It is shown that Gqp↑, the quantified propositional Gödel logic based on the truth-value set V↑ = {1 - 1/n : n≥1}∪{1}, is decidable. This result is obtained by reduction to Büchi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of Gqp↑ as the intersection of all finite-valued quantified propositional Gödel logics.

Propositionalism is the view that intentional attitudes, such as belief, are relations to propositions. Propositionalists argue that propositionalism follows from the intuitive validity of certain kinds of inferences involving attitude reports. Jubien (2001) argues powerfully against propositions and sketches some interesting positive proposals, based on Russell’s multiple relation theory of judgment, about how to accommodate “propositional phenomena” without appeal to propositions. This paper argues that none of Jubien’s proposals succeeds in accommodating an important range of propositional phenomena, such (...) as the aforementioned validity of attitude-report inferences. It then shows that the notion of a predication act-type, which remains importantly Russellian in spirit, is sufficient to explain the range of propositional phenomena in question, in particular the validity of attitude-report inferences. The paper concludes with a discussion of whether predication act-types are really just propositions by another name. (shrink)

This paper is the twin of (Duží and Jespersen, in submission), which provides a logical rule for transparent quantification into hyperprop- ositional contexts de dicto, as in: Mary believes that the Evening Star is a planet; therefore, there is a concept c such that Mary be- lieves that what c conceptualizes is a planet. Here we provide two logical rules for transparent quantification into hyperpropositional contexts de re. (As a by-product, we also offer rules for possible- world (...) class='Hi'>propositional contexts.) One rule validates this inference: Mary believes of the Evening Star that it is a planet; therefore, there is an x such that Mary believes of x that it is a planet. The other rule validates this inference: the Evening Star is such that it is believed by Mary to be a planet; therefore, there is an x such that x is believed by Mary to be a planet. Issues unique to the de re variant include partiality and existential presupposition, sub- stitutivity of co-referential (as opposed to co-denoting or synony- mous) terms, anaphora, and active vs. passive voice. The validity of quantifying-in presupposes an extensional logic of hyperinten- sions preserving transparency and compositionality in hyperinten- sional contexts. This requires raising the bar for what qualifies as co-denotation or equivalence in extensional contexts. Our logic is Tichý’s Transparent Intensional Logic. The syntax of TIL is the typed lambda calculus; its highly expressive semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The two non-standard features we need are a hyper- intension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hy- perintensions. (shrink)

Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like 'something' permit a replacement, preserving grammaticality or the same reading of the verb: (1) a. John claims that he won. b. ??? John claims a proposition / some thing. c. John claims something. In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements of various other (...) intensional predicates and argued for a Nominalization Theory of special quantifiers. In this paper, I will review and extend the range of linguistic generalizations that motivate the Nominalization Theory and show that they pose serious problems for higher-order and substitutional analyses of special quantifiers. (shrink)

Recent work in philosophy of language has raised significant problems for the traditional theory of propositions, engendering serious skepticism about its general workability. These problems are, I believe, tied to fundamental misconceptions about how the theory should be developed. The goal of this paper is to show how to develop the traditional theory in a way which solves the problems and puts this skepticism to rest. The problems fall into two groups. The first has to do with reductionism, specifically attempts (...) to reduce propositions to extensional entities-either extensional functions or sets. The second group concerns problems of fine grained content-both traditional 'Cicero'/'Tully' puzzles and recent variations on them which confront scientific essentialism. After characterizing the problems, I outline a non-reductionist approach-the algebraic approach-which avoids the problems associated with reductionism. I then go on to show how the theory can incorporate non-Platonic (as well as Platonic) modes of presentation. When these are implemented nondescriptively, they yield the sort of fine-grained distinctions which have been eluding us. The paper closes by applying the theory to a cluster of remaining puzzles, including a pair of new puzzles facing scientific essentialism. (shrink)

There are two broad approaches to theorizing about ontological categories. Quineans use first-order quantifiers to generalize over entities of each category, whereas type theorists use quantification on variables of different semantic types to generalize over different categories. Does anything of import turn on the difference between these approaches? If so, are there good reasons to go type-theoretic? I argue for positive answers to both questions concerning the category of propositions. I also discuss two prominent arguments for a Quinean conception (...) of propositions, concerning their role in natural language semantics and apparent quantification over propositions within natural language. It will emerge that even if these arguments are sound, there need be no deep question about Quinean propositions’ true nature, contrary to much recent work on the metaphysics of propositions. (shrink)

Relative to an ordinary context, an utterance of the sentence ‘Everything is in the car’ communicates a proposition about a restricted domain. But how does this work? One possibility is that quantifier expressions like 'everything' are context sensitive and range over different domains in different contexts. Another possibility is that quantifier expressions are not context sensitive, but have a fixed, absolutely general meaning, and ordinary utterances communicate a restricted content via Gricean mechanisms. I argue that, contrary to received opinion, the (...) latter view has both a number of methodological and also intuitive advantages over the former. I then reply to three objections to the latter view: the binding argument (due to Stanley and Szabo), the availability-based attack (due to Recanati), and an argument based on Recanati’s scope principle. (shrink)

This paper argues that the theory of structured propositions is not undermined by the Russell-Myhill paradox. I develop a theory of structured propositions in which the Russell-Myhill paradox doesn't arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the $\lambda$-calculus, about what properties and relations can be built. I argue that the structuralist had independent reasons to reject these underlying assumptions. The theory is given both a (...) diagrammatic representation, and a logical representation in a novel language. In the latter half of the paper I turn to some technical questions concerning the treatment of quantification, and demonstrate various equivalences between the diagrammatic and logical representations, and a fragment of the $\lambda$-calculus. (shrink)

[Edited from Conclusion section:] We have looked at various challenging issues to do with getting connectionism to cope with high-level cognitive activities such a reasoning and natural language understanding. The issues are to do with various facets of generalization that are not commonly noted. We have been concerned in particular with the special forms these issues take in the arena of propositional attitude processing. The main problems we have looked at are: (1) The need to construct explicit representations of (...) generalizations, not just generalize correctly to individual cases; (2) The need to be able to match two or more complex short-term information structures, to enable rapid generalization from recent examples rather than from long-term memories; (3) The need to represent and reason with anomalous combinations of concepts; (4) The need to perform embedded reasoning. This presents special problems for systems using non-concatenative representations (as in mainstream connectionist approaches). We also touched on vague quantification in attitude report complements. Neither this topic nor that of analogies between short-term structures (point 2) has been adequately addressed in the symbolic framework, let alone in connectionism. -/- The opportunities and problems covered are put forward as things worth being optimistic about or pessimistic about, respectively. They are not put forward as decisive arguments for or against connectionism. The hope is that this chapter contributes to a greater understanding of the connectionist/symbolist gap by presenting some unusual issues and by throwing new light on some well known ones. (shrink)

Jusqu'à maintenant, il semble qu'on n'ait pas établi de lien entre le rejet par Bolzano de la notation quantificationnelle des propositions universelles de la logique traditionnelle et l'articulation inédite de sa notion de validité universelle. C'est ce que je veux faire ici. En particulier, dans la mesure où l'analyticité est un cas spécial de la validité universelle, j'ai l'intention de défendre l'idée qui veut que la notion bolzanienne d'analyticité cherche à résoudre des problèmes qui sont intrinsèquement liés à la théorie (...) traditionnelle de la quantification universelle tels qu'ils surviennent, notamment avec le traitement kantien de l'analyticité. It seems that the connection between Bolzano's rejection of the traditional quantificational notation for universal propositions and the articulation of his notion of universal validity has remained, until today, perfectly unnoticed. In this paper, I will show that there is such a connection. Particularly, since analyticity is a special case of universal validity, my intention is to show that the problems to which Bolzano's perfectly original account of analyticity seeks to find an answer are intrinsically related to the traditional conception of universal quantification as it arises in the context of Kant's treatment of analyticity. (shrink)

Realists about possible worlds typically identify possible worlds with abstract objects, such as propositions or properties. However, they face a significant objection due to Lewis (1986), to the effect that there is no way to explain how possible worlds-as-abstract objects represent possibilities. In this paper, I describe a response to this objection on behalf of realists. The response is to identify possible worlds with propositions, but to deny that propositions are abstract objects, or indeed objects at all. Instead, I argue (...) that realists should follow Prior (1971) and others in treating higher-order quantification (e.g. quantification into predicate or sentence position) as a genuine form of quantification in its own right, and so in particular, not to be analysed in terms of first-order quantification over abstract objects. I argue that from this ‘higher-orderist’ perspective, there is a relatively straightforward answer to the question of how possible worlds-as-propositions succeed in representing possibilities. (shrink)

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

Subverting a once widely held Quinean paradigm, there is a growing consensus among philosophers of logic that higher-order quantifiers (which bind variables in the syntactic position of predicates and sentences) are a perfectly legitimate and useful instrument in the logico-philosophical toolbox, while neither being reducible to nor fully explicable in terms of first-order quantifiers (which bind variables in singular term position). This article discusses the impact of this quantificational paradigm shift on metaphysics, focussing on theories of properties, propositions, and identity, (...) as well as on the metaphysics of modality. (shrink)

I here argue for a particular formulation of truth-deflationism, namely, the propositionally quantified formula, (Q) “For all p, <p> is true iff p”. The main argument consists of an enumeration of the other (five) possible formulations and criticisms thereof. Notably, Horwich’s Minimal Theory is found objectionable in that it cannot be accepted by finite beings. Other formulations err in not providing non-questionbegging, sufficiently direct derivations of the T-schema instances. I end by defending (Q) against various objections. In particular, I argue (...) that certain circularity charges rest on mistaken assumptions about logic that lead to Carroll’s regress. I show how the propositional quantifier can be seen as on a par with first-order quantifiers and so equally acceptable to use. While the proposed parallelism between these quantifiers is controversial in general, deflationists have special reasons to affirm it. I further argue that the main three types of approach the truth-paradoxes are open to an adherent of (Q), and that the derivation of general facts about truth can be explained on its basis. (shrink)

Ramsification is a well-known method of defining theoretical terms that figures centrally in a wide range of debates in metaphysics. Prior's puzzle is the puzzle of why, given the assumption that that-clauses denote propositions, substitution of "the proposition that P" for "that P" within the complements of many propositional attitude verbs sometimes fails to preserve truth, and other times fails to preserve grammaticality. On the surface, Ramsification and Prior's puzzle appear to have little to do with each other. But (...) Prior's puzzle is much more general than is ordinarily appreciated, and Ramsification requires a solution to the generalized form of Prior's puzzle. Without such a solution, a wide range of theories will either fail to imply their Ramsey sentences, or have Ramsey sentences that are ill-formed. As a consequence, definitions of theoretical terms given using the Ramsey sentence will be either incorrect or nonsensical. I present a partial solution to the puzzle that requires making use of a neo-Davidsonian language for scientific theorizing, but the would-be Ramsifier still faces serious challenges. (shrink)

According to a prominent objection, deflationist theories of truth can’t account for the explanatory connection between true belief and successful action [Putnam 1978]. Canonical responses to the objection show how to reformulate truth-involving explanations of particular successful actions to omit any mention of truth [Horwich 1998]. According to recent critics, though, the canonical strategy misses the point. The deflated paraphrases lack the generality or explanatory robustness of the original explanatory appeals to truth [Kitcher 2002; Lynch 2009; Gamester 2018]. This article (...) diagnoses the canonical response’s failure and shows how deflationists can make sense of appeals to truth in explaining practical success, in all their generality and robustness, without construing truth as a substantial property. (shrink)

In this paper, we outline an approach to giving extensional truth-theoretic semantics for what have traditionally been seen as opaque sentential contexts. We outline an approach to providing a compositional truth-theoretic semantics for opaque contexts which does not require quantifying over intensional entities of any kind, and meets standard objections to such accounts. The account we present aims to meet the following desiderata on a semantic theory T for opaque contexts: (D1) T can be formulated in a first-order extensional language; (...) (D2) T does not require quantification over intensional entities­i.e., meanings, propositions, properties, relations, or the like­in its treatment of opaque contexts; (D3) T captures the entailment relations that hold in virtue of form between sentences in the language for which it is a theory; (D4) T has a finite number of axioms. If the approach outlined here is correct, it resolves a longstanding complex of problems in metaphysics, the philosophy of mind and the philosophy of language. (shrink)

This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order logics used in metaphysics, and indicate (...) a number of questions which can be raised in such systems using logical vocabulary alone. Using a further example, we return to applications of higher-order logics in metaphysics. We also mention key developments in the history of higher-order logic as it pertains to metaphysics. Finally, we mention certain arguments which have been raised against the use of higher-order logic, and some ways of responding to them. (shrink)

This paper addresses a certain objection to the quantificational theory of definite descriptions. According to this objection, the quantificational account cannot provide correct interpretations of definite descriptions embedded in the non-doxastic attitude ascriptions and therefore ought to be rejected. In brief, the objection says that the quantificational theory is committed to the view that a sentence of the form “The F is G” is equivalent to the claim that there is a unique F and it is G, while the ascription (...) such as, e.g., “S wants the F to be G” is not equivalent to the statement that S wants there to be a F and for it to be G. I argue that this objection is invalid as it rests on a false assumption concerning the substitutivity of the relative clauses in the non-doxastic attitude ascriptions. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

Certain commentators on Russell's “no class” theory, in which apparent reference to classes or sets is eliminated using higher-order quantification, including W. V. Quine and (recently) Scott Soames, have doubted its success, noting the obscurity of Russell’s understanding of so-called “propositional functions”. These critics allege that realist readings of propositional functions fail to avoid commitment to classes or sets (or something equally problematic), and that nominalist readings fail to meet the demands placed on classes by mathematics. I (...) show that Russell did thoroughly explore these issues, and had good reasons for rejecting accounts of propositional functions as extra-linguistic entities. I argue in favor of a reading taking propositional functions to be nothing over and above open formulas which addresses many such worries, and in particular, does not interpret Russell as reducing classes to language. (shrink)

This paper considers two reasons that might support Russell’s choice of a ramified-type theory over a simple-type theory. The first reason is the existence of purported paradoxes that can be formulated in any simple-type language, including an argument that Russell considered in 1903. These arguments depend on certain converse-compositional principles. When we take account of Russell’s doctrine that a propositional function is not a constituent of its values, these principles turn out to be too implausible to make these arguments (...) troubling. The second reason is conditional on a substitutional interpretation of quantification over types other than that of individuals. This reason stands up to investigation: a simple-type language will not sustain such an interpretation, but a ramified-type language will. And there is evidence that Russell was tacitly inclined towards such an interpretation. A strong construal of that interpretation opens a way to make sense of Russell’s simultaneous repudiation of propositions and his willingness to quantify over them. But that way runs into trouble with Russell’s commitment to the finitude of human understanding. (shrink)

Despite the wide acceptance of standard modal logic, there has always been a temptation to think that ordinary modal discourse may be correctly analyzed and adequately represented in terms of predicates rather than in terms of operators. The aim of the formal model outlined in this paper is to capture what I take to be the only plausible sense in which ‘possible’ and ‘necessary’ can be treated as predicates. The model is built by enriching the language of standard modal logic (...) with a quantificational apparatus that is “substitutional” rather than “objectual”, and by obtaining from the language so enriched another language in which constants for such predicates apply to singular terms that stand for propositions. (shrink)

The quantification theory of propositions in Russell’s Principles of Mathematics has been the subject of an intensive study and in reconstruction has been found to be complete with respect to analogs of the truths of modern quantification theory. A difficulty arises in the reconstruction, however, because it presents universally quantified exportations of five of Russell’s axioms. This paper investigates whether a formal system can be found that is more faithful to Russell’s original prose. Russell offers axioms that are (...) universally quantified implications that have antecedent clauses that are conjunctions. The presence of conjunctions as antecedent clauses seems to doom the theory from the onset, it will be found that there is no way to prove conjunctions so that, after universal instantiation, one can detach the needed antecedent clauses. Amalgamating two of Russell’s axioms, this paper overcomes the difficulty. (shrink)

The Operator Argument against eternalism holds that having non-vacuous tense operators in the language is incompatible with the claim that every proposition has its truth-value eternally. Assuming that (1) there are non-vacuous tense operators, (2) tense operators operate on propositions and (3) tense operators which operate on eternal entities are vacuous, it may be argued that eternalism is false. In this paper, I examine the Operator Argument. The goal is threefold. First, I want to present some aspects of the debate (...) in a more elaborate way, especially those concerning formal matters. Secondly, I will argue that eternalism can escape the Operator Argument. There are two main strategies for handling the Operator Argument. The first one is based on replacing temporal operators with object-language quantifiers. The second rejects the identification of compositional semantic value with assertoric content. My third goal is to show that none of them is as good as the strategy that adopts Timestamp Semantics (Fritz in Philosl Stud 176:2933–2959, 2019). I am going to argue that the quantificational treatment of tenses is compatible with temporalism and that the arguments for rejecting the identification of compositional semantic value with assertoric content provide, in fact, a motivation for the temporalist position. At the end, I will develop Timestamp Semantics by providing a novel formalization of it, and defend it against three potential counter-arguments. (shrink)

Why does Aristotle not use the copulative wording for categorical propositions, but instead the clumsier terminological formulations (e. g. the B belongs to every A) in his syllogistic? The proposed explanations by Alexander, Lukasiewicz and Patzig: Aristotle wants to make clear the difference between subject and predicate, seems to be insufficient. In quantified categorical propositions, this difference is always sufficiently clear by the use of the pronouns going with the subject expressions. Aristotle opts for the terminological wording because in premiss (...) pairs of figures two and three he can thus suppress the middle term in one of the premisses and connect the major and minor term, using connecting particles. This renders the syllogisms more transparent. Had he used the copulative wording instead, he would have run into difficulties, in particular with o-propositions among the premisses (i. e. in Baroco and Bocardo) because in these cases the pronoun expressing the quantification would have to go with the subject term, the negation with the predicate. (shrink)

When a proposition might be the case, for all an agent knows, we can say that the proposition is epistemically possible for the agent. In the standard possible worlds framework, we analyze modal claims using quantification over possible worlds. It is natural to expect that something similar can be done for modal claims involving epistemic possibility. The main aim of this paper is to investigate the prospects of constructing a space of worlds—epistemic space—that allows us to model what is (...) epistemically possible for ordinary, non-ideally rational agents like you and me. I will argue that the prospects look dim for successfully constructing such a space. In turn, this will make a case for the claim that we cannot use the standard possible worlds framework to model what is epistemically possible for ordinary agents. (shrink)

This work is compiled for the students, research scholars, academicians, who are interested in logic, philosophy, mathematics and critical thinking. The main objective of this book is to provide basics or fundamental knowledge for those who have chosen logic as their subject in order to develop analytical and critical ideas. It has been primarily developed to serve as an introductory piece of work which includes explanatory notes on different courses like Inductive logic, Deductive logic, propositional logic, Symbolic logic, (...) class='Hi'>Quantification logic, Modal logic and Critical thinking. Besides this, it also includes illustrations in decision making and scientific research methods in logic. This book is mainly devised to clear fundamental problems of logic. It contains eight chapters which are simply described and elaborated. (shrink)

Kit Fine has reawakened a puzzle about variables with a long history in analytic philosophy, labeling it “the antinomy of the variable”. Fine suggests that the antinomy demands a reconceptualization of the role of variables in mathematics, natural language semantics, and first-order logic. The difficulty arises because: (i) the variables ‘x’ and ‘y’ cannot be synonymous, since they make different contributions when they jointly occur within a sentence, but (ii) there is a strong temptation to say that distinct variables ‘x’ (...) and ‘y’ are synonymous, since sentences differing by the total, proper substitution of ‘x’ for ‘y’ always agree in meaning. We offer a precise interpretation of the challenge posed by (i) and (ii). We then develop some neglected passages of Tarski to show that his semantics for variables has the resources to resolve the antinomy without abandoning standard compositional semantics. (shrink)

The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails that \\) is (...) high but non-maximal and might \ that \\) is significantly greater than 0. Drawing on several observations concerning the behavior of must, might and similar epistemic operators in evidential contexts, deductive inferences, downplaying and retractions scenarios, and expressions of epistemic tension, I argue that those two influential accounts have systematic descriptive shortcomings. To better make sense of their complex behavior, I propose instead a broadly Kratzerian account according to which must \ entails that \ = 1\) and might \ that \ > 0\), given a body of evidence and a set of normality assumptions about the world. From this perspective, must and might are vehicles for expressing a common mode of reasoning whereby we draw inferences from specific bits of evidence against a rich set of background assumptions—some of which we represent as defeasible—which capture our general expectations about the world. I will show that the predictions of this Kratzerian account can be substantially refined once it is combined with a specific yet independently motivated ‘grammatical’ approach to the computation of scalar implicatures. Finally, I discuss some implications of these results for more general discussions concerning the empirical and theoretical motivation to adopt a probabilisitic semantic framework. (shrink)

I argue that taking the Practical Conditionals Thesis seriously demands a new understanding of the semantics of such conditionals. Practical Conditionals Thesis: A practical conditional [if A][ought] expresses B’s conditional preferability given A Paul Weirich has argued that the conditional utility of a state of affairs B on A is to be identified as the degree to which it is desired under indicative supposition that A. Similarly, exploiting the PCT, I will argue that the proper analysis of indicative practical conditionals (...) is in terms of what is planned, desired, or preferred, given suppositional changes to an agent’s information. Implementing such a conception of conditional preference in a semantic analysis of indicative practical conditionals turns out to be incompatible with any approach which treats the indicative conditional as expressing non-vacuous universal quantification over some domain of relevant antecedent-possibilities. Such analyses, I argue, encode a fundamental misunderstanding of what it is to be best, given some condition. The analysis that does the best vis-à-vis the PCT is, instead, one that blends a Context-Shifty account of indicative antecedents with an Expressivistic, or non-propositional, treatment of their practical consequents. (shrink)

Hybrid contingentism combines first-order contingentism, the view that it is contingent what individuals there are, with higher-order necessitism, the view that it is non-contingent what properties and propositions there are (where these are conceived as entities in the range of appropriate higher-order quantifiers). This combination of views avoids the most delicate problems afflicting alternative contingentist positions while preserving the central contingentist claim that ordinary, concrete entities exist contingently. Despite these attractive features, hybrid contingentism is usually faced with rejection. The main (...) reason for this is an objection that crucially involves haecceitistic properties, properties such as being identical to Plato or being identical to Aristotle. The objection alleges that by accepting the necessary existence of such haecceities, hybrid contingentists incur an explanatory commitment that they are unable to discharge, namely that of explaining how it is that certain haecceities ‘lock onto’ their target individuals even when those individuals are absent. To defend hybrid contingentism against this charge, I first clarify the haecceities objection in several respects and consider, in particular, what notion of explanation the objection is operating with. After arguing that it can be fruitfully understood as a challenge to provide metaphysical grounds for certain haecceity facts, I develop a contingentist response to the objection that draws on recent work on the connection between ground and essence. (shrink)

This article begins by distinguishing force and mood. Then it lays out desiderata on a successful account. It sketches as background the program of truth-theoretic semantics. Next, it surveys assimilation approaches and argues that they are inadequate. Then it shows how the fulfillment-conditional approach can be applied to imperatives, interrogatives, molecular sentences containing them, and quantification into mood markers. Next, it considers briefly the recent set of propositions approach to the semantics of interrogatives and exclamatives. Finally, it shows how (...) to integrate exclamatives and optatives into a framework similar to the fulfillment approach. (shrink)

This paper is about an underappreciated aspect of generics: their non-specificity. Many uses of generics, utterances like ‘Seagulls swoop down to steal food’, express non-specific generalisations which do not specify their quantificational force or flavour. I consider whether this non-specificity arises as a by-product of context-sensitivity or semantic incompleteness but argue instead that generics semantically express non-specific generalisations by default as a result of quantifying existentially over more specific ones.

In Frege’s Puzzle (1986), Salmon analyzed ‘a withholds believing p’ in terms of a ternary relation BEL of x believing a proposition p under a guise g. The proposed analysis is the following: There is a proposition guise g such that a grasps p by means of g but a does not stand in BEL to p and g. Sean Crawford has made a proposal for Millians to evade propositional guises through second-order belief. Specifically, in effect, Crawford’s proposes to (...) analyze the crucial notion of withheld belief instead as believing that one does not believe: a believes that a does not believe p. Crawford’s clever proposal thus avoids explicit quantification over guises. However, it is shown that the proposal is inadequate to avoid guises. The resulting notion is too weak to capture the relevant notion of withheld belief. (shrink)

I here develop a specific version of the deflationary theory of truth. I adopt a terminology on which deflationism holds that an exhaustive account of truth is given by the equivalence between truth-ascriptions and de-nominalised (or disquoted) sentences. An adequate truth-theory, it is argued, must be finite, non-circular, and give a unified account of all occurrences of “true”. I also argue that it must descriptively capture the ordinary meaning of “true”, which is plausibly taken to be unambiguous. Ch. 2 is (...) a critical historical survey of deflationary theories, where notably disquotationalism is found untenable as a descriptive theory of “true”. In Ch. 3, I aim to show that deflationism cannot be finitely and non-circularly formulated by using “true”, and so must only mention it. Hence, it must be a theory specifically about the word “true” (and its foreign counterparts). To capture the ordinary notion, the theory must thus be an empirical, use-theoretic, semantic account of “true”. The task of explaining facts about truth now becomes that of showing that various sentences containing “true” are (unconditionally) assertible. In Ch. 4, I defend the claim (D) that every sentence of the form “That p is true” and the corresponding “p” are intersubstitutable (in a use-theoretic sense), and show how this claim provides a unified and simple account of a wide variety of occurrences of “true”. Disquotationalism then only has the advantage of avoiding propositions. But in Ch. 5, I note that (D) is not committed to propositions. Use-theoretic semantics is then argued to serve nominalism better than truth-theoretic ditto. In particular, it can avoid propositions while sustaining a natural syntactic treatment of “that”-clauses as singular terms and of “Everything he says is true”, as any other quantification. Finally, Horwich’s problem of deriving universal truth-claims is given a solution by recourse to an assertibilist semantics of the universal quantifier. (shrink)

Presentists hold that only present things exist. But we all, presentists included, utter sentences that appear to involve quantification over non-present objects, and so we all, presentists included, seem to commit ourselves to such objects. Equally, we all, presentists included, take utterances of many past-tensed (and some future-tensed) sentences to be true. But if no past or future things exist, it’s hard to see how there can be anything that those utterances are about, which makes them true. This paper (...) presents a hitherto unexplored response to both problems: pretence fictionalism about the non-present. This view combines semantic factualism with psychological non-cognitivism. Sentences that appear to quantify over the non-present have propositional content and (almost all of) those propositions are false because the thing they are about—the non-present—does not exist. Nevertheless when we utter such sentences we don’t thereby utter something false. Our utterances do not report the belief that the propositional content of the sentence uttered is true; rather, they express a non-cognitive attitude towards that content: namely an attitude of pretence. Hence by thinking various thoughts, and uttering various sentences we are, collectively, pretending as though things were (or will be) thus and so. (shrink)

Kripke (1977) presents an argument designed to show that the considerations in Donnellan (1966) concerning attributive and referential uses of (definite) descriptions do not, by themselves, refute Russell’s (1905) unitary theory of description sentences (RTD), which takes (utterances of) them to express purely general, quantificational, propositions. Against Kripke, Marga Reimer (1998) argues that the two uses do indeed reflect a semantic ambiguity (an ambiguity at the level of literal truth conditions). She maintains a Russellian (quantificational) analysis of utterances involving attributively (...) used descriptions but attempts to defend the following two claims about utterances involving referentially used descriptions (referential utterances) (1998, p. 89). (shrink)

This paper develops and motivates an Expressivist theory of "experiential" talk and thought, focusing on speech acts and thoughts that contain taste predicates. According to this theory, one way for S to think that o tastes a way w is simply for o to taste w to S. When o tastes w to S (and, therefore, S thinks that o tastes w), S can express this thought, by saying that o tastes w. The speech act wherein S expresses the thought (...) that o tastes w, so understood, must be distinguished from the speech act wherein S says or asserts that S tastes w to them. This paper develops a formal model of these informal claims, and it argues that the resulting theory fits well with the linguistic data -- no worse than the best propositional theories when it comes to representing quantificational readings of attitude ascriptions, and strictly better than the best propositional theories when it comes to representing non-quantificational ("experiential") readings. (shrink)

In this paper I sketch some arguments that underlie Hegel's chapter on judgment, and I attempt to place them within a broad tradition in the history of logic. Focusing on his analysis of simple predicative assertions or ‘positive judgments’, I first argue that Hegel supplies an instructive alternative to the classical technique of existential quantification. The main advantage of his theory lies in his treatment of the ontological implications of judgments, implications that are inadequately captured by quantification. The (...) second concern of this paper is the manner in which Hegel makes logic not only dependent on ontology generally, but also variant in regard to domains of objects. In other words, he offers a domain-specific logical theory, according to which the form of judgment or inference is specific to the subject of judgment. My third concern lies with the metaphilosophical consequences of this theory, and this includes some more familiar Hegelian themes. It is well known that Hegel frequently questioned the adequacy of the sentential form for expressing higher order truths. My reading of his theory of predication explains and contextualizes this tendency by demystifying notions like the so-called speculative proposition. (shrink)

This essay aims to provide a modal logic for rational intuition. Similarly to treatments of the property of knowledge in epistemic logic, I argue that rational intuition can be codified by a modal operator governed by the modal $\mu$-calculus. Via correspondence results between fixed point modal propositional logic and the bisimulation-invariant fragment of monadic second-order logic, a precise translation can then be provided between the notion of 'intuition-of', i.e., the cognitive phenomenal properties of thoughts, and the modal operators regimenting (...) the notion of 'intuition-that'. I argue that intuition-that can further be shown to entrain conceptual elucidation, by way of figuring as a dynamic-interpretational modality which induces the reinterpretation of both domains of quantification and the intensions and hyperintensions of mathematical concepts that are formalizable in monadic first- and second-order formal languages. Hyperintensionality is countenanced via a topic-sensitive epistemic two-dimensional truthmaker semantics. (shrink)

Are there any things that are such that any things whatsoever are among them. I argue that there are not. My thesis follows from these three premises: (1) There are two or more things; (2) for any things, there is a unique thing that corresponds to those things; (3) for any two or more things, there are fewer of them than there are pluralities of them.

Indicative judgments pertain to what is true. Epistemic modal judgments pertain to what must or might be true relative to a body of information. A standard view is that epistemic modals implicitly quantify over alternative possibilities, or ways things could turn out. On this view, a proposition must be true just in case it is true in all the possibilities consistent with the available information, and a proposition might be true just in case it is true in at least one (...) possibility consistent with the available information. I report three experiments testing this view of epistemic modals. The results show that although modal judgments are sensitive to information about alternative possibilities, the standard quantification theory mischaracterizes the ordinary meaning of modals. I then report two more experiments testing the hypothesis that epistemic modals express willingness to attribute knowledge based on the available information. The results support this hypothesis. The results also show that the difference between “inside” and “outside” probabilistic information, familiar from the judgment and decision-making literature, affects epistemic modal judgments. (shrink)

This book is written for those who wish to learn some basic principles of formal logic but more importantly learn some easy methods to unpick arguments and assess their value for truth and validity. -/- The first section explains the ideas behind traditional logic which was formed well over two thousand years ago by the ancient Greeks. Terms such as ‘categorical syllogism’, ‘premise’, ‘deduction’ and ‘validity’ may appear at first sight to be inscrutable but will easily be understood with examples (...) bringing the subjects to life. Traditionally, Venn diagrams have been employed to test arguments. These are very useful but their application is limited and they are not open to quantification. The mid-section of this book introduces a methodology that makes the analysis of arguments accessible with the use of a new form of diagram, modified from those of the mathematician Leonhard Euler. These new diagrammatic methods will be employed to demonstrate an addition to the basic form of syllogism. This includes a refined definition of the terms ‘most’ and ‘some’ within propositions. This may seem a little obscure at the moment but one will readily apprehend these new methods and principles of a more modern logic. (shrink)

I explain why model theory is unsatisfactory as a semantic theory and has drawbacks as a tool for proofs on logic systems. I then motivate and develop an alternative, the truth-valuational substitutional approach (TVS), and prove with it the soundness and completeness of the first order Predicate Calculus with identity and of Modal Propositional Calculus. Modal logic is developed without recourse to possible worlds. Along the way I answer a variety of difficulties that have been raised against TVS and (...) show that, as applied to several central questions, model-theoretic semantics can be considered TVS in disguise. The conclusion is that the truth-valuational substitutional approach is an adequate tool for many of our logic inquiries, conceptually preferable over model-theoretic semantics. Another conclusion is that formal logic is independent of semantics, apart from its use of the notion of truth, but that even with respect to it its assumptions are minimal. (shrink)

Hossack's 'The Metaphysics of Knowledge' develops a theory of facts, entities in which universals are combined with universals or particulars, as the foundation of his metaphysics. While Hossack argues at length that there must be negative facts, facts in which the universal 'negation' is combined with universals or particulars, his conclusion that there are also general facts, facts in which the universal 'generality' is combined with universals, is reached rather more swiftly. In this paper I present Hossack with three arguments (...) for his conclusion. They all draw, as does Hossack's theory of facts, on views Russell expressed in various writings. Two arguments are based on Russell's explanation of universals as aspects of resemblance; the third on Russell's observation that general propositions do not follow logically from exclusively particular premises. Comparison with other metaphysics of generality show them to be wanting and Russell's and Hossack's accounts superior. (shrink)

The question whether natural language permits quantification over intentional objects as the ‘nonexistent’ objects of thought is the topic of a major philosophical controversy, as is the status of intentional objects as such. This paper will argue that natural language does reflect a particular notion of intentional object and in particular that certain types of natural language constructions (generally disregarded in the philosophical literature) cannot be analysed without positing intentional objects. At the same time, those intentional objects do not (...) come for free; rather they are strictly dependent on intentional acts that generally need to have a presence, in one way or another, in the semantic structure of the sentence. (shrink)

The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that in (...) order to specify the truth conditions of certain sentences involving constants or variables that don’t denote, one has to apparently quantify over things that are not identical to anything. In this paper I defend a contingentist, non-Meinongian metaphysics within a positive free logic. I argue that although certain names and free variables do not actually refer to anything, in each case there might have been something they actually refer to, allowing one to interpret the contingentist claims without quantifying over mere possibilia. (shrink)

This essay introduces a puzzle about the interaction between quantifiers and epistemic modals. The puzzle motivates the idea that whether an object satisfies an epistemically modalized predicate depends on the mode of presentation of the domain of quantification. I compare two ways of implementing this idea, one using counterpart theory, the other using Aloni's 'conceptual covers' theory, and then provides some evidence in favor of the former.

This book surveys research in quantification starting with the foundational work in the 1970s. It paints a vivid picture of generalized quantifiers and Boolean semantics. It explains how the discovery of diverse scope behavior in the 1990s transformed the view of quantification, and how the study of the internal composition of quantifiers has become central in recent years. It presents different approaches to the same problems, and links modern logic and formal semantics to advances in generative syntax. A (...) unique feature of the book is that it systematically brings cross-linguistic data to bear on the theoretical issues, discussing French, German, Dutch, Hungarian, Russian, Japanese, Telugu (Dravidian), and Shupamem (Grassfield Bantu), and pointing to formal semantic literature involving quantification in around thirty languages. -- -/- 1. What this book is about and how to use it; 2. Generalized quantifiers and their elements: operators and their scopes; 3. Generalized quantifiers in non-nominal domains; 4. Some empirically significant properties of quantifiers and determiners; 5. Potential challenges for generalized quantifiers; 6. Scope is not uniform and not a primitive; 7. Existential scope versus distributive scope; 8. Distributivity and scope; 9. Bare numeral indefinites; 10. Modified numerals; 11. Clause-internal scopal diversity; 12. Towards a compositional semantics of quantifier words. (shrink)