach to pronominal anaphora that avoids some of the difficulties that undermine previous (...) class='Hi'>type-theoretic analyses of this phenomenon. (shrink)

John Searle's Speech Acts made a highly original contribution to work in the philosophy of language. Expression and Meaning is a direct successor, concerned to develop and refine the account presented in Searle's earlier work, and to extend its application to other modes of discourse such as metaphor, fiction, reference, and indirect speech arts. Searle also presents a rational taxonomy of types of speech acts and explores the relation between the meanings of sentences and the contexts of their utterance. The (...) book points forward to a larger theme implicit in these problems - the basis certain features of speech have in the intentionality of mind, and even more generally, the relation of the philosophy of language to the philosophy of mind. (shrink)

This article explores the importance of mental expression in understanding the phenomenon of inner speech. Most accounts of inner speech assume from the outset the common idea that the expressions of a subject (e.g., a smile) and their mental states (e.g., joy) are two different types of items somehow related to each other. This relational view of expression is challenged in this article. Firstly, it is argued that relational views of expression cannot explain some features of inner speech. Secondly, (...) a non-relational view of expression is developed, according to which mental states are patterns of expressive behavior. Thirdly, it is argued that only from the framework of non-relational expressivism is it possible to explain the main features of inner speech. Finally, it is concluded that non-relational expressivism emerges as a prominent contender among contemporary views of the mind, as it provides the only account of inner speech that can fully explain the phenomenon. (shrink)

This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates (...) proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification. (shrink)

Mendler, N.P., Inductive types and type constraints in the second-order lambda calculus, Annals of Pure and Applied Logic 51 159–172. We add to the second-order lambda calculus the type constructors μ and ν, which give the least and greatest solutions to positively defined type expressions. Strong normalizability of typed terms is shown using Girard's candidat de réductibilité method. Using the same structure built for that proof, we prove a necessary and sufficient condition for determining when a (...) collection of equational type constraints admit the typing of only strongly normalizable terms. (shrink)

In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be extremely useful in the practice of interactive theorem proving, whereby users interact with a computational proof assistant to constructformal axiomatic derivations of mathematical theorems. This article explains some of the mechanisms for type inference used by the "Mathematical Components" project, (...) which is working towards a verification of the Feit-Thompson theorem. (shrink)

The spreading of COVID-19 misinformation on social media could have severe consequences on people's behavior. In this paper, we investigated the emotional expression of misinformation related to the COVID-19 crisis on Twitter and whether emotional valence differed depending on the type of misinformation. We collected 17,463,220 English tweets with 76 COVID-19-related hashtags for March 2020. Using Google Fact Check Explorer API we identified 226 unique COVID-19 false stories for March 2020. These were clustered into six types of misinformation. Applying (...) the 226 classifiers to the Twitter sample we identified 690,004 tweets. Instead of running the sentiment on all tweets we manually coded a random subset of 100 tweets for each classifier to increase the validity, reducing the dataset to 2,097 tweets. We found that only a minor part of the entire dataset was related to misinformation. Also, misinformation in general does not lean towards a certain emotional valence. However, looking at comparisons of emotional valence for different types of misinformation uncovered that misinformation related to “virus” and “conspiracy” had a more negative valence than “cures,” “vaccine,” “politics,” and “other.” Knowing from existing studies that negative misinformation spreads faster, this demonstrates that filtering for misinformation type is fruitful and indicates that a focus on “virus” and “conspiracy” could be one strategy in combating misinformation. As emotional contexts affect misinformation spreading, the knowledge about emotional valence for different types of misinformation will help to better understand the spreading and consequences of misinformation. (shrink)

In this paper I will argue that there is an inductive and a non-inductive argument from position to know, and will characterise the latter as an argument from authority because of providing content-independent reasons. I will also argue that both types of argument should be doubt-preserving: testimony cannot justify a stronger cognitive attitude in the arguer than the expert herself expresses when she testifies. Failure to appreciate this point undercuts Mizrahi’s claim that arguments from expert opinion are weak.

The paper is a critical discussion of the rich and insightful final chapter of Mitchell Green’s Self-Expression . There, Green seeks to elucidate the compelling, but inchoate intuition that when we’re fully and most expertly expressing ourselves, we can ‘push out’ from within not just our inner representations, but also the ways that we feel. I question, first, whether this type of ‘qualitative expression’ is really distinct from the other expressive forms that Green explores, and also whether it’s genuinely (...) ‘expressive’. I then scrutinize the nature of the ‘qualitative congruences’ that lie at the heart of Green’s theory; and I wonder whether they can play the role Green claims they can in providing a novel account of artistic expression. (shrink)

Ordinarily when someone tells us something about her beliefs, desires or intentions, we presume she is right. According to standard views, this deferential trust is justified on the basis of certain epistemic properties of her assertion. In this paper, I offer a non-epistemic account of deference. I first motivate the account by noting two asymmetries between the kind of deference we show psychological self-ascriptions and the kind we grant to epistemic experts more generally. I then propose a novel agency-based account (...) of deference. Drawing on recent work on self-knowledge, I argue that a person normally has a distinctive type of cognitive agency; specifically she is able to constitute her psychological attitudes by making judgments about what they ought to be. I then argue that a speaker expresses this agentive authority when she self-ascribes a psychological attitude and this is what justifies deferentially trusting what she says. Because the notion of expression plays a central role in this account, I contrast it with recent neo-expressivist theories. (shrink)

It’s generally assumed that a compositional semantic theory will have to recognise a semantic category of expressions which serve simply to pick out some one object: e-type expressions. Kripke’s views about names, Kaplan’s about indexicals and demonstratives, the standard Tarskian semantics for bound variables, Heim and Kratzer’s Strawsonian view about definites, even an analysis of indefinites, assume as much. In this thesis, I argue that recent advances in the semantics of names and of quotation, and in metaphysics, (...) give good reason to doubt there is such a category. I do so in two parts. In the first part, comprising about two thirds of the thesis, I combine two recent views, one from semantics and one from metaphysics. From semantics, I take over predicativism about names, the view, as one might have guessed, that names are predicates. From metaphysics, I take over the doctrine that there are temporal parts. Putting them together, I hold that the semantic contribution of the name ’Joan’, in a sentence like ’Joan is a barrister’, is a predicate, and in particular a predicate the extension of which is Joan’s temporal parts. Names are not, as is commonly thought, e-type expressions. In the second part, building on the first, I further undermine the existence of a semantically important category of e-type expressions by arguing that a construction which might be thought to mandate such a category, namely de re attitude ascriptions, in fact, when properly analysed, does not do so. I argue this by considering the nature of transparent occurrences of expressions in opaque contexts in general, and in particular by considering the phenomenon of mixed quotation. I present a new theory of it, and show how it can be parlayed into a new Fregean theory of de re attitude ascriptions. The thesis overall, then, will provide strong evidence against the semantic importance of e-type expressions either in language, or in thought. (shrink)

In my dissertation, I explore how emotions operate under conditions of injustice. Specifically, my interest is in how one should deploy their emotions in order to combat patriarchally informed, affective ways of making sense of and responding to the social world. My dissertation consists of the following three papers. In the first paper, “Vindictive Anger,” I argue for two claims. First, that anger is not necessarily made morally worse whenever and to the extent that it involves a desire for payback. (...) Second, that in certain cases, anger’s retributive component is precisely what moralizes the emotion. Victims of sexual violence, I argue, paradigmatically deploy their anger as a way of getting their transgressor or, in some cases, the broader moral community, to more fully understand, through affect, the wrongness of their action. One can see this occur in the anger expressed by Chanel Miller in her victim’s impact statement, read aloud during the case of People v. Turner. When anger functions in this way, I propose, it serves to moralize the emotion. In the second paper, titled “Feminism and Suspect Femininity,” I ask how feminists should feel towards women who conform to suspect norms of appearance, and of hyper-femininity in particular. I present a novel type of empathy – proleptic empathy – which avoids treating women as either pitiful victims or as accomplices deserving of harsh moral criticism. Proleptic empathy requires switching back and forth between two types of imaginings: on the one hand, simulating what it is like to be in the woman’s shoes on the assumption that her suspect behavior stems from her will. On the other, simulating what it is like to be in the woman’s shoes on the assumption that her suspect behavior stems from external cultural influences. In the third paper, “Transitional Moral Contexts,” I address how one should feel towards the perpetrators who figure in the cases that have gone by the language of ‘grey rape’ or ‘bad sex’. These cases are ones that are rife with disagreement, especially amongst members of the moral community, who even disagree over whether they ought to count as cases of ‘sexual assault’ or ‘rape’. My suggestion is that the reason we have such difficulty adjudicating individuals’ responsibility for cases of bad sex is because these are instances of transitional moral contexts where what it is to act morally is in the process of being actively negotiated by the moral community. With this analysis in place, I present reasons for and against deploying shame against those who falter in these cases. (shrink)

This chapter analyzes how Wittgenstein explicitly addresses the possibility of distinguishing between word types, and not only in the form of presentation of examples. Wittgenstein might be using the terms “kind of word” and “part of speech” in a quite unusual way. The author focuses on just one language, thus no longer being concerned with the possibility of developing diverse new languages without limit. It is not surprising that in the natural languages very many more word types than did “the (...) logicians,” above all Frege, Russell, and the Wittgenstein of the Tractatus, particularly if one does not limit one's interest in language to the expression of a “judgeable content.”. Wittgenstein hints that the classification of words or sentences by their ways of usage on one hand and by their belonging to different types on the other, is a result of two different standpoints on the classification of elements of language. (shrink)

We formulate a Curry-typed logic with fine-grained intensionality within Turner’s typed predicate logic. This allows for an elegant presentation of a theory that corresponds to Fox and Lappin’s property theory with curry typing, but without the need for a federation of languages. We then consider how the fine-grained intensionality of this theory can be given an operational interpretation. This interpretation suggests itself as expressions in the theory can be viewed as terms in the untyped lambda-calculus, which provides a model (...) of computation. (shrink)

Following Yik and Russell (1999) a judgement paradigm was used to examine to what extent differential accuracy of recognition of facial expressions allows evaluation of the well-foundedness of different theoretical views on emotional expression. Observers judged photos showing facial expressions of seven emotions on the basis of: (1) discrete emotion categories; (2) social message types; (3) appraisal results; or (4) action tendencies, and rated their confidence in making choices. Emotion categories and appraisals were judged significantly more accurately and (...) confidently than messages or action tendencies. These results do not support claims of primacy for message or action tendency views of facial expression. Based on a componential model of emotion it is suggested that judges can infer components from categories and vice versa. (shrink)

The two books on which this study is based represent the two branches of linguistic philosophy. One an anthology, the other an original work, they differ also in kind. In Logic and Language A.G.N. Flew has collected and ably prefaced nine essays by British analysts, the earliest of which, Ryle's "Systematically Misleading Expressions," appeared exactly twenty years ago. Nelson Goodman's The Structure of Appearance is a new reconstruction; not to recognize its vigor and impressiveness would be most ungracious even (...) if one rejects as radically as I do this particular Aufbau. Naturally, I shall say more about Goodman's book than about the essays. Yet I shall begin with the latter and say about Ryle's as much as about all the rest together. To justify this strategy I must put my own cards on the table, indicating where I stand on this controversy or near controversy between formalists and antiformalists. To my mind, then, it is gray against gray, not white against black. Both sides agree, and I agree with them, that there is no experience or, if you please, no experiment that decides what is presumably at issue between phenomenalists and realists. In this important sense, both sides agree, and I agree with them, that all philosophical problems are verbal. But in another equally important sense they are not verbal. This sense both formalists and antiformalists have lost or stand in danger of losing if what they do is no better than what they say they do. Now for my reasons for singling out and starting off with the essay that marks Ryle's sober-eyed and reluctant conversion to the linguistic philosophy. It so happens that he there states very aptly a body of doctrine on which both sides could still agree and from which they in fact branched off at about the time the paper was first published. Also, the doubts and dissatisfactions to which he there confessed contain the starting points of the peculiar dialectics by which both formalists and antiformalists may be driven to extremes. Even better than that, I believe I can make use of these hesitancies to lend color to my own argument for a middle position which, as one is tempted to say on such occasions, does justice to both sides. That Ryle himself has in the meantime become a hero of the antiformalists is merely a piquant detail and does not deter me. (shrink)

Summary I outline an approach to the phenomenology of improvised music which takes typification and the development of multi‐ordered phenomenological structures as central. My approach here is firmly in line with classical Husserlian phenomenology, taking the discussion of types in Experience and Judgment (Husserl, 1973) and Brudzińska (2015) as guide. I provide a phenomenological analysis of musical types as they are found in improvisational contexts, focusing on jazz in the 20th century. Styles are higher‐order musical types. Musical types are structures (...) that are temporally “thick,” relying on sedimented typification and knowledge, driving expectations as definitional. In most forms of music (including improvised music), musical styles involve maintaining a balance between confirming expectations and flouting expectations. I show that improvised music has a phenomenal structure which is enriched by the communicative and “ real‐time” nature of improvised music. Improvised music can be seen as an exploration of a possibility space rendered by the juxtaposition of the musical types afforded by a performance environment (instrumentation, harmonic and melodic traditions, etc.). I show that improvisation in music is a multi‐vectoral form of communication. The communication is founded in what Dieter Lohmar calls “non‐linguistic thinking.” The expression is constituted in the results of active and synthesis. The culmination of improvisational exploration of possibility spaces is the precisification and enrichment of styles‐as‐types, while in some cases developing new styles in the process. (shrink)

We present diverse evidence for the claim of Pullum and Rawlins (2007) that expressives behave differently from descriptives in constructions that enforce a particular kind of semantic identity between elements. Our data are drawn from a wide variety of languages and construction types, and they point uniformly to a basic linguistic distinction between descriptive content and expressive content (Kaplan 1999; Potts 2007).

It is plausible to think that our knowledge of linguistic types can bejustified by what we know about the tokens of these types. But one then hasto explain what it is about the relation a type bears to its tokens that makespossible the move from knowledge of the concrete to knowledge of theabstract. I argue that the standard solution to this difficulty, that the relevant relation is instantiation and that the transition is inductive generalization, is inadequate. I propose an (...) alternative, according to which tokens are representations of the type they belong to. I also defend this view against the charge that it cannot account for the systematic ambiguity of expressions like ‘word’ or ‘sentence’, and the objection that it leads to an implausible form of Platonism. (shrink)

We show that basic hybridization (adding nominals and @ operators) makes it possible to give straightforward Henkin-style completeness proofs even when the modal logic being hybridized is higher-order. The key ideas are to add nominals as expressions of type t, and to extend to arbitrary types the way we interpret $@_i$ in propositional and first-order hybrid logic. This means: interpret $@_i\alpha _a$ , where $\alpha _a$ is an expression of any type $a$ , as an expression of (...) type $a$ that rigidly returns the value that $\alpha_a$ receives at the i-world. The axiomatization and completeness proofs are generalizations of those found in propositional and first-order hybrid logic, and (as is usual inhybrid logic) we automatically obtain a wide range of completeness results for stronger logics and languages. Our approach is deliberately low-tech. We don’t, for example, make use of Montague’s intensional type s, or Fitting-style intensional models; we build, as simply as we can, hybrid logicover Henkin’s logic. (shrink)

This article argues that what Grice termed ‘particularized conversational implicatures’ can be divided into two types. In some cases, it is possible to reconstruct the inference from the explicit content of the utterance to the implicature without employing a premise to the effect that that the speaker expressed that content (by means of an utterance). I call these ‘material implicatures’. Those whose reconstruction relies on a premise about the speaker's verbal behaviour, by contrast, I call ‘behavioural implicatures’. After showing that (...) the division is theoretically significant, I ask whether current pragmatic theory is able to accommodate it. I conclude that, while (neo)-Gricean pragmatics cannot do so straightforwardly, the distinction is already implicit in Relevance Theory. The article ends by considering the question of whether, in the light of previous discussion, speaker meaning really is always an instance of non-natural meaning. (shrink)

Corcoran, John. 2005. Meanings of word: type-occurrence-token. Bulletin of Symbolic Logic 11(2005) 117. -/- Once we are aware of the various senses of ‘word’, we realize that self-referential statements use ambiguous sentences. If a statement is made using the sentence ‘this is a pronoun’, is the speaker referring to an interpreted string, a string-type, a string-occurrence, a string-token, or what? The listeners can wonder “this what?”. -/- John Corcoran, Meanings of word: type-occurrence-token Philosophy, University at Buffalo, Buffalo, (...) NY 14260-4150 E-mail: [email protected] The four-letter written-English expression ‘word’, which plays important roles in applications and expositions of logic and philosophy of logic, is ambiguous (multisense, or polysemic) in that it has multiple normal meanings (senses, or definitions). Several of its meanings are vague (imprecise, or indefinite) in that they admit of borderline (marginal, or fringe) cases. This paper juxtaposes, distinguishes, and analyses several senses of ‘word’ focusing on a constellation of senses analogous to constellations of senses of other expression words such as ‘expression’, ‘symbol’, ‘character’, ‘letter’, ‘term’, ‘phrase’, ‘formula’, ‘sentence’, ‘derivation’, ‘paragraph’, and ‘discourse’. Consider, e.g., the word ‘letter’. In one sense there are exactly twenty-six letters (letter-types or ideal letters) in the English alphabet and there are exactly four letters in the word ‘letter’. In another sense, there are exactly six letters (letter-repetitions or letter-occurrences) in the word-type ‘letter’. In yet another sense, every new inscription (act of writing or printing) of ‘letter’ brings into existence six new letters (letter-tokens or ink-letters) and one new word that had not previously existed. The number of letter-occurrences (occurrences of a letter-type) in a given word-type is the same as the number of letter-tokens (tokens of a letter-type) in a single token of the given word. Many logicians fail to distinguish “token” from “occurrence” and a few actually confuse the two concepts. Epistemological and ontological problems concerning word-types, word-occurrences, and word-tokens are described in philosophically neutral terms. This paper presents a theoretical framework of concepts and principles concerning logicography, including use of English in logic. The framework is applied to analytical exposition and critical evaluation of classic passages in the works of philosophers and logicians including Boole, Peirce, Frege, Russell, Tarski, Church and Quine. This paper is intended as a philosophical sequel to Corcoran et al. “String Theory”, Journal of Symbolic Logic 39(1974) 625-637. https://www.academia.edu/s/cdfa6c854e?source=link -/- . (shrink)

Church’s type theory, aka simple type theory, is a formal logical language which includes classical first-order and propositional logic, but is more expressive in a practical sense. It is used, with some modifications and enhancements, in most modern applications of type theory. It is particularly well suited to the formalization of mathematics and other disciplines and to specifying and verifying hardware and software. It also plays an important role in the study of the formal semantics of natural (...) language. When utilizing it as a meta-logic to semantically embed expressive non-classical logics further topical applications are enabled in artificial intelligence and philosophy. A great wealth of technical knowledge can be expressed very naturally in it. With possible enhancements, Church’s type theory constitutes an excellent formal language for representing the knowledge in automated information systems, sophisticated automated reasoning systems, systems for verifying the correctness of mathematical proofs, and a range of projects involving logic and artificial intelligence. Some examples and further references are given in Sections 1.2.2 and 5 below. Type theories are also called higher-order logics, since they allow quantification not only over individual variables, but also over function, predicate, and even higher order variables. Type theories characteristically assign types to entities, distinguishing, for example, between numbers, sets of numbers, functions from numbers to sets of numbers, and sets of such functions. As illustrated in Section 1.2.2 below, these distinctions allow one to discuss the conceptually rich world of sets and functions without encountering the paradoxes of naive set theory. Church’s type theory is a formulation of type theory that was introduced by Alonzo Church in Church 1940. In certain respects, it is simpler and more general than the type theory introduced by Bertrand Russell in Russell 1908 and Whitehead & Russell 1927a. Since properties and relations can be regarded as functions from entities to truth values, the concept of a function is taken as primitive in Church’s type theory, and the λ-notation which Church introduced in Church 1932 and Church 1941 is incorporated into the formal language. Moreover, quantifiers and description operators are introduced in a way so that additional binding mechanisms can be avoided, λ-notation is reused instead. λ-notation is thus the only binding mechanism employed in Church’s type theory. (shrink)

Understanding a work of representational art involves more than simply grasping what it represents. We can distinguish at least three types of content that representational works may possess. First, all representational works have explicit representational content. This includes the literal content of a linguistic work and the depictive content of a pictorial work. Second, they often have a conveyed content, which outstrips their explicit representational content, including much that is merely implicit in the work, and may exclude certain aspects of (...) explicit representational content, as when explicit representational content is used for nonliteral forms of representation such as irony, metaphor, symbolism, or allegory. It is part of the conveyed content of Bruegel's The Fall of Icarus (c. 1560) that Icarus has just fallen from the sky, although the landscape does not depict his fall. (shrink)