What makes a valid argument valid? Generally speaking, in a valid argument, if the premisses are true, then the conclusion must necessarily also be true. But on its own, this doesn’t tell us all that much. What is truth? And what is necessity? In what follows, I consider answers to these questions proposed by the fourteenth century logician John Buridan († ca. 1358). My central claim is that Buridan’s logic is downstream from his metaphysics. Accordingly, I treat his metaphysical discussions (...) as the key to his logic. As has been often noted, Buridan’s metaphysics are radically anti-realist about universals, though I think the depth and scope of his anti-realism has at times been papered over. Buridan constructs his logic on an amazingly spartan ontology, and this accomplishment is overdue for reconsideration. To the foregoing questions: truth is a feature of propositions, and of propositions only—not of proposition-like states of affairs, or anything like that. It is a function of the reference or supposition (suppositio) of their terms, which depends on predication in a propositional context. And necessary truth is grounded in causation: a predication is necessary if it cannot be falsified by any power, natural or supernatural, without ii annihilating what its terms stand for. “Socrates is a human”, for instance, can only be falsified by annihilating Socrates, and so it is a necessary truth. -/- These considerations provide an ample theoretical basis for a thorough examination of Buridan’s modal logic. This is what the thesis culminates with. In the final chapter, I set forth some novel and surprising findings, chief of which is this: Buridan’s modal syntax and semantics are nothing like Kripke’s—and indeed are incompatible with them. This has significant implications not only for modal logic and metaphysics, but for how we think about medieval logic and philosophy more generally. -/- Throughout the thesis, I advocate a methodology of emphasising the differences, rather than the similarities, between past and present thought. Buridan is wildly unlike what we’re used to, and we should let him speak for himself. (shrink)

Marsilius of Inghen’s account of imaginable impossibilities became paradigmatic in logic, semantics, and metaphysics throughout the later Middle Ages and well into the early modern period. The present study focuses on imaginable impossibilities in 14th-century logic, underlining the relevance of Marsilius of Inghen’s innovative approach through a comparison with the semantic accounts proposed by other mid-14th-century Parisian nominalists, namely John Buridan and Albert of Saxony. In particular, this paper tracks the specific issue of the admissibility of absolute impossibilities – (...) such as the chimera – within Marsilius of Inghen’s semantic analysis, proving that there is a sense in which the chimera is indeed treatable. The present study does so by analysing the issues involved in impossibilities on the levels of signification, supposition, and extended reference. In doing so it provides a clearer picture of the problems involved, where they emerge and why, as well as of the significance and range of Marsilius of Inghen’s approach. (shrink)

This paper is a study of a distinctively chemical notion of possibility. This is the notion of possibility that occurs in chemical discourses when chemists speak of the possibility or impossibility of achieving a given result through chemical means. This notion pertains to the possibility of processes, not of compounds, so it differs from the kind of chemical possibility mentioned in Wittgenstein's Philosophical Investigations or the kinds discussed in the literature on Putnam's Twin Earth argument. I argue that this process-oriented (...) notion of possibility cannot be reduced in a simple way to physical possibility, and that standard possible worlds semantics does not allow a natural analysis of this notion. I suggest an extension of possible worlds semantics that may overcome this limitation. I finish by pointing out some open questions about chemical possibility. (shrink)

According to Amie Thomasson's Modal Normativism (MN), knowledge of metaphysical modality is to be explained in terms of a speaker’s mastery of semantic rules, as opposed to one’s epistemic grasp of independent modal facts. In this chapter, I outline (MN)'s account of modal knowledge (§1) and argue that more than semantic mastery is needed for knowledge of metaphysical modality. Specifically (§2), in reasoning aimed at gaining such knowledge, a competent speaker needs to further deploy essentialist principles and (...) information. In response, normativists might contend that a competent speaker will only need to appeal to specific independence counterfactuals, on analogy with quasi-realism about morality. These conditionals fix the meaning of our terms at the actual world, independently of the particular context in which a statement is evaluated. However, I show that this strategy causes several problems for the account (§3). While those problems might perhaps be avoided by endorsing a certain picture of modal metaphysics (Modal Monism), such a picture involves notorious issues that normativists will have to address (§4). It is thus doubtful that (MN) can explain knowledge of metaphysical modality. Still, it may explain some modal knowledge without committing to Modal Monism. As I show (§5), semantic mastery may suffice for gaining knowledge of logical-conceptual modality or analyticity. (shrink)

Possible worlds semantics faces a range of difficulties for at least certain types of modals, especially deontic modals with their distinction between heavy and light permissions and obligations. This paper outlines a new semantics of modals that aims to overcome some of those difficulties. The semantics is based on an a novel ontology of modal objects, entities like obligations, permissions, needs, as well as epistemic states, abilities, and essences. Moreover, it is based on truthmaking, in the (...) sense of Fine’s recent truthmaker 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)

According to Amie Thomasson’s modal normativism, the function of modal discourse is to convey semantic rules. But what is a "semantic rule"? I raise three worries according to which there is no conception of a semantic rule that can serve the needs of a modal normativist. The first worry focuses on de re and a posteriori necessities. The second worry concerns Thomasson's inferential specification of the meaning of modal terms. The third worry asks about the normative (...) status of semantic rules. (shrink)

Expressivists about epistemic modals deny that ‘Jane might be late’ canonically serves to express the speaker’s acceptance of a certain propositional content. Instead, they hold that it expresses a lack of acceptance. Prominent expressivists embrace pragmatic expressivism: the doxastic property expressed by a declarative is not helpfully identified with that sentence’s compositional semantic value. Against this, we defend semantic expressivism about epistemic modals: the semantic value of a declarative from this domain is the property of doxastic attitudes it canonically serves (...) to express. In support, we synthesize data from the critical literature on expressivism—largely reflecting interactions between modals and disjunctions—and present a semantic expressivism that readily predicts the data. This contrasts with salient competitors, including: pragmatic expressivism based on domain semantics or dynamic semantics; semantic expressivism à la Moss [2015]; and the bounded relational semantics of Mandelkern [2019]. (shrink)

This paper gives an outline of truthmaker semantics for natural language against the background of standard possible-worlds semantics. It develops a truthmaker semantics for attitude reports and deontic modals based on an ontology of attitudinal and modal objects and on a semantic function of clauses as predicates of such objects. It also présents new motivations for 'object-based truthmaker semantics' from intensional transitive verbs such as ‘need’, ‘look for’, ‘own’, and ‘buy’ and gives an outline of (...) their semantics. This paper is a commissioned 'target' article, with commentaries by W. Davis, B. Arsenijevic, K. Moulton, K. Liefke, M. Kaufmann, R. Matthews, P. Portner and A. Rubinstein, P. Elliott, G. Ramchand and my reply. (shrink)

The integration challenge for modality states that metaphysical theories of modality tend to fail in one of two ways: either they render the meanings of modal sentences mysterious, or they render modal knowledge mysterious. I argue that there are specific semantic and epistemic constraints on metaphysics implied by the integration challenge and that a plausible metaphysical theory of modality will satisfy both of them. I further argue that no popular metaphysical theory of modality simultaneously satisfies both of the (...) constraints. Therefore, a new metaphysical theory of modality is needed, one that can offer a clear response to the integration challenge. I attempt to supply the needed theory and show that it satisfies the constraints of the integration challenge. The overall result is an argument for a new and unique metaphysical theory of modality that I call constructionism. (shrink)

Over the last fifteen years, linguists and philosophers of language have reexamined the canonical, Kratzerian semantics for modal expressions, with special attention paid to their epistemic and deontic uses. This article is an overview of the literature on deontic modal expressions. Section 1 provides an overview of the canonical semantics, noting some of its main advantages. Section 2 introduces a set of desiderata that have achieved the status of fixed points in the debates about whether the (...) canonical semantics is correct. These include the observations that deontic modal sentences have both deliberative and evaluative readings and both information-sensitive and -insensitive readings. Adequate resolutions of certain puzzles in deontic logic and resolving the Frege-Geach problem for Expressivism have also achieved this status. The third section provides an opinionated overview of some of the main extant rivals to the canonical semantics, including Cariani, Kaufmann, and Kaufmann’s (2013) complex contextualism , Yalcin’s (2012) Expressivism, Willer’s (2014) dynamic semantics, and Starr’s (2016) dynamic Expressivism. Section 4 provides an assessment of each of the views discussed in terms of the desiderata introduced in section 2. Section 5 is an overview of remaining issues that require more attention in the literature. (shrink)

This paper develops an update semantics for weak necessity modals like ‘ought’ and ‘should’. I start with the basic approach to the weak/strong necessity modal distinction developed in Silk 2018: Strong necessity modals are given their familiar semantics of necessity, predicating the necessity of the prejacent of the actual world (evaluation world). The apparent “weakness” of weak necessity modals derives from their bracketing the assumption that the relevant worlds in which the prejacent is necessary (deontically, epistemically, etc.) (...) need be candidates for actuality. ‘Should φ’ can be accepted without needing to settle that the relevant considerations (norms, preferences, expectations, etc.) that actually apply, given the facts, verify the necessity of φ. I formalize these ideas within an Update with Centering framework. The meaning of ‘Should φ’ is explained, fundamentally, in terms of how its use updates attention toward possibilities in which φ is necessary. The semantics is also extended to deontic conditionals. The proposed analyses capture various contrasting logical properties and discourse properties of ‘should’ and ‘must’ — e.g., in sensitivities to standing contextual assumptions, entailingness, and force — and provide an improved treatment of largely neglected data concerning information-sensitivity. (shrink)

This paper argues for contrastivism about the deontic modals, 'ought', 'must', and 'may'. A simple contrastivist semantics that predicts the desired entailment relations among these modals is offered.

I propose a unified solution to two puzzles: Ross's puzzle and free choice permission. I begin with a pair of cases from the decision theory literature illustrating the phenomenon of act dependence, where what an agent ought to do depends on what she does. The notion of permissibility distilled from these cases forms the basis for my analysis of 'may' and 'ought'. This framework is then combined with a generalization of the classical semantics for disjunction — equivalent to Boolean (...) disjunction on the diagonal, but with a different two-dimensional character — that explains the puzzling facts in terms of semantic consequence. (shrink)

Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices (which he called quasi-matrices), in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlev’s hierarchy, also proposing weaker six-valued systems in which the (T) axiom was replaced by the deontic (D) axiom. In (...) this paper, we propose even weaker systems, by eliminating both axioms, which are characterized by eight-valued non-deterministic matrices. In addition, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary (deterministic) logical matrices would be possible for all those Ivlev-like systems. We will show that finite deterministic matrices do not characterize any of them. (shrink)

This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the meanings (...) of modal operators in terms of rules of inference. (shrink)

In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new proof (...) of S4 as being "the logic of topological spaces", but now under the perspective of paraconsistency. (shrink)

This paper outlines a semantic account of attitude reports and deontic modals based on cognitive and illocutionary products, mental states, and modal products, as opposed to the notion of an abstract proposition or a cognitive act.

The standard account of modal expressions in natural language analyzes them as quantifiers over a set of possible worlds determined by the evaluation world and an accessibility relation. A number of authors have recently argued for an alternative account according to which modals are analyzed as quantifying over a domain of possible worlds that is specified directly in the points of evaluation. But the new approach only handles the data motivating it if it is supplemented with a non-standard account (...) of attitude verbs and conditionals. It can be shown the the relational account handles the same data equally well if it too is supplemented with a non-standard account of such expressions. (shrink)

In proof-theoretic semantics, meaning is based on inference. It may be seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a ‘base’ of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional (...) class='Hi'>modal systems K, KT , K4, and S4, with □ as the primary modal operator. We establish appropriate soundness and completeness theorems and establish the duality between □ and a natural presentation of ♢. We also show that our semantics is in its current form not complete with respect to euclidean modal logics. Our formulation makes essential use of relational structures on bases. (shrink)

ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be (...) equivalent; but, when regarded as consequence systems (ibid., p. 157), one diverges from the others in a fashion which suggests that two standard measures of semantic complexity may not be as closely linked as previously thought. -/- This 1974 paper uses the linear notation for natural deduction presented in [2]: each two-dimensional deduction is represented by a unique one-dimensional string of characters. Thus obviating need for two-dimensional trees, tableaux, lists, and the like—thereby facilitating electronic communication of natural deductions. The 1969 paper presents a (modal, sentential) logic which may be thought of as a partial systematization of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of this logic coincides those of standard formalizations of Lewis’s S4. Among the paper's innovations is its treatment of modal logic in the setting of natural deduction systems--as opposed to axiomatic systems. The author’s apologize for the now obsolete terminology. For example, these papers speak of “a proof of a sentence from a set of premises” where today “a deduction of a sentence from a set of premises” would be preferable. 1. Corcoran, John. 1969. Three Logical Theories, Philosophy of Science 36, 153–77. J P R -/- 2. Corcoran, John and George Weaver. 1969. Logical Consequence in Modal Logic: Natural Deduction in S5 Notre Dame Journal of Formal Logic 10, 370–84. MR0249278 (40 #2524). 3. Weaver, George and John Corcoran. 1974. Logical Consequence in Modal Logic: Some Semantic Systems for S4, Notre Dame Journal of Formal Logic 15, 370–78. MR0351765 (50 #4253). (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)

In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally (...) a non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras. (shrink)

It is often argued that inferential role semantics (IRS) entails semantic holism as long as theorists fail to answer the question about which inferences, among the many, are meaning-constitutive. Since analyticity, as truth in virtue of meaning, is a widely dismissed notion in indicating which inferences determine meaning, it seems that holism follows. Semantic holism is often understood as facing problems with the stability of content and many usual explanations of communication. Thus, we should choose between giving up IRS, (...) to avoid these holistic entailments, and defending holism against this charge, to rescue IRS. I try to pursue the second goal by analyzing certain patterns of counterfactual reasoning. Wilfrid Sellars and Robert Brandom claim that, to defend IRS, content-constitutive inferences are those counterfactually robust. While it is difficult to assess the goodness of such a view, it nonetheless entails that counterfactually non-robust inferences (which I call “modally ruled out inferences”) are not content-constitutive. If this is true, and if we take certain remarks about the grasp of concepts on board, there is a way to restrict the scope of the holism entailed by IRS to the extent of reshaping problems with the stability of content. (shrink)

Possible worlds are commonly seen as an interpretation of modal operators such as "possible" and "necessary". Here, we develop possible world semantics (PWS) which can be expressed in basic set theory and first-order logic, thus offering a reductionist account of modality. Specifically, worlds are understood as complete sets of statements and possible worlds are sets whose statements are consistent with a set of conceptual laws. We introduce the construction calculus (CC), a set of axioms and rules for truth, (...) possibility, worldness and consistency. We show that CC allows to prove fundamental theorems about necessity, possibility, impossibility and contigency, thus demonstrating prima-facie plausibility of PWS. Finally, we discuss the explanatory power of our approach and draw connections between our account and established philosophical conceptions of possible worlds. (shrink)

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations (...) of content and context are explored. (shrink)

Against the background of standard possible-worlds semantics, this paper outlines a truthmaker approach to the semantics of attitude reports and modal sentences based on an ontology of attitudinal and modal objects.

A dynamic semantics for epistemically modalized sentences is an attractive alternative to the orthodox view that our best theory of meaning ascribes to such sentences truth-conditions relative to what is known. This essay demonstrates that a dynamic theory about might and must offers elegant explanations of a range of puzzling observations about epistemic modals. The first part of the story offers a unifying treatment of disputes about epistemic modality and disputes about matters of fact while at the same time (...) avoiding the complexities of alternative theories. The second part of the story extends the basic framework to cover some complicated data about retraction and the interaction between epistemic modality and tense. A comparison between the suggestion made in this essay and current versions of the orthodoxy is provided. (shrink)

A new proof style adequate for modal logics is defined from the polynomial ring calculus. The new semantics not only expresses truth conditions of modal formulas by means of polynomials, but also permits to perform deductions through polynomial handling. This paper also investigates relationships among the PRC here defined, the algebraic semantics for modal logics, equational logics, the Dijkstra???Scholten equational-proof style, and rewriting systems. The method proposed is throughly exemplified for S 5, and can be (...) easily extended to other modal logics. (shrink)

In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop several (...) extensions of \SQEMA\ where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension \SSQEMA\ we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon's monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versions of \SSQEMA\ which guarantee canonicity, too. (shrink)

We outline a neo-Meinongian framework labeled as Modal Meinongian Metaphysics (MMM) to account for the ontology and semantics of fictional discourse. Several competing accounts of fictional objects are originated by the fact that our talking of them mirrors incoherent intuitions: mainstream theories of fiction privilege some such intuitions, but are forced to account for others via complicated paraphrases of the relevant sentences. An ideal theory should resort to as few paraphrases as possible. In Sect. 1, we make this (...) explicit via two methodological principles, called the Minimal Revision and the Acceptability Constraint. In Sect. 2, we introduce the standard distinction between internal and external fictional discourse. In Sects. 3–5, we discuss the approaches of (traditional) Meinongianism, Fictionalism, and Realism—and their main troubles. In Sect. 6 we propose our MMM approach. This is based upon (1) a modal semantics including impossible worlds (Subsect. 6.1); (2) a qualified Comprehension Principle for objects (Subsect. 6.2); (3) a notion of existence-entailment for properties (Subsect. 6.3). In Sect. 7 we present a formal semantics for MMM based upon a representation operator. And in Sect. 8 we have a look at how MMM solves the problems of the three aforementioned theories. (shrink)

We introduce an expected-value theory of linguistic modality that makes reference to expected utility and a likelihood-based confirmation measure for deontics and epistemics, respectively. The account is a probabilistic semantics for deontics and epistemics, yet it proposes that deontics and epistemics share a common core modal semantics, as in traditional possible-worlds analysis of modality. We argue that this account is not only theoretically advantageous, but also has far-reaching empirical consequences. In particular, we predict modal versions of (...) reasoning fallacies from the heuristics and biases literature. Additionally, we derive the modal semantics in an entirely transparent manner, as it is based on the compositional semantics of Korean modal expressions that are morphosyntactically decomposed into a conditional and an evaluative predicate. (shrink)

Sellars was an inferentialist about meaning. He thus effectively accorded modality a categorial function, maintaining that any meaningful assertion involves implicit commitment to rules of material inference, which modal propositions explicitly endorse. But Sellars was also a modal anti-realist, construing modality as “entirely immanent to thought” (LRB §40), not present in the world an sich. These two commitments, Klemick argues, render it impossible in principle for us to describe the world an sich adequately, undermining Sellars’ scientific realism, on (...) which, at the “ideal outcome of scientific inquiry,” “the gulf between appearances and things-in-themselves [... can] be bridged” (SM II §51). Sellars’ attempt to ground his modal anti-realism in an ideal “pure description of the world” (CDCM §79) cannot succeed, given modality’s categorial function. Further, his subsequent deployment of picturing as a naturalistic criterion of ontological commitment founders on an analogue of the Kantian problem of noumenal affection: the descriptions of picturing relations that render this proposal intelligible are emptied of content by the denial that the in-itself is modally characterized. Sellars’ worthy aim of preserving the world’s independence of our conceptual activity, Klemick concludes, doesn’t require denying that it exhibits modal relations isomorphic to the semantic relations within our conceptual scheme. (shrink)

Intellectual humility can be broadly construed as being conscious of the limits of one’s existing knowledge and capable to acquire more knowledge, which makes it a key virtue of the information age. However, the claim “I am (intellectually) humble” seems paradoxical in that someone who has the disposition in question would not typically volunteer it. There is an explanatory gap between the meaning of the sentence and the meaning the speaker ex- presses by uttering it. We therefore suggest analyzing intellectual (...) humility semantically, using a psycholexical approach that focuses on both synonyms and antonyms of ‘intellectual humili- ty’. We present a thesaurus-based methodology to map the semantic space of intellectual hu- mility and the vices it opposes as a heuristic to support philosophical and psychological anal- ysis of this disposition. We performed the mapping both in English and German in order to test for possible cultural differences in the understanding of intellectual humility. In both lan- guages, we find basically the same three semantic dimensions of intellectual humility (sensi- bility, discreetness, and knowledge dimensions) as well as three dimensions of its related vic- es (self-overrating, other-underrating and dogmatism dimensions). The resulting semantic clusters were validated in an empirical study with English (n=276) and German (n=406) par- ticipants. We find medium to high correlations (0.54-0.72) between thesaurus similarity and perceived similarity, and we can validate the labels of the three dimensions identified in the study. But we also find indications of the limitations of the thesaurus methodology in terms of cluster plausibility. We conclude by discussing the importance of these findings for construct- ing psychometric scales for intellectual humility. (shrink)

Upward monotonic semantics for necessity modals give rise to Ross’s Puzzle: they predict that □φ entails □(φ ∨ ψ), but common intuitions about arguments of this form suggest they are invalid. It is widely assumed that the intuitive judgments involved in Ross’s Puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from □(φ ∨ ψ), interpreters infer that the truth of each disjunct (φ, ψ) is compatible with the relevant set of worlds. I introduce two pieces (...) of data that this analysis fails to explain. Analyzing this data, I argue, suggests that necessity modals with embedded disjunctions license ‘Independence’ inferences: from the truth of □(φ ∨ ψ), interpreters infer that φ-without-ψ and ψ-without-φ are each compatible with the relevant set of worlds. I outline a bilateral inquisitive semantics for necessity modals that predicts the validity of the Independence inferences. I then argue that the resulting theory should be understood as one on which disjunctions denote pluralities of propositions, and necessity modals behave like collective predicates applied to these pluralities. (shrink)

We investigate an enrichment of the propositional modal language L with a "universal" modality ■ having semantics x ⊧ ■φ iff ∀y(y ⊧ φ), and a countable set of "names" - a special kind of propositional variables ranging over singleton sets of worlds. The obtained language ℒ $_{c}$ proves to have a great expressive power. It is equivalent with respect to modal definability to another enrichment ℒ(⍯) of ℒ, where ⍯ is an additional modality with the (...) class='Hi'>semantics x ⊧ ⍯φ iff Vy(y ≠ x → y ⊧ φ). Model-theoretic characterizations of modal definability in these languages are obtained. Further we consider deductive systems in ℒ $_{c}$ . Strong completeness of the normal ℒ $_{c}$ logics is proved with respect to models in which all worlds are named. Every ℒ $_{c}$ -logic axiomatized by formulae containing only names (but not propositional variables) is proved to be strongly frame-complete. Problems concerning transfer of properties ([in]completeness, filtration, finite model property etc.) from ℒ to ℒ $_{c}$ are discussed. Finally, further perspectives for names in multimodal environment are briefly sketched. (shrink)

ABSTRACT: This chapter offers a revenge-free solution to the liar paradox (at the centre of which is the notion of Gestalt shift) and presents a formal representation of truth in, or for, a natural language like English, which proposes to show both why -- and how -- truth is coherent and how it appears to be incoherent, while preserving classical logic and most principles that some philosophers have taken to be central to the concept of truth and our use of (...) that notion. The chapter argues that, by using a truth operator rather than truth predicate, it is possible to provide a coherent, model-theoretic representation of truth with various desirable features. After investigating what features of liar sentences are responsible for their paradoxicality, the chapter identifies the logic as the normal modal logic KT4M (= S4M). Drawing on the structure of KT4M (=S4M), the author proposes that, pace deflationism, truth has content, that the content of truth is bivalence, and that the notions of both truth and bivalence are semideterminable. (shrink)

What does 'might' mean? One hypothesis is that 'It might be raining' is essentially an avowal of ignorance like 'For all I know, it's raining'. But it turns out these two constructions embed in different ways, in particular as parts of larger constructions like Wittgenstein's 'It might be raining and it's not' and Moore's 'It's raining and I don't know it', respectively. A variety of approaches have been developed to account for those differences. All approaches agree that both Moore sentences (...) and Wittgenstein sentences are classically consistent. In this paper I argue against this consensus. I adduce a variety of new data which I argue can best be accounted for if we treat Wittgenstein sentences as being classically inconsistent. This creates a puzzle, since there is decisive reason to think that 'Might p' is classically consistent with 'Not p'. How can it also be that 'Might p and not p' and 'Not p and might p' are classically inconsistent? To make sense of this situation, I propose a new theory of epistemic modals and their interaction with embedding operators. This account makes sense of the subtle embedding behavior of epistemic modals, shedding new light on their meaning and, more broadly, the dynamics of information in natural language. -/- . (shrink)

Epistemic modals are a prominent topic in the literature on natural language semantics, with wide-ranging implications for issues in philosophy of language and philosophical logic. Considerations about the role that epistemic "might" and "must" play in discourse and reasoning have led to the development of several important alternatives to classical possible worlds semantics for natural language modal expressions. This is an opinionated overview of what I take to be some of the most exciting issues and developments in (...) the field. (shrink)

In this paper, we consider recent attempts to metaphysically explain agentive modality in terms of conditionals. We suggest that the best recent accounts face counterexamples, and more worryingly, they take some agentive modality for granted. In particular, the ability to perform basic actions features as a primitive in these theories. While it is perfectly acceptable for a semantics of agentive modal claims to take some modality for granted in getting the extension of action claims correct, a metaphysical explanation (...) of agentive modality cannot, at least not in the way that conditional approaches to agentive modality do. We argue that this problem was present even in the classical conditional analysis. By a pessimistic induction, we suggest that, probably, no conditional approach to agentive modality will succeed. (shrink)

When embedding data are used to argue against semantic theory A and in favor of semantic theory B, it is important to ask whether A could make sense of those data. It is possible to ask that question on a case-by-case basis. But suppose we could show that A can make sense of all the embedding data which B can possibly make sense of. This would, on the one hand, undermine arguments in favor of B over A on the basis (...) of embedding data. And, provided that the converse does not hold—that is, that A can make sense of strictly more embedding data than B can—it would also show that there is a precise sense in which B is more constrained than A, yielding a pro tanto simplicity-based consideration in favor of B. In this paper I develop tools which allow us to make comparisons of this kind, which I call comparisons of potential expressive power. I motivate the development of these tools by way of exploration of the recent debate about epistemic modals. Prominent theories which have been developed in response to embedding data turn out to be strictly less expressive than the standard relational theory, a fact which necessitates a reorientation in how to think about the choice between these theories. (shrink)

This paper motivates and develops a novel semantic framework for deontic modals. The framework is designed to shed light on two things: the relationship between deontic modals and substantive theories of practical rationality and the interaction of deontic modals with conditionals, epistemic modals and probability operators. I argue that, in order to model inferential connections between deontic modals and probability operators, we need more structure than is provided by classical intensional theories. In particular, we need probabilistic structure that interacts directly (...) with the compositional semantics of deontic modals. However, I reject theories that provide this probabilistic structure by claiming that the semantics of deontic modals is linked to the Bayesian notion of expectation. I offer a probabilistic premise semantics that explains all the data that create trouble for the rival theories. (shrink)

Williamsonian modal epistemology is characterized by two commitments: realism about modality, and anti-exceptionalism about our modal knowledge. Williamson’s own counterfactual-based modal epistemology is the best known implementation of WME, but not the only option that is available. I sketch and defend an alternative implementation which takes our knowledge of metaphysical modality to arise, not from knowledge of counterfactuals, but from our knowledge of ordinary possibility statements of the form ‘x can F’. I defend this view against a (...) criticism indicated in Williamson’s own work, and argue that it is better connected to the semantics of modal language. (shrink)

There is a common assumption in the semantics of modal auxiliaries in natural language; in utterances of MOD φ , where MOD is a modal and φ is the prejacent, context determines the particular flavor of modality expressed by the modal. Such is the standard contextualist semantics of Kratzer and related proposals. This winds up being a problem, because there is a significant class of modals which have constraints on the admissible modal flavor that (...) are not traceable to context. For example, in MUST φ , subsentential properties of φ, like the aspectual class of the predicate in the prejacent, can affect the flavor of MUST. By encoding the above assumption into the semantics, such contextualist accounts fail to be able to explain, much less to predict, this pattern. Worse yet, attempts to exploit the resources of the theory in service of an explanation run afoul of important commitments of the view, like the hypothesis that modals have a uniform semantics. Given these circumstances, these data might seem like a justification for dispensing with the uniformity hypothesis. The present paper lays out the above problem in detail. Against the pessimistic view, I argue that the the contextualist account can in fact explain and predict these patterns while preserving the uniformity hypothesis. This requires adopting an amendment to the semantics of modals based on the work of Valentine Hacquard. Aside from maintaining the contextualist paradigm and preserving uniformity, the proposal also clarifies the role of context in the interpretation of modals. As it will turn out, the role of context ought to be circumscribed in its flavor-determining role for modals. (shrink)

Modal logic is one of philosophy’s many children. As a mature adult it has moved out of the parental home and is nowadays straying far from its parent. But the ties are still there: philosophy is important to modal logic, modal logic is important for philosophy. Or, at least, this is a thesis we try to defend in this chapter. Limitations of space have ruled out any attempt at writing a survey of all the work going on (...) in our field—a book would be needed for that. Instead, we have tried to select material that is of interest in its own right or exemplifies noteworthy features in interesting ways. Here are some themes that have guided us throughout the writing: • The back-and-forth between philosophy and modal logic. There has been a good deal of give-and-take in the past. Carnap tried to use his modal logic to throw light on old philosophical questions, thereby inspiring others to continue his work and still others to criticise it. He certainly provoked Quine, who in his turn provided—and continues to provide—a healthy challenge to modal logicians. And Kripke’s and David Lewis’s philosophies are connected, in interesting ways, with their modal logic. Analytic philosophy would have been a lot different without modal logic! • The interpretation problem. The problem of providing a certain modal logic with an intuitive interpretation should not be conflated with the problem of providing a formal system with a model-theoretic semantics. An intuitively appealing model-theoretic semantics may be an important step towards solving the interpretation problem, but only a step. One may compare this situation with that in probability theory, where definitions of concepts like ‘outcome space’ and ‘random variable’ are orthogonal to questions about “interpretations” of the concept of probability. • The value of formalisation. Modal logic sets standards of precision, which are a challenge to—and sometimes a model for—philosophy. Classical philosophical questions can be sharpened and seen from a new perspective when formulated in a framework of modal logic. On the other hand, representing old questions in a formal garb has its dangers, such as simplification and distortion. • Why modal logic rather than classical (first or higher order) logic? The idioms of modal logic—today there are many!—seem better to correspond to human ways of thinking than ordinary extensional logic. (Cf. Chomsky’s conjecture that the NP + VP pattern is wired into the human brain.) In his An Essay in Modal Logic (1951) von Wright distinguished between four kinds of modalities: alethic (modes of truth: necessity, possibility and impossibility), epistemic (modes of being known: known to be true, known to be false, undecided), deontic (modes of obligation: obligatory, permitted, forbidden) and existential (modes of existence: universality, existence, emptiness). The existential modalities are not usually counted as modalities, but the other three categories are exemplified in three sections into which this chapter is divided. Section 1 is devoted to alethic modal logic and reviews some main themes at the heart of philosophical modal logic. Sections 2 and 3 deal with topics in epistemic logic and deontic logic, respectively, and are meant to illustrate two different uses that modal logic or indeed any logic can have: it may be applied to already existing (non-logical) theory, or it can be used to develop new theory. (shrink)

I present a case for a rapprochement between aspects of rationalism and scientific realism, by way of a general framework employing modal epistemology and elements of 2-dimensional semantics (2DS). My overall argument strategy is meta-inductive: The bulk of this paper establishes a “base case,” i.e., a concretely constructive example by which I demonstrate this linkage. The base case or constructive example acts as the exemplar for generating, in a constructively ‘bottom-up’ fashion, a more generally rigorous case for rationalism-realism (...) qua modal epistemology. The exemple I choose in D. Chalmers’ (2002) modal rationalism and R. Giere’s (1985, 1988) constructive realism. I show by way of a thorough analysis how Giere’s claims concerning modal scope are characterized as instances of Chalmers’ modal rationalism, both weak and strong. In essence, as I demonstrate via Chalmers’ notions, ceteris paribus the constructive realist ultimately opts for a comparatively wider gate, characterized by modal reasoning, to lead from the rooms of conceivability qua thought experiments and models, to the pastures of metaphysical possibility. Chalmers likewise tries to erect such a wider gate, in his general conceivability-possibility theses. Anti-realists, on the other hand, see a narrower passage and my contention herein is that they suffer from modal myopia, which hopefully the ‘corrective vision’ of Chalmers’ modal rationalism can restore. In the introduction and concluding sections I sketch out suggestions of constructing ‘inductive steps’ from my base case, to generate more extensively general claims regarding realism qua rationalism. -/- . (shrink)