Possible-worlds accounts of mental or linguistic content are often criticized for being too coarse-grained. To make room for more fine-grained distinctions among contents, several authors have recently proposed extending the space of possible worlds by "impossible worlds". We argue that this strategy comes with serious costs: we would effectively have to abandon most of the features that make the possible-worlds framework attractive. More generally, we argue that while there are intuitive and theoretical considerations against overly coarse-grained notions of content, the (...) same kinds of considerations also prohibit an overly fine-grained individuation of content. An adequate notion of content, it seems, should have intermediate granularity. However, it is hard to construe a notion of content that meets these demands. Any notion of content, we suggest, must be either implausibly coarse-grained or implausibly fine-grained (or both). (shrink)

Bertrand Russell offered an influential paradox of propositions in Appendix B of The Principles of Mathematics, but there is little agreement as to what to conclude from it. We suggest that Russell's paradox is best regarded as a limitative result on propositional granularity. Some propositions are, on pain of contradiction, unable to discriminate between classes with different members: whatever they predicate of one, they predicate of the other. When accepted, this remarkable fact should cast some doubt upon some (...) of the uses to which modern descendente of Russell's paradox of propositions have been put in recent literature. (shrink)

Soames's cognitive propositions are strings of acts to be performed by an agent, such as predicating a property of an individual. King takes these structured propositions to task for proliferating too easily. King's objection is based on an example that purports to show that three of Soames's propositions are really just one proposition. I translate the informally stated propositions King attributes to Soames into the intensional λ-calculus. It turns out that they are all β-equivalent to the proposition King claims Soames's (...) three propositions are identical to. I argue on philosophical grounds against identifying β-equivalent propositions. The reason is that β-conversion obliterates too many of the procedural distinctions that are central to an act-based theory such as Soames's and which are worth preserving. In fact, β-expansion allows the addition of a fifth proposition that highlights additional procedural distinctions and propositional structure. The welcome conclusion is that we have five procedurally distinct, if equivalent, propositions. (shrink)

In this paper I present a new theory of propositions, according to which propositions are abstract mathematical objects: well-formed formulas together with models. I distinguish the theory from a number of existing views and explain some of its advantages  chief amongst which are the following. On this view, propositions are unified and intrinsically truth-bearing. They are mind- and language-independent and they are governed by logic. The theory of propositions is ontologically innocent. It makes room for an appropriate interface with (...) formal semantics and it does not enforce an overly fine or overly coarse level of granularity. (shrink)

Propositional attitude verbs, such as think and want, have long held interest for both theoretical linguists and language acquisitionists because their syntactic, semantic, and pragmatic properties display complex interactions that have proven difficult to fully capture from either perspective. This paper explores the granularity with which these verbs’ semantic and pragmatic properties are recoverable from their syntactic distributions, using three behavioral experiments aimed at explicitly quantifying the relationship between these two sets of properties. Experiment 1 gathers a measure (...) of 30 propositional attitude verbs’ syntactic distributions using an acceptability judgment task. Experiments 2a and 2b gather measures of semantic similarity between those same verbs using a generalized semantic discrimination task and an ordinal scale task, respectively. Two kinds of analyses are conducted on the data from these experiments. The first compares both the acceptability judgments and the semantic similarity judgments to previous classifications derived from the syntax and semantics literature. The second kind compares the acceptability judgments to the semantic similarity judgments directly. Through these comparisons, we show that there is quite fine-grained information about propositional attitude verbs’ semantics carried in their syntactic distributions—whether one considers the sorts of discrete qualitative classifications that linguists traditionally work with or the sorts of continuous quantitative classifications that can be derived experimentally. (shrink)

This paper deals with two issues. First, it identifies structured propositions with logical procedures. Second, it considers various rigorous definitions of the granularity of procedures, hence also of structured propositions, and comes out in favour of one of them. As for the first point, structured propositions are explicated as algorithmically structured procedures. I show that these procedures are structured wholes that are assigned to expressions as their meanings, and their constituents are sub-procedures occurring in executed mode. Moreover, procedures are (...) not mere aggregates of their parts; rather, procedural constituents mutually interact. As for the second point, there is no universal criterion of the structural isomorphism of meanings, hence of co-hyperintensionality, hence of synonymy for every kind of language. The positive result I present is an ordered set of rigorously defined criteria of fine-grained individuation in terms of the structure of procedures. Hence procedural semantics provides a solution to the problem of the granularity of co-hyperintensionality. (shrink)

Relations computed by finite-state transducers are applied to interpret temporal propositions in terms of strings representing finite contexts or situations. Carnap–Montague intensions mapping indices to extensions are reformulated as relations between strings that can serve as indices and extensions alike. Strings are related according to information content, temporal span and granularity, the bounds on which reflect the partiality of natural language statements. That partiality shapes not only strings-as-extensions (indicating what statements are about) but also strings-as-indices (underlying truth conditions).

This is the first comprehensive textbook on higher order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages -- their model theory and proof theory, the theory of λ-abstraction and its generalizations -- and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making it more appropriate for foundational metaphysics (...) than other introductions to the subject from computer science, mathematics, and linguistics. A Philosophical Introduction to Higher Order Logics assumes only that readers have a basic knowledge of first-order logic. With an emphasis on exercises, it can be used as a textbook though is also ideal for self-study. Author Andrew Bacon organizes the book's 18 chapters around four main parts: I. Typed Language II. Higher Order Languages III. General Higher-Order Languages IV. Higher-Order Model Theory In addition, two appendices cover the Curry-Howard isomorphism and its applications for modeling propositional structure. Each chapter includes exercises that move from easier to more difficult, strategically placed throughout the chapter, and concludes with an annotated suggested reading list providing graduate students with most valuable additional resources. Key Features Is the first comprehensive introduction to higher-order logic as a grounding for addressing problems in metaphysics Introduces the basic formal tools that are needed to theorize in, and model, higher order languages Offers an abundance of: - Simple exercises throughout the book, serving as comprehension checks on basic concepts and definitions - More difficult exercises designed to facilitate long-term learning Contains annotated sections on further reading, pointing the reader to related literature, learning resources, and historical context. (shrink)

Some propositions are true, and it is true that some propositions are true. Each of these facts looks like an impeccable ground of the other. But they cannot both ground each other, since grounding is asymmetric. This paper explores two new diagnoses of this much discussed puzzle. The tools of higher-order logic are used to show how both diagnoses can be fleshed out into strong and consistent theories of grounding. These theories of grounding in turn demand new theories of the (...) granularity of propositions, properties, and relations. Even those who are uninterested in grounding should take seriously these pictures of reality’s logical structure, which are in many ways reminiscent of Russell’s and Wittgenstein’s logical atomism. (shrink)

This three-part chapter explores a higher-order logic we call ‘Classicism’, which extends a minimal classical higher-order logic with further axioms which guarantee that provable coextensiveness is sufficient for identity. The first part presents several different ways of axiomatizing this theory and makes the case for its naturalness. The second part discusses two kinds of extensions of Classicism: some which take the view in the direction of coarseness of grain (whose endpoint is the maximally coarse-grained view that coextensiveness is sufficient for (...) identity), and some which take the view in the direction of fineness of grain (whose endpoint is the maximally fine-grained theory containing all distinctness claims compatible with Classicism). The third part introduces some techniques for constructing models of Classicism, and uses them to prove the consistency of many of the extensions of Classicism introduced in the second part. (shrink)

Propositions are defined by abstraction from an equivalence relation on sentences. The equivalence is synonymy. The resulting view, Propositional Abstractionism, has roots in Frege’s work, and considerable advantages over competitors. The key to the advantages is that Propositional Abstractionism puts language first. Consequently, in metaphysics, granularity debates benefit from linguistic evidence; in logic, abstraction is a safeguard against higher-order paradoxes; in epistemology, questions of knowledge of propositions can be approached as questions about semantic competence. These benefits form (...) a package that make Propositional Abstractionism a compelling hypothesis. (shrink)

In explaining the notion of a fundamental property or relation, metaphysicians will often draw an analogy with languages. The fundamental properties and relations stand to reality as the primitive predicates and relations stand to a language: the smallest set of vocabulary God would need in order to write the “book of the world.” This paper attempts to make good on this metaphor. To that end, a modality is introduced that, put informally, stands to propositions as logical truth stands to sentences. (...) The resulting theory, formulated in higher-order logic, also vindicates the Humean idea that fundamental properties and relations are freely recombinable and a variant of the structural idea that propositions can be decomposed into their fundamental constituents via logical operations. Indeed, it is seen that, although these ideas are seemingly distinct, they are not independent, and fall out of a natural and general theory about the granularity of reality. (shrink)

An increasing amount of twenty-first century metaphysics is couched in explicitly hyperintensional terms. A prerequisite of hyperintensional metaphysics is that reality itself be hyperintensional: at the metaphysical level, propositions, properties, operators, and other elements of the type hierarchy, must be more fine-grained than functions from possible worlds to extensions. In this paper I develop, in the setting of type theory, a general framework for reasoning about the granularity of propositions and properties. The theory takes as primitive the notion of (...) a substitution on a proposition (property, etc.) and, among other things, uses this idea to elucidate a number of theoretically important distinctions. A class of structures are identified which can be used to model a wide range of positions about the granularity of reality; certain of these structures are seen to receive a natural treatment in the category of M-sets. (shrink)

We outline a novel theory of natural language meaning, Rich Situated Semantics [RSS], on which the content of sentential utterances is semantically rich and informationally situated. In virtue of its situatedness, an utterance’s rich situated content varies with the informational situation of the cognitive agent interpreting the utterance. In virtue of its richness, this content contains information beyond the utterance’s lexically encoded information. The agent-dependence of rich situated content solves a number of problems in semantics and the philosophy of language (...) (cf. [14, 20, 25]). In particular, since RSS varies the granularity of utterance contents with the interpreting agent’s informational situation, it solves the problem of finding suitably fine- or coarse-grained objects for the content of propositional attitudes. In virtue of this variation, a layman will reason with more propositions than an expert. (shrink)

The aim of the article is to intervene in debates about the digital and, in particular, framings that imagine the digital in terms of epochal shifts or as redefining life. Instead, drawing on recent developments in digital methods, we explore the lively, productive and performative qualities of the digital by attending to the specificities of digital devices and how they interact, and sometimes compete, with older devices and their capacity to mobilize and materialize social and other relations. In doing so, (...) our aim is to explore the implications of digital devices and data for reassembling social science methods or what we call the social science apparatuses that assemble digital devices and data to ‘know’ the social and other relations. Building on recent work at CRESC on the social life of methods, we recommend a genealogical approach that is alive to the ways in which digital devices are simultaneously shaped by social worlds, and can in turn become agents that shape those worlds. This calls for attending to the specificities of digital devices themselves, how they are varied and composed of diverse socio-technical arrangements, and are enrolled in the creation of new knowledge spaces, institutions and actors. Rather than exploring what large-scale changes can be revealed and understood through the digital, we argue for explorations of how digital devices themselves are materially implicated in the production and performance of contemporary sociality. To that end we offer the following nine propositions about the implications of digital data and devices and argue that these demand rethinking the theoretical assumptions of social science methods: transactional actors; heterogeneity; visualization; continuous time; whole populations; granularity; expertise; mobile and mobilizing; and non-coherence. (shrink)

In coal mining industry, the running state of mine ventilators plays an extremely significant role for the safe and reliable operation of various industrial productions. To guarantee the better reliability, safety, and economy of mine ventilators, in view of early detection and effective fault diagnosis of mechanical faults which could prevent unscheduled downtime and minimize maintenance fees, it is imperative to construct some viable mathematical models for mine ventilator fault diagnosis. In this article, we plan to establish a data-based mine (...) ventilator fault diagnosis method to handle situations where engineers are absent or they are incapable of coming to a conclusion from multisource data. In the process of building the mine ventilator fault diagnosis model, considering that probabilistic rough sets could reduce the errors triggered by incompleteness, inconsistency, and inaccuracy without needing any additional assumptions and Pythagorean fuzzy multigranulation rough sets over the two universes’ model could effectively handle data representation, fusion, and analysis issues, we generalize the existing PF MGRSs over the two universes’ model to the PRS setting, as well as to further establish a novel model named Pythagorean fuzzy multigranulation probabilistic rough sets over two universes. In the granular computing paradigm, three types of PF MG-PRSs over two universes based on the risk attitude of engineers are proposed at first. Afterwards, several basic propositions of the newly proposed model are explored. Moreover, a PF multigranulation probabilistic model for mine ventilator fault diagnosis based on PF MG-PRSs over two universes is investigated. At last, a real-world case study of dealing with a mine ventilator fault diagnosis problem is given to illustrate the practicality of the presented model, and a validity test, a sensitivity analysis, and a comparison analysis are further explored to demonstrate the effectiveness of the presented model. (shrink)

The theory of rough sets starts with the notion of an approximation space , which is a pair ( U , R ), U being the domain of discourse, and R an equivalence relation on U . R is taken to represent the knowledge base of an agent, and the induced partition reflects a granularity of U that is the result of a lack of complete information about the objects in U . The focus then is on approximations of (...) concepts on the domain, in the context of the granularity. The present article studies the theory in the situation where information is obtained from different sources. The notion of approximation space is extended to define a multiple-source approximation system with distributed knowledge base , which is a tuple , where N is a set of sources and P ranges over all finite subsets of N . Each R P is an equivalence relation on U satisfying some additional conditions, representing the knowledge base of the group P of sources. Thus each finite group of sources and hence individual source perceives the same domain differently (depending on what information the group/individual source has about the domain), and the same concept may then have approximations that differ with the groups. In order to express the notions and properties related with rough set theory in this multiple-source situation, a quantified modal logic LMSAS D is proposed. In LMSAS D , quantification ranges over modalities, making it different from modal predicate logic and modal logic with propositional quantifiers. Some fragments of LMSAS D are discussed and it is shown that the modal system KTB is embedded in LMSAS D . The epistemic logic is also embedded in LMSAS D , and cannot replace the latter to serve our purpose. The relationship of LMSAS D with first and second-order logics is presented. Issues of expressibility, axiomatization and decidability are addressed. (shrink)

This dissertation lays the foundation for a new theory of non-relational intentionality. The thesis is divided into an introduction and three main chapters, each of which serves as an essential part of an overarching argument. The argument yields, as its conclusion, a new account of how language and thought can exhibit intentionality intrinsically, so that representation can occur in the absence of some thing that is represented. The overarching argument has two components: first, that intentionality can be profi tably studied (...) through examination of the semantics of intensional transitive verbs (ITVs), and second, that providing intensional transitive verbs with a nonrelational semantics will serve to provide us with (at least the beginnings of) a non-relational theory of intentionality. This approach is a generalization of Anscombe's views on perception. Anscombe held that perceptual verbs such as "see" and "perceive" were ITVs, and that understanding the semantics of their object positions could help us to solve the problems of hallucination and illusion, and provide a theory of perception more generally. I propose to apply this strategy to intentional states and the puzzles of intentionality more generally, and so Anscombe's influence will be felt all through the dissertation. -/- In the first chapter, titled "Semantic Verbs are Intensional Transitives", I argue that semantic verbs such as "refers to", "applies to", and "is true of" have all of the features of intensional transitive verbs, and discuss the consequences of this claim for semantic theory and the philosophy of language. One theoretically enriching consequence of this view is that it allows us to perspicuously express, and partially reconcile two opposing views on the nature and subject-matter of semantics: the Chomskian view, on which semantics is an internalistic enterprise concerning speakers' psychologies, and the Lewisian view, on which semantics is a fully externalistic enterprise issuing in theorems about how the world must look for our natural language sentences to be true. Intensional Transitive Verbs have two readings: a de dicto reading and a de re reading; the de dicto reading of ITVs is plausibly a nonrelational reading, and the intensional features peculiar to this reading make it suitable for expressing a Chomskian, internalist semantic program. On the other hand, the de re reading is fully relational, and make it suitable for expressing the kinds of word-world relations essential to the Lewisian conception of semantics. And since the de dicto and de re readings are plausibly related as two distinct scopal readings of the very same semantic postulates, we can see these two conceptions of semantics as related by two scopal readings of the very same semantic postulates. -/- In chapter two, titled "Hallucination and the New Problem of Empty Names", I argue that the problem of hallucination and the problem of empty names are, at bottom, the same problem. I argue for this by reconstructing the problem of empty names in way that is novel, but implicit in much of the discussion on empty names. I then show how, once recast in this light, the two problems are structurally identical down to an extremely fine level of granularity, and also substantially overlap in terms of their content. If the problems are identical in the way I propose, then we should expect that their spaces of solutions are also identical, and there is signi cant support for this conclusion. However, there are some proposed solutions to the problem of hallucination that have been overlooked as potential solutions to the problem of empty names, and this realization opens new non-relational approaches to the problem of empty names, and to the nature of meaning more generally. -/- In chapter three, titled "Intensionality is Additional Phrasal Unity", I argue for a novel approach to the semantics of intensional contexts. At the heart of my proposal is the Quinean view that intensional contexts should, from the perspective of the semantics, be treated as units, with the material in them contributing to the formation of a single predicate. However, this proposal is subject to a number of objections, including the criticism that taken at face value, this would render intensional contexts, which seem to be fully productive, non-compositional. I begin by discussing the concept of the unity of the phrase, and pointing to various ways that phrases can gain additional unity. I then proposes that the intensionality of intensional transitive verbs is best construed as a form of semantic incorporation; ITVs, on their intensional readings, meet all of the criteria for qualifying as incorporating the nominals in their object positions. I then give a semantics for ITVs that builds on existing views of the semantics of incorporation structures, and gesture at how this can be extended to intensional clausal verbs, including the so-called propositional attitude verbs. (shrink)

Logics of discrete time are, in Arthur Prior’s words, “applicable in limited fields of discourse in which we are concerned with what happens in a sequence of discrete states,” independent of “any serious metaphysical assumption that time is discrete.” This insight is applied to natural language semantics, a widespread assumption in which is that time is, as is the real line, dense. “Limited fields of discourse” are construed as finite sets of temporal propositions, inducing bounded notions of temporal granularity (...) that can be refined to expand the discourse. The construal is developed in line with Prior’s view of what is “metaphysically fundamental”. (shrink)

Finite-state methods are applied to the Russell-Wiener notion of time (based on events) and developed into an account of interval relations and temporal propositions. Strings are formed and collected in regular languages and regular relations that are argued to embody temporal relations in their various underspecified guises. The regular relations include retractions that reduce computations by projecting strings down to an appropriate level of granularity, and non-deterministic relations defining notions of partiality within and across such levels.

I take some initial steps toward a theory of real definition, drawing upon recent developments in higher-order logic. The resulting account allows for extremely fine- grained distinctions (i.e., it can distinguish between any relata that differ in their syntactic structure, while avoiding the Russell-Myhill problem). It is the first account that can consistently embrace three desirable logical principles that initially appear to be incompatible: the Identification Hypothesis (if F is, by definition, G then F is the same as G), Irreflexivity (...) (there are no reflexive definitions) and Leibniz’s Law. Additionally, it possesses the resources to resolve the paradox of analysis. (shrink)

Eliminative materialism is the thesis that our common-sense conception of psychological phenomena constitutes a radically false theory, a theory so fundamentally defective that both the principles and the ontology of that theory will eventually be displaced, rather than smoothly reduced, by completed neuroscience. Our mutual understanding and even our introspection may then be reconstituted within the conceptual framework of completed neuroscience, a theory we may expect to be more powerful by far than the common-sense psychology it displaces, and more substantially (...) integrated within physical science generally. My purpose in this paper is to explore these projections, especially as they bear on (1) the principal elements of common-sense psychology: the propositional attitudes (beliefs, desires, etc.), and (2) the conception of rationality in which these elements figure. (shrink)

It is widely agreed that perceptual experience is a form of intentionality, i.e., that it has representational content. Many philosophers take this to mean that like belief, experience has propositional content, that it can be true or false. I accept that perceptual experience has intentionality; but I dispute the claim that it has propositional content. This claim does not follow from the fact that experience is intentional, nor does it follow from the fact that experiences are accurate or (...) inaccurate. I end by considering the relationship between this question and the question of whether experience has non-conceptual content. (shrink)

A central theme in recent research on attitudes is the distinction between deliberate, "explicit" attitudes and automatic, "implicit" attitudes. The present article provides an integrative review of the available evidence on implicit and explicit attitude change that is guided by a distinction between associative and propositional processes. Whereas associative processes are characterized by mere activation independent of subjective truth or falsity, propositional reasoning is concerned with the validation of evaluations and beliefs. The proposed associative-propositional evaluation model makes (...) specific assumptions about the mutual interplay of the 2 processes, implying several mechanisms that lead to symmetric or asymmetric changes in implicit and explicit attitudes. The model integrates a broad range of empirical evidence and implies several new predictions for implicit and explicit attitude change. (shrink)

I argue against the orthodox view of the relationship between propositional and doxastic justification. The view under criticism is: if p is propositionally justified for S in virtue of S's having reason R, and S believes p on the basis of R, then S's belief that p is doxastically justified. I then propose and evaluate alternative accounts of the relationship between propositional and doxastic justification, and conclude that we should explain propositional justification in terms of doxastic justification. (...) If correct, this proposal would constitute a significant advance in our understanding of the sources of epistemic justification. (shrink)

Looking out the window, I see that it's raining outside. Do I know that it’s raining outside? According to proponents of the Entailment Thesis, I do. If I see that p, I know that p. In general, the Entailment Thesis is the thesis that if S perceives that p, S knows that p. But recently, some philosophers (McDowell 2002, Turri 2010, Pritchard 2011, 2012) have argued that the Entailment Thesis is false. On their view, we can see p and not (...) know that p. In this paper, I argue that their arguments are unsuccessful. (shrink)

This study introduces refutation-aware Gentzen-style sequent calculi and Kripke-style semantics for propositional until-free linear-time temporal logic. The sequent calculi and semantics are constructed on the basis of the refutation-aware setting for Nelson’s paraconsistent logic. The cut-elimination and completeness theorems for the proposed sequent calculi and semantics are proven.

The idea that sentences can be closer or further apart in meaning is highly intuitive. Not only that, it is also a pillar of logic, semantic theory and the philosophy of science, and follows from other commitments about similarity. The present paper proposes a novel way of comparing the ‘distance’ between two pairs of propositions. We define ‘\ is closer in meaning to \ than \ is to \’ and thereby give a precise account of comparative propositional similarity facts. (...) Notably, our definition eschews metric assumptions, which are unrealistic in most applications of interest. (shrink)

This paper presents a formalization of the classical proof of completeness in Henkin-style developed by Troelstra and van Dalen for intuitionistic logic with respect to Kripke models. The completeness proof incorporates their insights in a fresh and elegant manner that is better suited for mechanization. We discuss details of our implementation in the Lean theorem prover with emphasis on the prime extension lemma and construction of the canonical model. Our implementation is restricted to a system of intuitionistic propositional logic (...) with implication, conjunction, disjunction, and falsity given in terms of a Hilbert-style axiomatization. As far as we know, our implementation is the first verified Henkin-style proof of completeness for intuitionistic logic following Troelstra and van Dalen's method in the literature. (shrink)

(2013). Two aspects of propositional unity. Canadian Journal of Philosophy: Vol. 43, Essays on the Nature of Propositions, pp. 518-533.

Habitual actions have a history of practice and repetition that frees us from attending to what we are doing. Nevertheless, habitual actions seem to be intentional. What does account for the intentionality of habitual actions if they are automatically performed and controlled? In this paper, we address a possible response to a particular version of this issue, that is, the problem of understanding how the intention to execute a habitual action, which comes in a propositional format, interlocks with motor (...) representations, which come in a motoric-pragmatic format. In order to solve this issue, we propose an account according to which the propositional intentions and the motor representations related to our habitual actions interlock through executable action concepts. This allows us to maintain that habitual actions can be, at the same time, automatically initiated, performed, and controlled and, still, intentional. (shrink)

Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. This accounting is made possible by removing the ‘structural’ rules of contraction and weakening, adding a modal operator and adding finer versions of the propositional connectives. Linear logic has fundamental logical interest and applications to computer science, particularly to Petri nets, concurrency, storage allocation, garbage collection and the control structure of logic programs. In addition, there is a direct correspondence between polynomial-time (...) computation and proof normalization in a bounded form of linear logic. In this paper we show that unlike most other propositional logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes PSPACE-complete. We also establish membership in NP for the multiplicative fragment, NP-completeness for the multiplicative fragment extended with unrestricted weakening, and undecidability for fragments of noncommutative propositional linear logic. (shrink)

According to proponents of the face-value account, a beliefreport of the form ‘S believes that p’ is true just in case the agentbelieves a proposition referred to by the that-clause. As againstthis familiar view, I argue that there are cases of true beliefreports of the relevant form in which there is no proposition that thethat-clause, or the speaker using the that-clause, can plausibly betaken as referring to. Moreover, I argue that given the distinctiveway in which the face-value theory of belief-reports (...) fails, there ispressure to give up the metaphysical thesis that belief is apropositional attitude. I conclude by suggesting that we allownon-propositional entities to be amongst the relata of thebelief-relation, and make some speculative remarks concerning whatsuch entities might be like. (shrink)

In two of the earliest papers on extending modal logic with propositional quantifiers, R. A. Bull and K. Fine studied a modal logic S5Π extending S5 with axioms and rules for propositional quantification. Surprisingly, there seems to have been no proof in the literature of the completeness of S5Π with respect to its most natural algebraic semantics, with propositional quantifiers interpreted by meets and joins over all elements in a complete Boolean algebra. In this note, we give (...) such a proof. This result raises the question: For which normal modal logics. (shrink)

Determiner phrases embedded under a propositional attitude verb have traditionally been taken to denote answers to implicit questions. For example, 'the capital of Vermont' as it occurs in 'John knows the capital of Vermont' has been thought to denote the proposition which answers the implicit question 'what is the capital of Vermont?' Thus, where 'know' is treated as a propositional attitude verb rather than an acquaintance verb, 'John knows the capital of Vermont' is true iff John knows that (...) Montpelier is the capital of Vermont. The traditional view lost its popularity long ago, because it was thought to rest on the controversial assumption that determiner phases embedded under a propositional attitude verb function semantically in the same way as the corresponding wh-clauses. Here we defend the traditional assumption against objections. We then argue that wh-clauses are not to be given a uniform treatment as indirect questions. When occurring under a propositional attitude verb, wh-clauses are better treated as having a predicate-type semantic value. We conclude by considering some possible objections to the predicate view. (shrink)