In this paper non-normal worlds semantics is presented as a basic, general, and unifying approach to epistemic logic. The semantical framework of non-normal worlds is compared to the model theories of several logics for knowledge and belief that were recently developed in Artificial Intelligence (AI). It is shown that every model for implicit and explicit belief (Levesque), for awareness, general awareness, and local reasoning (Fagin and Halpern), and for awareness and principles (van der Hoek and Meyer) induces a non-normal worlds (...) model validating precisely the same formulas (of the language in question). (shrink)

The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds (...) of linguistic context in a fully compositional and anti-contextual way. (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)

This paper offers a defense against the primary objection to the view that goodness and other value properties give normative reasons, which is T. M. Scanlon’s influential redundancy argument. Scanlon reasons that value properties cannot add anything over and above what non-evaluative properties contribute. I suggest this line of reasoning is analogous to Jaegwon Kim’s causal exclusion argument against non-reductive physicalism, and adapt Ned Block’s objection to exclusion—a generalization and regress argument—into a reason for rejecting Scanlon’s argument. Differences between reasons (...) and causes make Scanlon’s task more difficult than Kim’s. (shrink)

The paper develops a proof-theoretic semantics for belief reports by extending the constructive type-theoretical formalism presented in Więckowski with a specific kind of set-forming operator suited for the representation of belief attitudes. The extended formalism allows us to interpret constructions which involve, e.g., iteration of belief, quantifying into belief contexts, and anaphora in belief reports. Moreover, constructive solutions to canonical instances of the problem of hyperintensionality are suggested. The paper includes a discussion of Ranta’s constructive account of belief reports.

We construct a a system PLRI which is the classical propositional logic supplied with a ternary construction , interpreted as the intensional identity of statements and in the context . PLRI is a refinement of Roman Suszko’s sentential calculus with identity (SCI) whose identity connective is a binary one. We provide a Hilbert-style axiomatization of this logic and prove its soundness and completeness with respect to some algebraic models. We also show that PLRI can be used to give a partial (...) solution to the paradox of analysis. (shrink)

A world is trivial if it makes every proposition true all at once. Such a world is impossible, an absurdity. Our world, we hope, is not an absurdity. It is important, nevertheless, for semantic and metaphysical theories that we be able to reason cogently about absurdities—if only to see that they are absurd. In this note we describe methods for ‘observing’ absurd objects like the trivial world without falling in to incoherence, using some basic techniques from modal logic. The goal (...) is to begin to locate the trivial world’s relative position in modal space; the outcome is that the less we assume about relative possibility, the more detail we can discern at the edge of reason. (shrink)

My chief aim has been to convey the thought that the application of model theoretic techniques to natural languages needn't force a distortion of intentional phenomena. I hope that at least I have succeeded in accomplishing this.

In this paper, we present a new semantic framework designed to capture a distinctly cognitive or epistemic notion of meaning akin to Fregean senses. Traditional Carnapian intensions are too coarse-grained for this purpose: they fail to draw semantic distinctions between sentences that, from a Fregean perspective, differ in meaning. This has led some philosophers to introduce more fine-grained hyperintensions that allow us to draw semantic distinctions among co-intensional sentences. But the hyperintensional strategy has a flip-side: it risks drawing semantic distinctions (...) between sentences that, from a Fregean perspective, do not differ in meaning. This is what we call the ‘new problem’ of hyperintensionality to distinguish it from the ‘old problem’ that faced the intensional theory. We show that our semantic framework offers a joint solution to both these problems by virtue of satisfying a version of Frege’s so-called ‘equipollence principle’ for sense individuation. Frege’s principle, we argue, not only captures the semantic intuitions that give rise to the old and the new problem of hyperintensionality, but also points the way to an independently motivated solution to both problems. (shrink)

In this paper, we introduce a variant of second-order propositional modal logic interpreted on general (or Henkin) frames, \(SOPML^{\mathcal {H}}\), and present a decidable fragment of this logic, \(SOPML^{\mathcal {H}}_{dec}\), that preserves important expressive capabilities of \(SOPML^{\mathcal {H}}\). \(SOPML^{\mathcal {H}}_{dec}\) is defined as a _modal loosely guarded fragment_ of \(SOPML^{\mathcal {H}}\). We demonstrate the expressive power of \(SOPML^{\mathcal {H}}_{dec}\) using examples in which modal operators obtain (a) the epistemic interpretation, (b) the dynamic interpretation. \(SOPML^{\mathcal {H}}_{dec}\) partially satisfies the principle of (...) non-Fregean logic: two different _atomic_ propositions with the same truth value can have different contents. In \(SOPML^{\mathcal {H}}_{dec}\), we also define _relating connectives_ and show that the _weak Boethius’ Thesis_ built using these connectives is a valid formula of \(SOPML^{\mathcal {H}}_{dec}\). (shrink)

We introduce a general representation of unary hyperintensional modalities and study various hyperintensional modal logics based on the representation. It is shown that the major approaches to hyperintensionality known from the literature, that is state-based, syntactic and structuralist approaches, all correspond to special cases of the general framework. Completeness results pertaining to our hyperintensional modal logics are established.

Tarski characterized logical notions as invariant under permutations of the domain. The outcome, according to Tarski, is that our logic, which is commonly said to be a logic of extension rather than intension, is not even a logic of extension—it is a logic of cardinality. In this paper, I make this idea precise. We look at a scale inspired by Ruth Barcan Marcus of various levels of meaning: extensions, intensions and hyperintensions. On this scale, the lower the level of meaning, (...) the more coarse-grained and less “intensional” it is. I propose to extend this scale to accommodate a level of meaning appropriate for logic. Thus, below the level of extension, we will have a more coarse-grained level of form. I employ a semantic conception of form, adopted from Sher, where forms are features of things “in the world”. Each expression in the language embodies a form, and by the definition we give, forms will be invariant under permutations and thus Tarskian logical notions. I then define the logical terms of a language as those terms whose extension can be determined by their form. Logicality will be shown to be a lower level analogue of rigidity. Using Barcan Marcus’s principles of explicit and implicit extensionality, we are able to characterize purely logical languages as “sub-extensional”, namely, as concerned only with form, and we thus obtain a wider perspective on both logicality and extensionality. (shrink)

A hyperintensional semantics for natural language is proposed which is agnostic about the question of whether propositions are sets of worlds or worlds are sets of propositions. Montague’s theory of intensional senses is replaced by a weaker theory, written in standard classical higher-order logic, of fine-grained senses which are in a many-to-one correspondence with intensions; Montague’s theory can then be recovered from the proposed theory by identifying the type of propositions with the type of sets of worlds and adding an (...) axiom to the effect that each world is the set of propositions which are true there. Senses are compositionally assigned to linguistic expressions by a categorial grammar with only two rule schemas, based on the implicative fragment of intuitionistic linear propositional logic, and a fully explicit grammar fragment is provided that illustrates the compositional assignment of sense to a variety of constructions, including dummy-subject constructions, infinitive complements, predicative adjectives and nominals, raising to subject, ‘tough-movement’, and quantifier scope ambiguities. Notably, the grammar and the derivations that it licenses never make reference to either worlds or to the extensions of senses. (shrink)

Self-reference has played a prominent role in the development of metamathematics in the past century, starting with Gödel’s first incompleteness theorem. Given the nature of this and other results in the area, the informal understanding of self-reference in arithmetic has sufficed so far. Recently, however, it has been argued that for other related issues in metamathematics and philosophical logic a precise notion of self-reference and, more generally, reference is actually required. These notions have been so far elusive and are surrounded (...) by an aura of scepticism that has kept most philosophers away. In this paper I suggest we shouldn’t give up all hope. First, I introduce the reader to these issues. Second, I discuss the conditions a good notion of reference in arithmetic must satisfy. Accordingly, I then introduce adequate notions of reference for the language of first-order arithmetic, which I show to be fruitful for addressing the aforementioned issues in metamathematics. (shrink)

In this work, we illustrate applications of a semantic framework for non-congruential modal logic based on hyperintensional models. We start by discussing some philosophical ideas behind the approach; in particular, the difference between the set of possible worlds in which a formula is true (its intension) and the semantic content of a formula (its hyperintension), which is captured in a rigorous way in hyperintensional models. Next, we rigorously specify the approach and provide a fundamental completeness theorem. Moreover, we analyse examples (...) of non-congruential systems that can be semantically characterized within this framework in an elegant and modular way. Finally, we compare the proposed framework with some alternatives available in the literature. In the light of the results obtained, we argue that hyperintensional models constitute a basic, general and unifying semantic framework for (non-congruential) modal logic. (shrink)

We compare the logic HYPE recently suggested by H. Leitgeb as a basic propositional logic to deal with hyperintensional contexts and Heyting-Ockham logic introduced in the course of studying logical aspects of the well-founded semantics for logic programs with negation. The semantics of Heyting-Ockham logic makes use of the so-called Routley star negation. It is shown how the Routley star negation can be obtained from Dimiter Vakarelov’s theory of negation and that propositional HYPE coincides with the logic characterized by the (...) class of all involutive Routley star information frames. This result provides a much simplified semantics for HYPE and also a simplified axiomatization, which shows that HYPE is identical with the modal symmetric propositional calculus introduced by G. Moisil in 1942. Moreover, it is shown that HYPE can be faithfully embedded into a normal bi-modal logic based on classical logic. Against this background, we discuss the notion of hyperintensionality. (shrink)

Should objects count as necessarily having certain properties, despite their not having those properties when they do not exist? For example, should a cat that passes out of existence, and so no longer is a cat, nonetheless count as necessarily being a cat? In this essay I examine different ways of adapting Aldo Bressan’s MLν so that it can accommodate an affirmative answer to these questions. Anil Gupta, in The Logic of Common Nouns, creates a number of languages that have (...) a kinship with Bressan’s MLν , three of which are also tailored to affirmatively answering these questions. After comparing their languages, I argue that metaphysicians and philosophers of language should prefer MLν to Gupta’s languages in most applications because it can accommodate essential properties, like being a cat, while being more uniform and less cumbersome. (shrink)

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

In this paper, I take up three tasks in turn. The first is to set out what Routley thought we should demand of an all-purpose universal logic, and some of his reasons for those demands. The second is to sketch Routley's own response to those demands. The third is to explore how else we could satisfy some of the theoretical demands Routley identified, if we are not to follow him in endorsing Routleyan Ultralogic as a foundational logic. As part of (...) this third project, I articulate what seems to me a preferable way of going to respond to the challenges Routley correctly identifies: and while I doubt what I will have to say would have convinced Routley himself, I will try to show that the approach I prefer has several advantages over Routley's. (shrink)

In the last few decades of the twentieth century there was a revolution in metaphysics: the intensional revolution. Many metaphysicians rejected the doctrine, associated with Quine and Davidson, that extensional analyses and theoretical resources were the only acceptable ones. Metaphysicians embraced tools like modal and counterfactual analyses, claims of modal and counterfactual dependence, and entities such as possible worlds and intensionally individuated properties and relations. The twenty-first century is seeing a hypterintensional revolution. Theoretical tools in common use carve more finely (...) than by necessary equivalence: two pieces of language can apply to the same entities across all possible worlds but not be equivalent; thoughts can be necessarily equivalent in truth value but not synonymous. This paper argues that hyperintensional resources are valuable in metaphysics outside theories of representation, and discusses some promising areas of hyperintensional metaphysics. (shrink)

After introducing Millianism and touching on two problems raised by genuinely empty names for Millianism (section I), I provide a brief exposition of the Gappy Proposition View (GPV) and of how different versions of this view can reply to the problems in question (section II). In the following sections I develop my reasons against the GPV. First, I will try to argue that apparently promising arguments for the claim that gappy propositions are propositions are not successful (section III). Then, I (...) will develop two arguments against GPs via demonstrating two odd consequences of the GPV: (a) that there can be an atomic proposition which contains other propositions that are not the semantic contents of any part of the .. (shrink)

A mathematical model in science can be formulated as a counterfactual conditional, with the model’s assumptions in the antecedent and its predictions in the consequent. Interestingly, some of these models appear to have assumptions that are metaphysically impossible. Consider models in ecology that use differential equations to track the dynamics of some population of organisms. For the math to work, the model must assume that population size is a continuous quantity, despite that many organisms are necessarily discrete. This means our (...) counterfactual representation of the model can have an impossible antecedent, giving us a counterpossible. Analogous counterpossibles arise in other sciences, as we’ll see. According to a prominent view in counterfactual semantics, the vacuity thesis, all counterpossibles are vacuously true, that is, true merely because their antecedents are necessarily false. But some counterpossible formulations of differential equation models in science are not all vacuously true—some are non-vacuously true, and some are false. I go on to show how an alternative semantics, one that employs impossible worlds, can deliver this judgment. (shrink)

To talk about simple concepts presupposes that the notion of concept has been aptly explicated. I argue that a most adequate explication should abandon the set-theoretical paradigm and use a procedural approach. Such a procedural approach is offered by Tichý´s Transparent Intensional Logic (TIL). Some main notions and principles of TIL are briefly presented, and as a result, concepts are explicated as a kind of abstract procedure. Then it can be shown that simplicity, as applied to concepts, is well definable (...) as a property relative to conceptual systems, each of which is determined by a finite set of simple (‘primitive’) concepts. Refinement as a method of replacing simple concepts by compound concepts is defined. (shrink)

The author defends the view that the notion of concept, if used in the logical tradition, should be explicated procedurally . He argues that Tichý’s Transparent Intensional Logic is an apt tool for such an explication and derives the respective definition. Some consequences of this definition concern the notions of emptiness, simple concepts, empirical concepts and algorithmic concepts.

If concepts are explicated as abstract procedures, then we can easily show that each empirical concept is a not an effective procedure. Some, but not all empirical concepts are shown to be of a special kind: they cannot in principle guarantee that the object they identify satisfies the intended conditions.

R. Suszko’s Sentential Calculus with Identity \( SCI \) results from classical propositional calculus \( CPC \) by adding a new connective \(\equiv \) and axioms for identity \(\varphi \equiv \psi \) (which we interpret here as ‘propositional identity’). We reformulate the original semantics of \( SCI \) using Boolean prealgebras which, introduced in different ways, are known in the literature as structures for the modeling of (hyper-) intensional semantics. We regard intensionality here as a measure for the discernibility of (...) propositions (and hyperintensionality as a high degree of intensionality). As concrete examples of \( SCI \) -based intensional modeling, we review and study algebraic semantics of some Lewis-style modal logics in the vicinity of \( S3 \) and present conditions under which those modal systems can be restored, in a precise sense, as certain axiomatic extensions of \( SCI \). This generalizes work of Suszko which is focused on the modal systems \( S4 \) and \( S5 \). Our approach is particularly intended as a proposal to consider and to further study \( SCI \) (and its extensions) as a general framework for the modeling of (hyper-) intensional semantics. (shrink)

This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the (...) predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE’s logical connectives. Furthermore, HYPE’s first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to follow-up work. (shrink)

Among philosophers, Fregeanism and sententialism are widely considered two of the leading theories of the semantics of attitude reports. Among linguists, these approaches have received little recent sustained discussion. This paper aims to bridge this divide. I present a new formal implementation of Fregeanism and sententialism, with the goal of showing that these theories can be developed in sufficient detail and concreteness to be serious competitors to the theories which are more popular among semanticists. I develop a modern treatment of (...) quantifying in for Fregeanism and sententialism, in the style of Heim and Kratzer, and then show how these theories can—somewhat surprisingly—account for “third readings” on the model of the “Standard Solution” from possible-worlds semantics. The resulting Fregean/sententialist proposal has a distinctive attraction: it treats data related to counterfactual attitudes —which have proven challenging to accommodate in the setting of possible worlds semantics—straightforwardly as third readings. (shrink)

This paper is about the most important technical problem faced by Structured Meanings Semantics: the reiteration of hyperintensional functors (i.e., functors of -categorial languages of the sort defined by Max Cresswell in [6]). A way to solve this problem in a general and natural way by using Scott's Domains is both suggested and shown. The result is a semantics which unrestrictedly allows reiterations of hyperintensional functors. The semantics is also extended to accommodate -categorial languages with variables.

We present a series of proof systems for exact entailment (i.e. relevant truthmaker preservation from premises to conclusion) and prove soundness and completeness. Using the proof systems, we observe that exact entailment is not only hyperintensional in the sense of Cresswell but also in the sense recently proposed by Odintsov and Wansing.

This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that (...) the theory is a proof-theoretically conservative extension of the theory PT of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground. (shrink)

A response to certain parts of Rumfitt : I defend Davidson's project in semantics, suggest that Rumfitt's use of sentential quantification renders his definition of truth needlessly elaborate, and pose a question for Rumfitt's handling of the strengthened Liar.

Logical semantics includes once again structured meanings in its repertoire. The leading idea is that semantic and syntactic structure are more or less isomorphic. A key motive for reintroducing sensitivity to semantic structure is to obtain fine‐grained meanings, which are individuated more finely than in possible‐world semantics, namely up to necessary equivalence. Just getting the truth‐conditions right is deemed insufficient for a full semantic analysis of sentences. This paper surveys some of the most recent contributions to the program of structured (...) meaning, while providing historical background. I suggest that to make substantial advances the program needs to solve the problem of propositional unity and develop an intensional mereology of abstract objects. (shrink)

The topic of this special issue of Synthese is hyperintensionality. This introduction offers a brief survey of the very notion of hyperintensionality followed by a summary of each of the papers in this collection. The papers are foundational studies of hyperintensionality accompanied by ample philosophical applications.Hyperintensionality concerns the individuation of non-extensional entities such as propositions and properties, relations-in-intension and individual roles, as well as, for instance, proofs and judgments and computational procedures, in case these do not reduce to any of (...) the former. Hyperintensional individuation is frequently also referred to as ‘fine-grained’ or sometimes simply ‘intensional’ individuation, when ‘intensional’ is not understood in the specific sense of possible-world semantics or in the pejorative sense of flouting various logical rules of extensional logic. A principle of individuation qualifies as hyperintensional as soon as it is finer than necessary .. (shrink)

Impossible worlds are regarded with understandable suspicion by most philosophers. Here we are concerned with a modal argument which might seem to show that acknowledging their existence, or more particularly, the existence of some hypothetical (we do not say “possible”) world in which everything was the case, would have drastic effects, forcing us to conclude that everything is indeed the case—and not just in the hypothesized world in question. The argument is inspired by a metaphysical (rather than modal-logical) argument of (...) Paul Kabay’s which would have us accept this unpalatable conclusion, though its details bear a closer resemblance to a line of thought developed by Jc Beall, in response to which Graham Priest has made some philosophical moves which are echoed in our diagnosis of what goes wrong with the present modal argument. Logical points of some interest independent of the main issue arise along the way. (shrink)

After putting forward a formal account of value disagreement via imprecise measures, I develop a logic of value attribution and of agreement based on truthmaker semantics.

In this paper I argue that deontic modals are hyperintensional, i.e. logically equivalent contents cannot be substituted in their scope. I give two arguments, one deductive and the other abductive. First, I show that the contrary thesis leads to falsity; second, I argue that a hyperintensional theory of deontic modals fares better than its rivals in terms of elegance, theoretical simplicity and explanatory power. I then propose a philosophical analysis of this thesis and outline some consequences. In Section 1 I (...) introduce and define deontic modality and hyperintensionality. In Section 2 I give a reductio for the hyperintensionality of deontic modals. If the argument is sound, a useful corollary is that deontic modals are also non-intensional, and therefore possible-world semantics accounts are illfitted for them. I then show how the main result can be strengthened or weakened by varying the definition of logical validity. In Section 3 I give an abductive argument for the hyperintensionality of deontic modals, arguing that with a single move we are able to solve many paradoxes and puzzles traditionally troubling deontic logic. I present a version of a hyperintensional deontic logic in an appendix, which I prove is sound and complete with respect to a version of truthmaker semantics. (shrink)

Co-hyperintensionality, or hyperintensional equivalence, is a relation holding between two or more contents that can be substituted in a hyperintensional context salva veritate. I argue that two strategies used to provide criteria for co-hyperintensionality fail. I argue that there is no generalized notion of co-hyperintensionality that meets plausible desiderata, by showing that the opposite thesis leads to falsity. As a conclusion, I suggest to take co-hyperintensionality as a primitive and I provide a general criterion of co-hyperintensionality whose content depends on (...) each hyperintensional notion we aim to formalize. (shrink)

In this paper we argue that normative reasons are hyperintensional and put forward a formal account of this thesis. That reasons are hyperintensional means that a reason for a proposition does not imply that it is also a reason for a logically equivalent proposition. In the first part we consider three arguments for the hyperintensionality of reasons: an argument from the nature of reasons, an argument from substitutivity and an argument from explanatory power. In the second part we describe a (...) hyperintensional logic of reasons based on justification logics. Eventually we discuss the philosophical import of this proposal and highlight some limitations and possible developments. (shrink)

The goal of this paper is a philosophical explication and logical rectification of the notion of concept. We take into account only those contexts that are relevant from the logical point of view. It means that we are not interested in contexts characteristic of cognitive sciences, particularly of psychology, where concepts are conceived of as some kind of mental objects or representations. After a brief recapitulation of various theories of concept, in particular Frege’s and Church’s ones, we propose our own (...) theory based on procedural semantics of Transparent Intensional Logic (TIL) and explicate concept in terms of the key notion of TIL, namely construction viewed as an abstract, algorithmically structured procedure. (shrink)

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