This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of linear logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic linear logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of Kripke (...) resource models extended with a neighbourhood function: modal Kripke resource models. We propose a Hilbert-style axiomatisation and a Gentzen-style sequent calculus. We show that the proof theories are sound and complete with respect to the class of modal Kripke resource models. We show that the sequent calculus admits cut elimination and that proof-search is in PSPACE. We then show how to extend the results when non-commutative connectives are added to the language. Finally, we put the l.. (shrink)

This note considers deductive systems for the operator a of unprovability in some particular propositional normal modal logics. We give thus complete syntactic characterization of these logics in the sense of Lukasiewicz: for every formula  either `  or a  (but not both) is derivable. In particular, purely syntactic decision procedure is provided for the logics under considerations.

One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...) for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C1, each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E+E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI 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)

We study a fragment of Intuitionistic Linear Logic combined with non-normal modal operators. Focusing on the minimal modal logic, we provide a Gentzen-style sequent calculus as well as a semantics in terms of Kripke resource models. We show that the proof theory is sound and complete with respect to the class of minimal Kripke resource models. We also show that the sequent calculus allows cut elimination. We put the logical framework to use by instantiating it as a logic of (...) agency. In particular, we apply it to reason about the resource-sensitive use of artefacts. (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)

In this article, I define and then defend the principle of information closure (pic) against a sceptical objection similar to the one discussed by Dretske in relation to the principle of epistemic closure. If I am successful, given that pic is equivalent to the axiom of distribution and that the latter is one of the conditions that discriminate between normal and non-normal modal logics, a main result of such a defence is that one potentially good reason to look (...) for a formalization of the logic of “ $S$ is informed that $p$ ” among the non-normal modal logics, which reject the axiom, is also removed. This is not to argue that the logic of “ $S$ is informed that $p$ ” should be a normal modal logic, but that it could still be insofar as the objection that it could not be, based on the sceptical objection against pic, has been removed. In other word, I shall argue that the sceptical objection against pic fails, so such an objection provides no ground to abandon the normal modal logic B (also known as KTB) as a formalization of “ $S$ is informed that $p$ ”, which remains plausible insofar as this specific obstacle is concerned. (shrink)

Max Cresswell and Hilary Putnam seem to hold the view, often shared by classical logicians, that paraconsistent logic has not been made sense of, despite its well-developed mathematics. In this paper, I examine the nature of logic in order to understand what it means to make sense of logic. I then show that, just as one can make sense of non-normal modal logics (as Cresswell demonstrates), we can make `sense' of paraconsistent logic. Finally, I turn the tables on classical (...) logicians and ask what sense can be made of explosive reasoning. While I acknowledge a bias on this issue, it is not clear that even classical logicians can answer this question. (shrink)

Many classically valid meta-inferences fail in a standard supervaluationist framework. This allegedly prevents supervaluationism from offering an account of good deductive reasoning. We provide a proof system for supervaluationist logic which includes supervaluationistically acceptable versions of the classical meta-inferences. The proof system emerges naturally by thinking of truth as licensing assertion, falsity as licensing negative assertion and lack of truth-value as licensing rejection and weak assertion. Moreover, the proof system respects well-known criteria for the admissibility of inference rules. Thus, supervaluationists (...) can provide an account of good deductive reasoning. Our proof system moreover brings to light how one can revise the standard supervaluationist framework to make room for higher-order vagueness. We prove that the resulting logic is sound and complete with respect to the consequence relation that preserves truth in a model of the non-normal modal logic _NT_. Finally, we extend our approach to a first-order setting and show that supervaluationism can treat vagueness in the same way at every order. The failure of conditional proof and other meta-inferences is a crucial ingredient in this treatment and hence should be embraced, not lamented. (shrink)

We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal (...) class='Hi'>modalities to ensure a number of basic principles. In this way, a viable consistent modelling of collective attitudes is obtained. (shrink)

Nearly thirty years ago, Robert Alexy in his book The Concept and Validity of Law as well as in other early articles raised non-positivistic arguments in the Continental European tradition against legal positivism in general, which was assumed to be held by, among others, John Austin, Hans Kelsen and H.L.A. Hart. The core thesis of legal positivism that was being discussed among contemporary German jurists, just as with their Anglo- American counterparts, is the claim that there is no necessary connection (...) between law and morality. Robert Alexy has argued, however, that the law, besides consisting conceptually of elements of authoritative issuance and social efficacy, necessarily lays a claim to substantial correctness, which is derived from analytical arguments. Furthermore, if this claim to substantial correctness necessarily requires the incorporation of moral elements into law, then the ‘necessary connection thesis’, as defended by non-positivism, can be justified. Some of the most significant objections to this sort of claim, stemming from the Anglo-American world, are those introduced by Joseph Raz. In his ‘Reply’ to Robert Alexy, Raz raises at least three interesting criticisms, including, first, the ambiguity of ‘legal theory in the positivistic tradition’, second, the indeterminate formulations of the ‘separation thesis’, and, third, the necessary claim of law to legitimate authority as a moral claim. As a point of departure, I will argue that Raz’s three criticisms are misleading. For they do not enhance our understanding of the genuine compatibility or incompatibility between legal positivism and non-positivism. Despite the frequently reformulated theses of legal positivism and the various kinds of opponents responding thereto, the essential divergence between legal positivism and non-positivism was and remains the answer to the question of the relation between law and morality. Furthermore, I will clarify that in the strictest sense there can be three and only three logically possible positions concerning the relation between law and morality: the connection between them is either necessary, or impossible (i. e. they are necessarily separate), or contingent (i. e. they are neither necessarily connected nor necessarily separate). The first position is non-positivistic, while the latter two positions are, indeed, both positivistic, but in different forms: one may be called ‘exclusive’ legal positivism, the other ‘inclusive’ legal positivism. I will continue by showing that these three positions stand to one another in the relation of contraries, not contradictories, and that, taken together, they exhaust the logically possible positions concerning the relation between law and morality, never mind the tradition or authority from which these positions are derived. Raz mentions, however, many changeable formulations of the separation thesis, which even leads him to acknowledge ‘necessary connections between law and morality’. One who is trying to understand legal positivism would no doubt be puzzled by this claim. Nevertheless, I will argue that this is an alternative strategy of legal positivism, and it points to naturalistically oriented view. Although this necessary separation between law and morality, understood naturalistically, strikes one as strengthening the separation, in the end it leads to a weakened notion of necessity. This weakened necessary separation thesis, however, cannot be justified through the so-called claim of the law to legitimate authority, defended by Raz, for it is difficult to answer the question of whether a normally justified but factual authority can gain legitimate authority. Finally, the necessary connection between law and morality in a strong sense can still be justified by the claim of law to correctness, as per Alexy’s argument. (shrink)

The topic of this paper may be introduced by fast zooming in and out of the philosophy of information. In recent years, philosophical interest in the nature of information has been increasing steadily. This has led to a focus on semantic information, and then on the logic of being informed, which has attracted analyses concentrating both on the statal sense in which S holds the information that p (this is what I mean by logic of being informed in the rest (...) of this article) and on the actional sense in which S becomes informed that p. One of the consequences of the logic debate has been a renewed epistemological interest in the principle of information closure (henceforth PIC), which finally has motivated a revival of a skeptical objection against its tenability first made popular by Dretske. This is the topic of the paper, in which I seek to defend PIC against the skeptical objection. If I am successful, this means – and we are now zooming out – that the plausibility of PIC is not undermined by the skeptical objection, and therefore that a major epistemological argument against the formalization of the logic of being informed based on the axiom of distribution in modal logic is removed. But since the axiom of distribution discriminates between normal and non-normal modal logics, this means that a potentially good reason to look for a formalization of the logic of being informed among the non-normal modal logics, which reject the axiom, is also removed. And this in turn means that a formalization of the logic of being informed in terms of the normal modal logic B (also known as KTB) is still very plausible, at least insofar as this specific obstacle is concerned. In short, I shall argue that the skeptical objection against PIC fails, so it is not a good reason to abandon the normal modal logic B as a good formalization of the logic of being informed. (shrink)

Scroggs's theorem on the extensions of S5 is an early landmark in the modern mathematical studies of modal logics. From it, we know that the lattice of normal extensions of S5 is isomorphic to the inverse order of the natural numbers with infinity and that all extensions of S5 are in fact normal. In this paper, we consider extending Scroggs's theorem to modal logics with propositional quantifiers governed by the axioms and rules analogous to the usual ones for (...) ordinary quantifiers. We call them Π-logics. Taking S5Π, the smallest normal Π-logic extending S5, as the natural counterpart to S5 in Scroggs's theorem, we show that all normal Π-logics extending S5Π are complete with respect to their complete simple S5 algebras, that they form a lattice that is isomorphic to the lattice of the open sets of the disjoint union of two copies of the one-point compactification of N, that they have arbitrarily high Turing-degrees, and that there are non-normal Π-logics extending S5Π. (shrink)

Most descriptions of higher-order vagueness in terms of traditional modal logic generate so-called higher-order vagueness paradoxes. The one that doesn't is problematic otherwise. Consequently, the present trend is toward more complex, non-standard theories. However, there is no need for this.In this paper I introduce a theory of higher-order vagueness that is paradox-free and can be expressed in the first-order extension of a normal modal system that is complete with respect to single-domain Kripke-frame semantics. This is the system QS4M+BF+FIN. It (...) corresponds to the class of transitive, reflexive and final frames. With borderlineness defined logically as usual, it then follows that something is borderline precisely when it is higher-order borderline, and that a predicate is vague precisely when it is higher-order vague.Like Williamson's, the theory proposed here has no clear borderline cases in Sorites sequences. I argue that objections that there must be clear borderline cases ensue from the confusion of two notions of borderlineness—one associated with genuine higher-order vagueness, the other employed to sort objects into categories—and that the higher-order vagueness paradoxes result from superimposing the second notion onto the first. Lastly, I address some further potential objections. (shrink)

This paper focuses on the Enkratic principle of rationality, according to which rationality requires that if an agent sincerely and with conviction believes she ought to X, then X-ing is a goal in her plan. We analyze the logical structure of Enkrasia and its implications for deontic logic. To do so, we elaborate on the distinction between basic and derived oughts, and provide a multi-modal neighborhood logic with three characteristic operators: a non-normal operator for basic oughts, a non-normal (...) operator for goals in plans, and a normal operator for derived oughts. We prove two completeness theorems for the resulting logic, and provide a dynamic extension of the logic by means of product updates. We illustrate how this setting informs deontic logic by considering issues related to the filtering of inconsistent oughts, the restricted validity of deontic closure, and the stability of oughts and goals under dynamics. (shrink)

Responsibility has entered the academic discourse of logicians hardly more than few decades ago. I suggest a logical concept of responsibility which employs ideas both from a number of theories belonging to different branches of logic as well from other academic areas. As a comment to this concept, I suggest five steps narrative scenario in order to show how the logical dimension of responsibility emerges from diverse tendencies in logic and other sciences. Here are the five steps briefly stated: Step (...) 1. Developing modal formalisms capable of evaluative analysis of situations (deontic, epistemic and etc.). Step 2. Drawing a conceptual borderline between normal and non-normal (weak) logical systems. Step 3. Using different kinds of models. Step 4. Agent- and action- friendly turn in logic. Step 5. Creating formalisms for modeling different types of agency. An idea advocated here within 5-Steps route to responsibility is that this concept is a complex causal and evaluative (axiological) relation. A logical account may be given for causal and normative aspects of this relation. Unfolding the responsibility back and forth through 5 Steps will result in different concepts. The technicalities are minimized for the sake of keeping the philosophical scope of the paper. For the same reason I also refrain from discussing legal and juridical ramifications of the issue. (shrink)

World semantics for relevant logics include so-called non-normal or impossible worlds providing model-theoretic counterexamples to such irrelevant entailments as (A ∧ ¬A) → B, A → (B∨¬B), or A → (B → B). Some well-known views interpret non-normal worlds as information states. If so, they can plausibly model our ability of conceiving or representing logical impossibilities. The phenomenon is explored by combining a formal setting with philosophical discussion. I take Priest’s basic relevant logic N4 and extend it, on (...) the syntactic side, with a representation operator, (R), and on the semantic side, with particularly anarchic non-normal worlds. This combination easily invalidates unwelcome “logical omniscience” in- ferences of standard epistemic logic, such as belief-consistency and closure under entailment. Some open questions are then raised on the best strategies to regiment (R) in order to express more vertebrate kinds of conceivability. (shrink)

Some philosophers advance the claim that the phenomena of logical omniscience and of the indiscernibility of metaphysical statements, which arise in (certain) interpretations of normal modal logic, provide strong reasons in favour of impossible world approaches. These two specific lines of argument will be presented and discussed in this paper. Contrary to the recent much-held view that the characteristics of these two phenomena provide us with strong reasons to adopt impossible world approaches, the view defended here is that no (...) such ‘knock-down arguments’ do emanate on those grounds. This is not to rule out that there cannot be any other good reasons for assuming impossible world semantics. However, the discussion of a further argument for impossible worlds will suggest that different attempts to argue for them likely present intertwined problems. (shrink)

This paper addresses a recent suggestion that moral particularists can extend their view to countenance default reasons (at a first stab, reasons that are pro tanto unless undermined) by relying on certain background expectations of normality. I first argue that normality must be understood non-extensionally. Thus if default reasons rest on normality claims, those claims won't bestow upon default reasons any definite degree of extensional generality. Their generality depends rather on the contingent distributional aspects of the world, which no theory (...) of reasons should purport to settle. Appeals to default reasons cannot therefore uniquely support particularism. But this argument also implies that if moral generalism entailed that moral reasons by necessity have invariant valence (in the natural extensional sense), it would be a non-starter. Since generalism is not a non-starter, my argument forces us to rethink the parameters of the generalism-particularism debate. Here I propose to clarify the debate by focusing on its modal rather than extensional aspects. In closing, I outline the sort of generalism that I think is motivated by my discussion, and then articulate some worries this view raises about the theoretical usefulness of the label ‘default reason’. -/- [Note: The outline of moral generalism provided in this paper is superseded by those in "Moral Generalism: Enjoy in Moderation" and "A Theory of Hedged Moral Principles".]. (shrink)

How to say no less, no more about conditional than what is needed? From a logical analysis of necessary and sufficient conditions (Section 1), we argue that a stronger account of conditional can be obtained in two steps: firstly, by reminding its historical roots inside modal logic and set-theory (Section 2); secondly, by revising the meaning of logical values, thereby getting rid of the paradoxes of material implication whilst showing the bivalent roots of conditional as a speech-act based on affirmations (...) and rejections (Section 3). Finally, the two main inference rules for conditional, viz. Modus Ponens and Modus Tollens, are reassessed through a broader definition of logical consequence that encompasses both a normal relation of truth propagation and a weaker relation of falsity non-propagation from premises to conclusion (Section 3). (shrink)

Philosophers often make exotic-sounding modal claims, such as: “A timeless world is impossible”, “The laws of physics could have been different from what they are”, “There could have been an additional phenomenal colour”. Otherwise popular empiricist modal epistemologies in the contemporary literature cannot account for whatever epistemic justification we might have for making such modal claims. Those who do not, as a result of this, endorse scepticism with respect to their epistemic status typically suggest that they can be justified but (...) have yet to develop some distinct, workable theory of how. That is, they endorse a form of non-uniformism about the epistemology of modality, according to which claims about philosophically interesting modal matters need to be justified differently from e.g. everyday or scientific modal claims, but they fail to provide any more detail. This article aims to fill this gap by outlining how such a non-uniformist view could be spelled out and what story about philosophically interesting modal justification it could contain. (shrink)

We defend the view of epistemic `must' as weak and claim that `must p' is used when the speaker does not know p. Novel arguments for this well-known account are provided. The theory is extended to epistemic future.

This qualitative study utilized the narrative approach to determine the advantages and disadvantages of printed modular distance learning in terms of lesson preparation and assessment of students’ outputs based on the experiences of six teachers in a public elementary school in Negros Occidental in the School Year 2021-2022, the strategies they employed in lesson preparation and assessment of students’ outputs, and the insights they gained into their strategies when they engaged in printed modular distance learning modality. The findings reveal the (...) following: (a) Modules are readily available for the only advantage of the printed modular distance learning in terms of lesson preparation; (b) Students’ outputs are well-thought-out for the only advantage of the printed modular distance learning in terms of assessment of students’ outputs; (c) Lessons are inappropriate and lesson preparation is delayed for the disadvantages of printed modular distance learning in terms of lesson preparation; (d) The authenticity of students’ outputs is dubitable for the only disadvantage of printed modular distance learning; (e) Be creative and flexible for the strategies employed by teachers in lesson preparation; (f) Verify the authenticity for the only strategy employed by teachers in the assessment of students’ outputs; (g) Flexibility and creativity may make lesson preparation easy for the insights gained by teachers into their strategies in terms of lesson preparation; and (h) Time management and appropriate assessment tools may facilitate assessment of students’ outputs for the insights gained by teachers into their strategies in terms of assessment of students’ outputs. The teachers were able to prepare their lessons and assess their students’ outputs despite the drawbacks of printed modular distance learning with effective strategies. (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)

There is a common approach to metaphysical disputes, which takes language as its starting point, and leads to a view about the range of acceptable metaphysical positions in any such dispute. I argue that this approach rests on accepting what I call the Strong Linguistic Thesis (SLT). In the metaphysical debate about time I argue that the new B-theory has rejected SLT, and for good reasons. The metaphysical debate about modality parallels the early metaphysical debate about time. I argue that (...) a position analogous to the new B-theory of time is available in the modal debate, and has some advantages over its rivals. (shrink)

Nella sua straordinaria opera scientifica, Franco Selleri si è sempre opposto alla rinuncia alla comprensione della struttura della realtà e della natura degli oggetti fisici, che egli considera come l’elemento caratterizzante delle principali teorie della fisica del Novecento e che è stata stigmatizzata da Karl Popper come tesi della “fine della strada in fisica”. Sin dalla fine degli anni ’60, egli ha sviluppato quella riflessione critica nei confronti delle teorie fondamentali della fisica moderna, in particolar modo della teoria delle particelle (...) elementari e della meccanica quantistica, e in un secondo tempo delle teorie relativistiche, che contraddistingue il suo programma di ricerca. Nel corso della sua intensa e infaticabile attività scientifica, Selleri è entrato in proficuo contatto con molti grandi fisici e filosofi della scienza, instaurando un intenso dialogo critico con Louis de Broglie, John Bell e Karl Popper. Le sue originali e non convenzionali ricerche lo hanno portato a risultati significativi non solo nell’ambito dei fondamenti della fisica, ma anche della storia e della filosofia della fisica. Per questo abbiamo voluto dedicare un numero speciale di Isonomia al nostro impareggiabile amico e collega, sia per la sua passione instancabile e la sua profonda conoscenza dei fondamenti formali, concettuali e filosofici delle teorie della fisica contemporanea, sia e forse ancor più come maestro di una prospettiva perennemente critica che egli ha sempre seguito e proposto con particolare rigore ed estrema determinazione. (shrink)

This paper proposes a new model of graded modal judgment. It begins by problematizing the phenomenon: given plausible constraints on the logic of epistemic modality, it is impossible to model graded attitudes toward modal claims as judgments of probability targeting epistemically modal propositions. This paper considers two alternative models, on which modal operators are non-proposition-forming: (1) Moss (2015), in which graded attitudes toward modal claims are represented as judgments of probability targeting a “proxy” proposition, belief in which would underwrite belief (...) in the modal claim. (2) A model on which graded attitudes toward modal claims are represented as judgments of credence taking as their objects (non-propositional) modal representations (rather than proxy propositions). The second model, like Moss’ model, is shown to be semantically and mathematically tractable. The second model, however, can be straightforwardly integrated into a plausible model of the role of graded attitudes toward modal claims in cognition and normative epistemology. (shrink)

According to the simple modal account of essence, an object has a property essentially just in case it has it in every world in which it exists. As many have observed, the simple modal account is implausible for a number of reasons. This has led to various proposals for strengthening the account, for example, by adding a restriction to the intrinsic or sparse properties. I argue, however, that these amendments to the simple modal account themselves fail. Drawing on lessons from (...) these failures, I propose a new version of a modal account, inspired by Ruth Barcan Marcus's defense of the coherence of quantified modal logic, according to which an object has a property essentially just in case (i) it has it in every world in which it exists, (ii) the property is discriminating (or non-trivial), and (iii) the property is qualitative. The resulting account of essence does not face any of the standard objections other accounts face, and I defend it from other potential objections. (shrink)

This note identifies and corrects some problems in developments of the thesis that predictive expressions, such as English "will", are modals. I contribute a new argument supporting Cariani and Santorio's recent claim that predictive expressions are non-quantificational modals. At the same time, I improve on their selectional semantics by fixing an important bug. Finally, I show that there are benefits to be reaped by integrating the selection semantics framework with standard ideas about the future orientation of modals.

Well-known results due to David Makinson show that there are exactly two Post complete normal modal logics, that in both of them, the modal operator is truth-functional, and that every consistent normal modal logic can be extended to at least one of them. Lloyd Humberstone has recently shown that a natural analog of this result in congruential modal logics fails, by showing that not every congruential modal logic can be extended to one in which the modal operator is (...) truth-functional. As Humberstone notes, the issue of Post completeness in congruential modal logics is not well understood. The present article shows that in contrast to normal modal logics, the extent of the property of Post completeness among congruential modal logics depends on the background set of logics. Some basic results on the corresponding properties of Post completeness are established, in particular that although a congruential modal logic is Post complete among all modal logics if and only if its modality is truth-functional, there are continuum many modal logics Post complete among congruential modal logics. (shrink)

In, Kosterec attempts to provide ``model-theoretic proofs'' of certain theses involving the normal modal operators $\Diamond$ and $\square$ and the truth-in-fiction operator $F$ which he then goes on to show have counterexamples in Kripke models. He concludes from this that the embedding of modal logic under the truth-in-fiction operator is unsound. We show instead that it is the ``model-theoretic proofs'' that are themselves unsound, involving illicit substitution, a subtle error that nevertheless allows us to draw an important conclusion about (...) intensional contexts and semantic equivalences. (shrink)

Some central epistemological notions are expressed by sentential operators O that entail the possibility of knowledge in the sense that 'Op' entails 'It is possible to know that p'. We call these modal-epistemological notions. Using apriority and being in a position to know as case studies, we argue that the logics of modal epistemological notions are extremely weak. In particular, their logics are not normal and do not include any closure principles.

Modal Meinongianism is a form of Meinongianism whose main supporters are Graham Priest and Francesco Berto. The main idea of modal Meinongianism is to restrict the logical deviance of Meinongian non-existent objects to impossible worlds and thus prevent it from “contaminating” the actual world: the round square is round and not round, but not in the actual world, only in an impossible world. In the actual world, supposedly, no contradiction is true. I will show that Priest’s semantics, as originally formulated (...) in Towards Non-being, tell us something different. According to certain models, there are true contradictions in the actual world. Berto and Priest have noticed this unexpected consequence and have suggested a solution, but I will show that their solution is highly questionable. In the last section of this paper, I will introduce a new and simpler version of modal Meinongianism that avoids the problem. (shrink)

Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advantages when dealing with the (...) so-called paradoxes of higher-order vagueness. We offer a proposal that makes strides on both issues. We argue that the intuitionist’s characteristic rejection of any third alethic value alongside true and false is best elaborated by taking the normal modal system S4M to be the sentential logic of the operator ‘it is clearly the case that’. S4M opens the way to an account of higher-order vagueness which avoids the paradoxes that have been thought to infect the notion. S4M is one of the modal counterparts of the intuitionistic sentential calculus and we use this fact to explain why IPC is the correct sentential logic to use when reasoning with vague statements. We also show that our key results go through in an intuitionistic version of S4M. Finally, we deploy our analysis to reply to Timothy Williamson’s objections to intuitionistic treatments of vagueness. (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 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)

The philosophy of necessity and possibility has flourished in the last half-century, but much less attention has been paid to the question of how we know what can be the case and what must be the case. Many friends of modal metaphysics and many enemies of modal metaphysics have agreed that while empirical discoveries can tell us what is the case, they cannot shed much light on what must be the case or on what non-actual possibilities there are. In this (...) paper, in contrast, I discuss and defend naturalistic approaches to discovering the facts about necessity and possibility. After some remarks about what methodological naturalism in philosophy might amount to, I argue that naturalistic method in modal investigations may not need to be particularly revisionary of much of what is currently being done in modal investigation. I then discuss a number of respects in which a naturalistic orientation in modal investigation may improve on our current epistemic situation. (shrink)

The practice of scientific modelling often resorts to hypothetical, false, idealised, targetless, partial, generalised, and other types of modelling that appear to have at least partially non-actual targets. In this paper, I will argue that we can avoid a commitment to non-actual targets by sketching a framework where models are understood as having networks of possibilities as their targets. This raises a further question: what are the truthmakers for the modal claims that we can derive from models? I propose that (...) we can find truthmakers for the modal claims derived from models in actuality, even in the case of supposedly non-actual targets. I then put this framework to use by examining a case study concerning the modelling of superheavy elements. (shrink)

The modal ontological argument (MOA) proceeds from God’s possible existence to God’s actual existence. A prominent objection to the MOA is that it suffers from a symmetry problem: an exactly parallel modal ontological argument can be given for God's non-existence. Several attempts have been made to break the symmetry between the arguments. This draft is a mostly comprehensive survey of those attempts. -/- The draft was initially written as a supplement to the 2024 Summer edition of the SEP entry on (...) Ontological Arguments. However, the draft is not included in the SEP entry. (shrink)

There has been much discussion of powers or real dispositions in the past decade, but there remains an issue that has been inadequately treated. This concerns the precise modal value that comes with dispositionality. We contend in this paper that dispositionality involves a non-alethic, sui generis, irreducible modality. Dispositions only tend towards their manifestations; they do not necessitate them. Tendency is, of course, a dispositional term itself, so this last statement offers little by way of illumination. But given our thesis (...) on the irreducible nature of dispositionality, we maintain that it cannot be explicated correctly in non-dispositional terms. Nevertheless, we all have experience of dispositionality at work, through the exercise or our own powers and the action of other powers upon us. The notion of dispositionality that we acquire is one that involves a modality stronger than pure contingency but weaker than necessity. The recognition of this distinct modal value for dispositionality is one of the biggest oversights in the growing literature in the area. Yet it is there for all to see in even the most mundane example. (shrink)

The quantified argument calculus (Quarc) is a novel logic that departs in several ways from mainstream first-order logic. In particular, its quantifiers are not sentential operators attached to variables, but attach to unary predicates to form arguments – quantified arguments – of other predicates. Furthermore, Quarc includes devices to account for anaphora, active-passive-voice distinctions, and sentence- versus predicate-negation. While this base system has already been shown to be sound and complete, modal extensions still lack such results. The present paper fills (...) this lacuna by developing a modal extension of Quarc, including identity. The semantics will invalidate the Quarc-analogues of the Barcan-formula and its converse, as well as treat identity as contingent by default. Furthermore, an unlabelled Gentzen-style natural deduction system will be presented, which includes the full expressive power of Quarc. It will be shown to be strongly sound and complete with respect to relational frames. The paper closes off with considerations on how to extend the system to cover other normal modal logics as well as extensions to suitable three-valued semantics that capture relevant types of presupposition-failure. (shrink)

Time and modality show remarkable similarities. Each of the most discussed theories in philosophy of time finds an analogous counterpart in modal metaphysics, suggesting that the parallel between the two notions is metaphysically deep. This chapter offers a brief overview of their analogies. Section 1 addresses the analogy between presentism and actualism. Section 2 explores the analogy between non-presentist theories and possibilism. Section 3 discusses the analogy between temporal and modal persistence.

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)

Abstract Timothy Williamson has recently proposed to undermine modal skepticism by appealing to the reducibility of modal to counterfactual logic ( Reducibility ). Central to Williamson’s strategy is the claim that use of the same non-deductive mode of inference ( counterfactual development , or CD ) whereby we typically arrive at knowledge of counterfactuals suffices for arriving at knowledge of metaphysical necessity via Reducibility. Granting Reducibility, I ask whether the use of CD plays any essential role in a Reducibility-based reply (...) to two kinds of modal skepticism. I argue that its use is entirely dispensable, and that Reducibility makes available replies to modal skeptics which show certain propositions to be metaphysically necessary by deductive arguments from premises the modal skeptic accepts can be known. Content Type Journal Article Pages 1-19 DOI 10.1007/s11098-011-9784-4 Authors Juhani Yli-Vakkuri, Wolfson College, Oxford University, Oxford, OX2 6UD UK Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116. (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)

The Brock-Rosen problem has been one of the most thoroughly discussed objections to the modal fictionalism bruited in Gideon Rosen’s ‘Modal Fictionalism’. But there is a more fundamental problem with modal fictionalism, at least as it is normally explained: the position does not resolve the tension that motivated it. I argue that if we pay attention to a neglected aspect of modal fictionalism, we will see how to resolve this tension—and we will also find a persuasive reply to the Brock-Rosen (...) objection. Finally, I discuss an alternative reading of Rosen, and argue that this position is also able to fend off the Brock-Rosen objection. (shrink)

Kriegel described the problem of intentional inexistence as one of the ‘perennial problems of philosophy’, 307–340, 2007: 307). In the same paper, Kriegel alluded to a modal realist solution to the problem of intentional inexistence. However, Kriegel does not state by name who defends the kind of modal realist solution he has in mind. Kriegel also points out that even what he believes to be the strongest version of modal realism does not pass the ‘principle of representation’ and thus modal (...) realism is not an adequate solution to the problem of intentional inexistence. In this paper, I respond to Kriegel by defending a modal realist solution that he did not consider in 2007, called ‘extended modal realism’. EMR is a version of modal realism where possible worlds are not completely isolated as they are under the Lewisian model. Rather, under EMR worlds are, in a way, spatiotemporally related. The fact EMR worlds are related allows EMR to sufficiently pass the principle of representation and thus can be deemed a legitimate solution to the problem of intentional inexistence. I conclude that either EMR can pass the principle of representation in some cases or, and I think the more sensible option, we give up on the principle of representation altogether. (shrink)

Imperialism seems to be deeply antithetical to democracy. Yet, at least one form of imperialism – what I call “hands-off imperialism" – seems to be perfectly compatible with the kind of self-governance commonly thought to be the hallmark of democracy. The solution to this puzzle is to recognize that democracy involves more than self-governance. Rather, it involves what I call self-rule. Self-rule is an example of what Philip Pettit has called a modally demanding value. Modally demanding values are, roughly, values (...) the instantiation of which depends not only on what actually happens, but on what would happen in certain non-actual circumstances. Self-rule is the modally demanding counterpart of self-governance, since it requires, not merely that the members of a state actually govern themselves, but that they would continue to do so across a range of non-actual situations. Moreover, the value of self-rule (and hence democracy) is not reducible to the value of self-governance. Understanding the modally demanding character of democracy allows us to appreciate what is democratically objectionable about occupation by a foreign power, even if there is no prospect of the foreign power intervening in the governance of the occupied state by its members. (shrink)

The fourteen papers in this collection offer a variety of original contributions to the epistemology of modality. In seeking to explain how we might account for our knowledge of possibility and necessity, they raise some novel questions, develop some unfamiliar theoretical perspectives, and make some intriguing proposals. Collectively, they advance our understanding of the field. In Part I of this Introduction, I give some general background about the contemporary literature in the area, by sketching a timeline of the main tendencies (...) of the past twenty-five years or so, up to the present debates. Next, I focus on four features that largely characterize the latest literature, and the papers in the present collection in particular: (i) an endorsement of the importance of essentialism; (ii) a shift to a “metaphysics-first” approach to modal epistemology; (iii) a focus on metaphysical modality as opposed to other kinds of modality; and (iv) a preference for non-uniform modal epistemology. In Part II, I present the individual papers in the volume. These are organized around the following four chapters, based on their topic: (A) Skepticism & Deflationism; (B) Essentialism; (C) Non-Essentialist Accounts; (D) Applications. -/- LIST OF CONTRIBUTORS: Francesco Berto; Stephen Biggs & Jessica Wilson; Justin Clark-Doane; Philip Goff; Bob Hale; Frank Jackson; Mark Jago; Boris Kment; Antonella Mallozzi; Graham Priest; Gabriel Rabin; Amie Thomasson; Anand Vaidya & Michael Wallner; Jennifer Wang. -/- The volume is dedicated to the memory of Bob Hale. -/- . (shrink)

There are three theories in the epistemology of modality that have received sustained attention over the past 20 years: conceivability-theory, counterfactual-theory, and deduction-theory. In this paper we argue that all three face what we call the problem of modal epistemic friction. One consequence of the problem is that for any of the three accounts to yield modal knowledge, the account must provide an epistemology of essence. We discuss an attempt to fend off the problem within the context of the internalism (...) versus externalism debate about epistemic justification. We then investigate the effects that the PMEF has on reductive and non-reductive theories of the relation between essence and modality. (shrink)

The paper outlines and immediately discusses the so-called ‘soft’ impossibility, i.e., non-logical impossibility generated by modal realism. It will be shown that although in a particular case genuine modal realism, straightforwardly applied, deems impossible a proposition that other philosophers have claimed to be (intuitively) possible, there is a variety of methodologically acceptable moves available in order to avoid the problem. The impossibility at issue is the existence of island universes. Given the Lewisian analysis there are three points at which we (...) might try to square genuine modal realism with such a controversial and problematic claim of (im)possibility, namely: a) the contraction of our pre-theoretical opinions about possibility, b) the revision of some Lewisian definitions and/or c) the extension of our ontological commitments. I shall look at each of these approaches applied to the problematic case. (shrink)