In 2001, W. Carnielli and Marcos considered a 3-valued logic in order to prove that the schema ϕ ∨ (ϕ → ψ) is not a theorem of da Costa’s logic Cω. In 2006, this logic was studied (and baptized) as G'3 by Osorio et al. as a tool to define semantics of logic programming. It is known that the truth-tables of G'3 have the same expressive power than the one of Łukasiewicz 3-valued logic as well as the one of Gödel (...) 3-valued logic G3. From this, the three logics coincide up-to language, taking into acccount that 1 is the only designated truth-value in these logics. -/- From the algebraic point of view, Canals-Frau and Figallo have studied the 3-valued modal implicative semilattices, where the modal operator is the well-known Moisil-Monteiro-Baaz Δ operator, and the supremum is definable from this. We prove that the subvariety obtained from this by adding a bottom element 0 is term-equivalent to the variety generated by the 3-valued algebra of G'3. The algebras of that variety are called G'3-algebras. From this result, we obtain the equations which axiomatize the variety of G'3-algebras. Moreover, we prove that this variety is semisimple, and the 3-element and the 2-element chains are the unique simple algebras of the variety. Finally an extension of G'3 to first-order languages is presented, with an algebraic semantics based on complete G'3-algebras. The corresponding soundness and completeness theorems are obtained. (shrink)

Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for their (...) primitive operations arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of _weak implicative semilattices_, whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus. (shrink)

The paper defends the view that that a significant part of metaphysics should be understood as conceptual engineering, and explores its epistemological advantages and metaphysical implications. It discusses the challenge raised by moderate modal skepticism, which points out the lack of reliable methods for verifying modal statements through thought experiments. As I argue, a normative stance on metaphysical methodology, understanding it as engaging in conceptual engineering project, justifies the use of this method. By adopting an approach where the (...) method of cases offers reasons for adopting specific normative constraints on concept usage, the method becomes justifiable. Consequently, it can be employed to justify the revision of conceptual schemes and, in turn, validate certain modal claims about entities falling under the scrutinized concepts. The paper explores how this approach can methodologically enrich conceptual engineering-focused perspectives in metaphysics and examines its metaphysical consequences. In particular, it demonstrates that despite the mind-dependency of the method of cases results, it still leaves room for a metaphysically realistic viewpoint. (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.

Sider (2011, 2013) proposes a reductive analysis of metaphysical modality—‘(modal) Humeanism’—and goes on to argue that it has interesting epistemological and methodological implications. In particular, Humeanism is supposed to undermine a class of ‘arguments from possibility’, which includes Sider's (1993) own argument against mereological nihilism and Chalmers's (1996) argument against physicalism. I argue that Sider's arguments do not go through, and moreover that we should instead expect Humeanism to be compatible with the practice of arguing from possibility in philosophy.

Modal intuitions are the primary source of modal knowledge but also of modal error. According to the theory of modal error in this paper, modal intuitions retain their evidential force in spite of their fallibility, and erroneous modal intuitions are in principle identifiable and eliminable by subjecting our intuitions to a priori dialectic. After an inventory of standard sources of modal error, two further sources are examined in detail. The first source - namely, (...) the failure to distinguish between metaphysical possibility and various kinds of epistemic possibility - turns out to be comparatively easy to untangle and poses little threat to intuition-driven philosophical investigation. The second source is the local misunderstanding of one's concepts . This pathology may be understood on analogy with a patient who is given a clean bill of health at his annual check-up, despite his having a cold at the time of the check-up: although the patient's health is locally disrupted, his overall health is sufficiently good to enable him to overcome the cold without external intervention. Even when our understanding of certain pivotal concepts has lapsed locally, our larger body of intuitions is sufficiently reliable to allow us, without intervention, to ferret out the modal errors resulting from this lapse of understanding by means of dialectic and/or a process of a priori reflection. This source of modal error, and our capacity to overcome it, has wide-ranging implications for philosophical method - including, in particular, its promise for disarming skepticism about the classical method of intuition-driven investigation itself. Indeed, it is shown that skeptical accounts of modal error are ultimately self-defeating. (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)

Modal intuitions are not only the primary source of modal knowledge but also the primary source of modal error. An explanation of how modal error arises — and, in particular, how erroneous modal intuitions arise — is an essential part of a comprehensive theory of knowledge and evidence. This chapter begins with a summary of certain preliminaries: the phenomenology of intuitions, their fallibility, the nature of concept-understanding and its relationship to the reliability of intuitions, and (...) so forth. It then identifies two sources of modal error: the first has to do with the failure to distinguish between metaphysical possibility and various kinds of epistemic possibility; the second, with the local misunderstanding of one's concepts. The first source of error is widely misunderstood; the second source has not been discussed in philosophical literature. This source of modal error, and the potential to overcome it, has wide-ranging implications for philosophical method. The failure to understand these sources of modal error has recently led to sceptical accounts of intuition and modal error, which are, ultimately self-defeating. (shrink)

This manuscript presents an English translation of the work titled “Begründung Einer Strengen Implikation” by the German logician and mathematician Wilhelm Ackermann (1896-1962), first published in June 1956.

The thesis of this paper is that the capacity to think of one’s perceptions as cross-modally integrated is incompatible with a reductionist account of the self. In §2 I distinguish three versions of the argument from cross-modality. According to the ‘unification’ version of the argument, what needs to be explained is one’s capacity to identify an object touched as the same as an object simultaneously seen. According to the ‘recognition’ version, what needs to be explained is one’s capacity, having once (...) seen an object, to reidentify that same object by touch alone. According to the ‘objectivity’ version, what needs to be explained is one’s capacity to think of one’s perceptions in different modalities as perceptions of one and the same object. The third version seems to establish that one must conceive of oneself substantially, as the numerically identical owner of one’s experiences, a conclusion in agreement with recent work in developmental psychology claiming to show that an infant’s cross-modal capacities are essentially implicated in their development of a sense of self. There is further work to be done if this is to be tumed into an argument against reductionism: there is no swift route from the epistemology of self-consciousness to the metaphysics of the self. In the §3, I will claim that there is, nevertheless, an argument linking the two. What I propose is an argument derived, not from the token-reflexive rule for the first-person, but resting on its anaphoric behaviour spanning intensional operators. (shrink)

Kagan argues that human beings who are neither persons nor even potential persons — if their impairment is independent of genetic constitution — are modal persons: individuals who might have been persons. Moreover, he proposes a view according to which both personhood and modal personhood are sufficient for counting more, morally, than nonhuman animals. In response to this proposal, I raise one relatively minor concern about Kagan's reasoning — that he judges too quickly that insentient beings can have (...) interests — before engaging the appeal to modal personhood. I challenge the thesis that modal personhood is relevant to one's moral status, first, by way of analogy to a kicker who misses a field goal though he might have made it; second, by casting doubt on implications for two impaired infants ; and, finally, by examining implications for dogs who would count as modal persons when genetic enhancements are capable of transforming them into persons. (shrink)

Cohen (2023) takes a fair and measured approach to the question of what ChatGPT means for bioethics. The hype cycles around AI often obscure the fact that ethicists have developed robust frameworks...

Davies argues that the ontology of artworks as performances offers a principled way of explaining work-relativity of modality. Object oriented contextualist ontologies of art (Levinson) cannot adequately address the problem of work-relativity of modal properties because they understand looseness in what counts as the same context as a view that slight differences in the work-constitutive features of provenance are work-relative. I argue that it is more in the spirit of contextualism to understand looseness as context-dependent. This points to the (...) general problem—the context of appreciation is not robust enough to ground modal intuitions about objective entities. In general, when epistemology dictates ontology there is always a threat of anti-realism, scepticism and relativism. Davies also appeals to the modality principle—an entity’s essential properties are all and only its constitutive properties. Davies understands essentiality in a traditional way: a property P is an essential property of an object o iff o could not exist and lack P. Kit Fine has recently made a convincing case for the view that the notion of essence is not to be understood in modal terms. I explore some of the implications of this view for Davies’ modal argument for the performance theory. (shrink)

One type of deflationism about metaphysical modality suggests that it can be analysed strictly in terms of linguistic or conceptual content and that there is nothing particularly metaphysical about modality. Scott Soames is explicitly opposed to this trend. However, a detailed study of Soames’s own account of modality reveals that it has striking similarities with the deflationary account. In this paper I will compare Soames’s account of a posteriori necessities concerning natural kinds with the deflationary one, specifically Alan Sidelle’s account, (...) and suggest that Soames’s account is vulnerable to the deflationist’s critique. Furthermore, I conjecture that both the deflationary account and Soames’s account fail to fully explicate the metaphysical content of a posteriori necessities. Although I will focus on Soames, my argument may have more general implications towards the prospects of providing a meaning-based account of metaphysical modality. (shrink)

This paper presents a recent formalization of a Henkin-style completeness proof for the propositional modal logic S5 using the Lean theorem prover. The proof formalized is close to that of Hughes and Cresswell, but the system, based on a different choice of axioms, is better described as a Mendelson system augmented with axiom schemes for K, T, S4, and B, and the necessitation rule as a rule of inference. The language has the false and implication as the only primitive (...) logical connectives and necessity as the only primitive modal operator. The full source code is available online and has been typechecked with Lean 3.4.2. (shrink)

In this paper I introduce the idea of a higher-order modal logic—not a modal logic for higher-order predicate logic, but rather a logic of higher-order modalities. “What is a higher-order modality?”, you might be wondering. Well, if a first-order modality is a way that some entity could have been—whether it is a mereological atom, or a mereological complex, or the universe as a whole—a higher-order modality is a way that a first-order modality could have been. First-order modality is (...) modeled in terms of a space of possible worlds—a set of worlds structured by an accessibility relation, i.e., a relation of relative possibility—each world representing a way that the entire universe could have been. A second-order modality would be modeled in terms of a space of spaces of (first-order) possible worlds, each space representing a way that (first-order) possible worlds could have been. And just as there is a unique actual world which represents the way that things actually are, there is a unique actual space which represents the way that first-order modality actually is. -/- One might wonder what the accessibility relation itself is like. Presumably, if it is logical or metaphysical modality that is being dealt with, it is reflexive; but is it also symmetric, or transitive? Especially in the case of metaphysical modality, the answer is not clear. And whichever of these properties it may or may not have, could that itself have been different? Could at least some rival modal logics represent different ways that first-order modality could have been? -/- To be clear, the idea behind my proposal is not just that some things which are possible or necessary might not have been so at the first order, as determined by the actual accessibility relation, but also that the actual accessibility relation, and hence the nature or structure of actual modality, could have been different at some higher order of modality. Even if the accessibility relation is actually both symmetric and transitive, perhaps it could (second-order) have been otherwise: There is a (second-order) possible space of worlds in which it is different, where it fails to be symmetric, or transitive. We must, therefore, introduce the notion of a higher-order accessibility relation, one that in this case relates spaces of first-order worlds. The question then arises as to whether that relation is symmetric, or transitive. We can then consider third-order modalities, spaces of spaces of spaces of possible worlds, where the second-order accessibility relation differs from how it actually is. I can see no reason why there should be a limit to this hierarchy of higher-order modalities, any more than I can see a reason why there should be a limit to the hierarchy of higher-order properties. There will thus be an infinity of orders, one for each positive integer, and each order will have an accessibility relation of its own. To keep things as clear as possible, a space of first-order points (i.e., of possible worlds) shall be called a galaxy, a space of second-order points, a universe, and a space of any higher order, a cosmos. However, to keep things as simple as possible, in what follows I will deal with but a single cosmos, and hence will not deal with modalities higher than the third order. -/- The accessibility relation is not the only thing that might be thought to vary between spaces of worlds: Perhaps the contents of the spaces can vary as well. While I presume that the contents of the worlds themselves remain constant—it makes doubtful sense to suppose that in one space some entity e exists in a world w and in another space e doesn’t exist in that same world w—we may suppose that different spaces differ as to which worlds they contain, just as different worlds may differ as to which objects they contain. Thus we might have a higher-order analogue of a variable-domain modal logic. There seem, then, to be three ways in which spaces can differ: First, as to the properties of the accessibility relation; second, as to which worlds the relation relates; and third, as to which worlds or spaces are parts of their domains. -/- The paper will be structured as follows. In Section 2 I provide some reasons why one might want to pursue this kind of project in the first place. In Section 3 I outline the syntax and semantics of my proposed logic. Section 4 covers semantic tableaux for this system; and after giving the rules for their construction, I construct a few of them myself to establish some logical consequences of the system and give the reader a feel for how it works. In Sections 5, 6 and 7 I explore some of its potential philosophical implications for areas besides logic, namely the philosophy of language; metaphysics, including the metaphysics of modality and the philosophy of time, and finally the philosophy of religion, before concluding the paper in Section 8. (shrink)

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)

Perception can provide us with a privileged source of evidence about the external world – evidence that makes it rational to believe things about the world. In Reasons First, Mark Schroeder offers a new view on how perception does so. The central motivation behind Schroeder’s account is to offer an answer to what evidence perception equips us with according to which it is what he calls world-implicating but non-factive, and thereby to glean some of the key advantages of both externalism (...) and internalism, respectively. He answers this motivation by developing a more specific view that he calls the Apparent Factive Attitude view, which pairs an answer to what evidence is provided by a perceptual experience with an answer to why having that perceptual experience provides you with that evidence. In this paper we advance two interconnected problems for Schroeder’s Apparent Factive Attitude view. A traditional intuitive judgment that often motivates internalists is the idea that internal duplicates must necessarily be equally rational in whatever beliefs they have. Schroeder’s arguments rely on a weaker claim - that people who are both internal and historical external duplicates but differ only in the veridicality of a single perceptual experience must be equally rational in whatever beliefs they have. In this way he preserves what he argues to be a more compelling internalist intuition. But our arguments will show that Schroeder’s view is committed to denying an even more compelling internalist intuition yet - that internal duplicates must have the same phenomenology. (shrink)

An account of the nature of knowledge must explain the value of knowledge. I argue that modal conditions, such as safety and sensitivity, do not confer value on a belief and so any account of knowledge that posits a modal condition as a fundamental constituent cannot vindicate widely held claims about the value of knowledge. I explain the implications of this for epistemology: We must either eschew modal conditions as a fundamental constituent of knowledge, or retain the (...) modal conditions but concede that knowledge is not more valuable than that which falls short of knowledge. This second horn—concluding that knowledge has no distinctive value—is unappealing since it renders puzzling why so much epistemological theorising focuses on knowledge, and why knowledge seems so important. (shrink)

In response to paradigm shifts in education, teacher education institutions have increasingly adopted flexible learning modalities such as online courses, blended learning approaches, and personalized instruction to meet the diverse needs of students and prepare educators for the demands of modern classrooms. This study used a mixed-method research design to gain a comprehensive understanding of the flexible teaching and learning modalities it brought to mathematics teacher educators (MTEs) and learners in a state university in West Philippines. Since ethical considerations preclude (...) random sampling, the study comprised nonrandom participants using purposive sampling, where 189 learners were surveyed, and six MTEs and 16 learners were interviewed. A researcher-made interview guide was prepared to describe the flexible teaching and learning modalities and opportunities of the MTEs. Also, a researcher-made questionnaire was used to describe the learners’ general assessment of the flexible teaching and learning modalities in mathematics education. Quantitative data were gathered online, while qualitative data were gathered through interviews. Results showed that flexible teaching-learning approaches have implications for education, overcoming barriers, and promoting engagement. The findings highlight the importance of technology integration, inclusive assessment modalities, infrastructure support, and professional development opportunities in enhancing the quality and accessibility of flexible teaching and learning, ultimately leading to inclusive educational environments. Therefore, the educational institution must adopt flexible instructional modalities, emphasize diverse assessment methods, and personalize the learning experience by integrating online platforms and various assessments for effective mathematics instruction. (shrink)

Recently, the relationship between evolutionary ecology and perceptual science has received renewed attention under perception-mediated selection, a mode of natural selection linking perceptual saliency, rather than veridicality, to fitness. The Interface Theory of Perception (ITP) has been especially prominent in claiming that an organism’s perceptual interface is populated by icons, which arise as a function of evolved, species-specific perceptual interfaces that produce approximations of organisms’ environments through fitness-tuned perceptions. According to perception-mediated selection, perception and behavior calibrate one another as organisms’ (...) capacities to experience and know the objects and properties of their environments lead to responses highlighting certain environmental features selected for survival. We argue this occurs via the Umwelt/Umgebung distinction in ethology, demonstrating that organisms interact with their external environments (Umgebung) through constructed perceptual schema (Umwelt) that produce constrained representations of environmental objects and their properties. Following Peircean semiotics, we claim that ITP’s focus on icons as saliency-simplified markers corresponds to biosemiotics’ understanding of perceptual representations, which manifest as iconic (resembling objects), indexical (referring), or symbolic (arbitrary) modalities, which provide for organisms’ semiotic scaffolding. We argue that ITP provides the computational evidence for biosemiotics’ notion of iconicity, while biosemiotics provides explanation within ITP for how iconicity can build up into indices and symbols. The common contention of these separate frameworks that the process of perception tracks saliency rather than veridicality suggests that digital/dyadic perceptual strategies will be outcompeted by their semiotic/triadic counterparts. This carries implications for evolutionary theory as well as theories of cognition. (shrink)

My aim is to propose a better way to understand moral demandingness: a counterfactual view that requires us to consider the demands that moral theories make across other possible worlds. Seemingly, the demandingness of any moral theory or principle should be evaluated in terms of that theory’s general demandingness. This, in turn, implies that we ought to be concerned about the possible demandingness of moral theories and not just about how demanding they actually are. This counterfactual view might also have (...) some surprising implications about how demanding commonsense morality really is. After all, commonsense morality might be extremely demanding in many possible worlds. This consideration, in turn, risks undermining the commonsense moral theorist's ability to make purely cost-based demandingness objections against consequentialism, giving us strong reasons to worry about the purely cost-based demandingness objection’s viability in general. (shrink)

The sample space of the chance distribution at a given time is a class of possible worlds. Thanks to this connection between chance and modality, one’s views about modal space can have significant consequences in the theory of chance and can be evaluated in part by how plausible these implications are. I apply this methodology to evaluate certain forms of modal contingentism, the thesis that some facts about what is possible are contingent. Any modal contingentist view that (...) meets certain conditions that I specify generates difficulties in the philosophy of chance, including a problem usually associated with Humeanism that is known as ‘the problem of undermining futures’. I consider two well-known versions of modal contingentism that face this difficulty. The first version, proposed by Hugh Chandler and Nathan Salmon, rests on an argument for the claim that many individuals have their modal features contingently. The second version is motivated by the thesis that the existence of a possible world depends on the existence of the contingent individuals inhabiting it, and that many worlds are therefore contingent existents. (shrink)

The pandemic has clearly affected higher education institutions through the transition of its learning modality to online. Furthermore, this study investigates the relationship between social support and burnout among college students amidst the COVID-19 pandemic. Utilizing descriptive-correlational design, the result of the statistical analysis indicated that social support and academic burnout has a significant relationship (r=0.158). Implications of the study were discussed and recommendations for future research were suggested.

This paper explores the physical and metaphysical implications of time travel, focusing on the possibility of changing the past, through a comparative analysis of David Lewis' modal realism and Everett's many-worlds interpretation of quantum mechanics. The existence of closed timelike curves (CTCs) in certain solutions to Einstein's field equations provides a theoretical basis for the possibility of backwards time travel, but this leads to a range of paradoxes, most notably the grandfather paradox. David Lewis argues that time travel must (...) maintain consistency and that the past cannot be changed, even if time travel were possible. His view is supported by his modal realism, which posits the existence of a plurality of possible worlds. In contrast, Everett's many-worlds interpretation, which holds that quantum mechanics describes a multiverse of branching realities, might seem to allow for the possibility of multiple, inconsistent histories. By examining these two ontological frameworks, this paper aims to shed light on the paradoxes of time travel and to explore whether the many-worlds interpretation provides a more satisfactory resolution to these paradoxes than Lewis' modal realism. It is argued that while Lewis' view provides a coherent model for maintaining consistency in time travel, Everett's interpretation may offer a more physically grounded and philosophically compelling account of the metaphysics of time travel. The paper concludes by suggesting that the many-worlds interpretation, by locating the branching of timelines within the structure of quantum mechanics itself, may provide a more promising framework for understanding the possibility and implications of time travel than Lewis' modal realism. However, significant questions remain about the nature of personal identity and free will in a branching multiverse. This comparative analysis aims to contribute to the ongoing debate about the metaphysical possibility of time travel and to highlight the value of engaging with interpretations of quantum mechanics in this context. Keywords: time travel, closed timelike curves, modal realism, many-worlds interpretation, grandfather paradox, metaphysics of time. (shrink)

This paper concerns a thorny problem posed by conditional requirements: we expect some modal conditionals of the form ‘if p, then it must be that p’ to be false, yet they all come out true given two basic assumptions needed to account for ordinary conditional requirement like ‘If the light turns red, then cars must stop’. The first assumption is a semantic expectation linking conditional requirements with absolute ones, the second is the possible-worlds-based definition of modal sentences. Keeping (...) the former means giving up the latter, a result with profound implications for Kratzer’s formal semantics, modifications thereof, as well as deontic logics. (shrink)

The topic of this article is the closure of a priori knowability under a priori knowable material implication: if a material conditional is a priori knowable and if the antecedent is a priori knowable, then the consequent is a priori knowable as well. This principle is arguably correct under certain conditions, but there is at least one counterexample when completely unrestricted. To deal with this, Anderson proposes to restrict the closure principle to necessary truths and Horsten suggests to restrict it (...) to formulas that belong to less expressive languages. In this article it is argued that Horsten’s restriction strategy fails, because one can deduce that knowable ignorance entails necessary ignorance from the closure principle and some modest background assumptions, even if the expressive resources do not go beyond those needed to formulate the closure principle itself. It is also argued that it is hard to find a justification for Anderson’s restricted closure principle, because one cannot deduce it even if one assumes very strong modal and epistemic background principles. In addition, there is an independently plausible alternative closure principle that avoids all the problems without the need for restriction. (shrink)

This review article summarizes and in part criticizes Hugh J. McCann’s detailed elaboration of the consequences of the idea that God is absolutely sovereign and thus unlimited in knowledge and power in his 2012 Creation and the Sovereignty of God. While there is much to agree with in McCann’s treatment, it is argued that divine sovereignty cannot extend as far as he would like to extend it. The absolute lord of the natural and moral orders cannot be absolutely sovereign over (...) the conceptual and modal orders. (shrink)

Resolving the Ross and Prior paradoxes proved to be a difficult task. Its first two stages, involving the identification of the true natures of the implication and truth values, are described in the articles "Solving the Paradox of Material Implication – 2024" and "Solving Jörgensen's Dilemma – 2024". This article describes the third stage, which involves the discovery of missing modal operators and the Classical Modal Calculus. Finally, procedures for solving both paradoxes are provided.

Hsueh M. Qu has recently argued that Hume’s famed ‘Separability Principle’ from the Treatise entangles him in a contradiction. Qu offers a modified principle as a solution but also argues that the mature Hume would not have needed to avail himself of it, given that Hume’s arguments in the first Enquiry do not depend on this principle in any form. To the contrary, I show that arguments in the first Enquiry depend on this principle, but I agree with Qu that (...) Qu’s solution to Hume’s quandary frees him of the contradiction. Next, I compare Qu’s solution to Hume’s original position. By analysing the divergent forms of 'Hume’s Dictum’ that follow from them, I show that Qu’s solution and Hume’s original position have significantly different consequences in a range of domains, including Hume’s modality. Generally, Qu’s solution fits better with Hume’s other commitments—even though Hume often fails to recognize it—thereby increasing its plausibility. (shrink)

The hole argument purports to show that all spacetime theories of a certain form are indeterministic, including the General Theory of Relativity. The argument has given rise to an industry of searching for a metaphysics of spacetime that delivers the right modal implications to rescue determinism. In this paper, I first argue that certain prominent extant replies to the hole argument—namely, those that appeal to an essentialist doctrine about spacetime—fail to deliver the requisite modal implications. As part of (...) my argument, I show that threats to determinism of the sort brought out by the hole argument are more general than has heretofore been recognized. I then use these results to propose a novel essentialist doctrine about spacetime that successfully rescues determinism, what I call sufficiency metric essentialism. However, I go on to argue that once we realize what an essentialist doctrine about spacetime must look like in order to address the hole argument, we should reject all such doctrines, because they can't fulfill their ambition of improving on standard modal replies to the argument. I close by suggesting some lessons for future work on spacetime and the metaphysics of physics more broadly, and also drawing some general morals for contemporary metaphysics, in particular about (i) whether essence can be used to articulate a precise structuralist doctrine, and (ii) the relationship between essence and modality. (shrink)

In recent years, there has been a growing interest in truthmaker semantics as a framework for understanding a range of phenomena in philosophy and linguistics. Despite this interest, there has been limited study of the various logics that arise from the semantics. This paper aims to address this gap by exploring numerous ‘truthmaker logics’ and proving their compactness and decidability. This is in continuation with the inquiry of Fine and Jago (2019), who proved compactness and decidability for a particular kind (...) of truthmaker logic. The key results going into this are (1) ‘standard translations’ into first-order logic; (2) a truthmaker analogue of the finite model property; and (3) a proof showing that truthmaker consequence on semilattices coincides with truthmaker consequence on complete lattices. Finally, the connection with modal logic is examined. Specifically, it is illustrated how endowing truthmaker semantics with classical negation results in modal information logics. (shrink)

What is it to believe something might be the case? We develop a puzzle that creates difficulties for standard answers to this question. We go on to propose our own solution, which integrates a Bayesian approach to belief with a dynamic semantics for epistemic modals. After showing how our account solves the puzzle, we explore a surprising consequence: virtually all of our beliefs about what might be the case provide counterexamples to the view that rational belief is closed under logical (...) implication. (shrink)

This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of (...) two arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics. (shrink)

A strongly deterministic theory of physics is one that permits exactly one possible history of the universe. In the words of Penrose (1989), "it is not just a matter of the future being determined by the past; the entire history of the universe is fixed, according to some precise mathematical scheme, for all time.” Such an extraordinary feature may appear unattainable in a world like ours. In this paper, I show that it can be achieved in a simple way and (...) discuss its implications for metaphysics and philosophy of science, including natural properties, free will, explanation, and modality. First, I propose a precise definition of strong determinism. Next, I discuss its philosophical ramifications and a toy example. Finally, I provide a realistic example of a strongly deterministic (and simple) physical theory---the Everettian Wentaculus. A surprising consequence is that whether or not our world is strongly deterministic may be empirically underdetermined. (shrink)

In this paper ontological implications of the Barcan formula and its converse will be discussed at the conceptual and technical level. The thesis that will be defended is that sentential moods are not ontologically neutral since the rejection of ontological implications of Barcan formula and its converse is a condition of a possibility of the imperative mood. The paper is divided into four sections. In the first section a systematization of semantical systems of quantified modal logic is introduced for (...) the purpose of making explicit their ontological presuppositions. In this context Jadacki's ontological difference between being and existence is discussed and analyzed within the framework of hereby proposed system of quantified modal logic. The second section discusses ontological implications of the Barcan formula and its converse within the system accommodating the difference between being and existence. The third section presents a proof of incompatibility of the Barcan formula and its converse with the use of imperatives. In the concluding section, a thesis on logical pragmatics foreclosing the dilemma between necessitism and contingentism is put forward and defended against some objections. (shrink)

The distinction between potentiality and possibility in Aristotle’s modal teleology is sometimes conflated by the implicative conjunction that potentiality implies possibility and possibility implies potentiality. In his unpublished doctoral dissertation Richard Rorty warns that trying to pin down Aristotle’s definition of potentiality often leads to treating the term as a “mere façon de parler.” Consonant with Rorty, this paper observes that the definition of possibility in Aristotle’s works is not without its own share of semantic snags. Subsequently, I (...) abide by Rorty’s caveat not only to resist the lure of expressive convenience some commentators have taken in describing potentiality, but also to elucidate possibility’s two-fold field of modal application. Consequently, this paper aims to present a nuanced account of how notions of potentiality and possibility are presented in Aristotle’s treatises for the sake of demonstrating that both sides of the potentiality/possibility conjunction do not mutually imply. (shrink)

Metaphysical rationalism, the doctrine which affirms the Principle of Sufficient Reason (the PSR), is out of favor today. The best argument against it is that it appears to lead to necessitarianism, the claim that all truths are necessarily true. Whatever the intuitive appeal of the PSR, the intuitive appeal of the claim that things could have been otherwise is greater. This problem did not go unnoticed by the great metaphysical rationalists Spinoza and Leibniz. Spinoza’s response was to embrace necessitarianism. Leibniz’s (...) response was to argue that, despite appearances, rationalism does not lead to necessitarianism. This paper examines the debate between these two rationalists and concludes that Leibniz has persuasive grounds for his opinion. This has significant implications both for the plausibility of the PSR and for our understanding of modality. (shrink)

Dispositional essentialists argue that physical properties have their causal roles essentially. This is typically taken to mean that physical properties are identical to dispositions. I argue that this is untenable, and that we must instead say that properties bestow dispositions. I explore what it is for a property to have such a role essentially. Dispositional essentialists argue for their view by citing certain epistemological and metaphysical implications, and I appeal to these implications to place desiderata on the concept of essence (...) involved. I argue that the traditional modal theory of essence meets these desiderata, but that the resulting theory wrongly implies that certain dispositions essential to mass are essential to charge, thereby offering a new argument against modal theories of essence. I argue that dispositional essentialism requires a primitive notion of essence, and develop a primitivist theory based on Kit Fine's views. I show that the primitivist theory has all the virtues of the modal alternative, and none of the vices. I develop a novel way of thinking about the relationship between properties, laws and dispositions, and argue that it has distinct advantages over standard dispositional essentialist formulations. (shrink)

A new puzzle about material constitution is presented and its implications are discussed. The moral of the story is that familiar intuitions supporting a neo-Aristotelian view of the material world are contradictory. To accommodate these intuitions is to embrace inconsistency. Therefore, neo-Aristotelianism is worse off for its intuitive appeal. Furthermore, the puzzle is used to argue for an account of ordinary modal thought and language that’s reconstructive, or ameliorative.

Necessity is a touchstone issue in the thought of Charles Peirce, not least because his pragmatist account of meaning relies upon modal terms. We here offer an overview of Peirce’s highly original and multi-faceted take on the matter. We begin by considering how a self-avowed pragmatist and fallibilist can even talk about necessary truth. We then outline the source of Peirce’s theory of representation in his three categories of Firstness, Secondness and Thirdness, (monadic, dyadic and triadic relations). These have (...) modal purport insofar as the first category corresponds to possibility, the second to mechanical necessity and the third to a kind of semantic or intentional necessity. We then turn to Peirce’s explicit modal epistemology and show how it began as information-relative, with different modalities (e.g. logical, physical, practical) distinguished in terms of respective ‘designated states of information’, and shifted later in his life towards a more robust realism founded in direct perception of ideas in their relations. We then turn to Peirce’s formal logic, focusing on his diagrammatic system of Existential Graphs where he did his most serious logical research. Finally we discuss Peirce’s modal metaphysics and its implications for determinism and realism about universals. (shrink)

Discussions about the nature of essence and about the inference problem for non-Humean theories of nomic modality have largely proceeded independently of each other. In this article I argue that the right conclusions to draw about the inference problem actually depend significantly on how best to understand the nature of essence. In particular, I argue that this conclusion holds for the version of the inference problem developed and defended by Alexander Bird. I argue that Bird’s own argument that this problem (...) is fatal for David Armstrong’s influential theory of the laws of nature but not for dispositional essentialism is seriously flawed. In place of this argument, I develop an argument that whether Bird’s inference problem raises serious difficulties for Armstrong’s theory depends on the answers to substantial questions about how best to understand essence. The key consequence is that considerations about the nature of essence have significant, underappreciated implications for Armstrong’s theory. (shrink)

kk states that knowing entails knowing that one knows, and K¬K states that not knowing entails knowing that one does not know. In light of the arguments against kk and K¬K⁠, one might consider modally qualified variants of those principles. According to weak kk, knowing entails the possibility of knowing that one knows. And according to weakK¬K⁠, not knowing entails the possibility of knowing that one does not know. This paper shows that weak kk and weakK¬K are much stronger than (...) they initially appear. Jointly, they entail kk and K¬K⁠. And they are susceptible to variants of the standard arguments against kk and K¬K⁠. This has interesting implications for the debate on positive introspection and for deeper issues concerning the structure and limits of knowability. (shrink)

I reply to recent criticisms by Uygar Abaci and Peter Yong, among others, of my reading of Kant's pre-Critical of God's existence, and of its fate in the Critical period. Along the way I discuss some implications of this debate for our understanding of Kant's modal metaphysics and modal epistemology generally.

Necessity, but not possibility, is typically thought to be rare and suspicion-worthy. This manifests in an asymmetry in the burden of proof incurred by modal claims. In general, claims to the effect that some proposition is impossible/necessary require significant argumentative support and, in general, claims to the effect that some proposition is possible/contingent are thought to be justified freely or by default. Call this the possibility bias. In this paper, I argue that the possibility bias is not epistemically justified. (...) We should regard possibility with at least as much suspicion, that is to say as incurring at least as much of an explanatory demand, as necessity. In fact, I suggest that we might even be justified in reversing the burden of proof asymmetry and adopting a necessity bias. This has quite radical implications for philosophical methodology and hence for many first-order philosophical concerns. (shrink)

From playing basketball to ordering at a food counter, we frequently and effortlessly coordinate our attention with others towards a common focus: we look at the ball, or point at a piece of cake. This non-verbal coordination of attention plays a fundamental role in our social lives: it ensures that we refer to the same object, develop a shared language, understand each other’s mental states, and coordinate our actions. Models of joint attention generally attribute this accomplishment to gaze coordination. But (...) are visual attentional mechanisms sufficient to achieve joint attention, in all cases? Besides cases where visual information is missing, we show how combining it with other senses can be helpful, and even necessary to certain uses of joint attention. We explain the two ways in which non-visual cues contribute to joint attention: either as enhancers, when they complement gaze and pointing gestures in order to coordinate joint attention on visible objects, or as modality pointers, when joint attention needs to be shifted away from the whole object to one of its properties, say weight or texture. This multisensory approach to joint attention has important implications for social robotics, clinical diagnostics, pedagogy and theoretical debates on the construction of a shared world. (shrink)

One implication of Vetter's theory of modality is that necessity and possibility are regarded as unitary natural kinds. In this paper, I argue that from the perspective of the philosophy of causation, there are good reasons to distinguish between different kinds of necessity: causal necessity, which is nomologically necessary, and non-causal necessity, which is metaphysically necessary. One challenge for Vetter's approach is to explain this distinction.

Paintings of music are a significant presence in modern art. They are cross-modal representations, aimed at representing music, say, musical works or forms, using colors, lines, and shapes in the visual modality. This article aims to provide a conceptual framework for understanding paintings of music. Using examples from modern art, the article addresses the question of what a painting of music is. Implications for the aesthetic appreciation of paintings of music are also drawn.

The claim that perfect hallucination is introspectively indistinguishable from perception has been a centrepiece of philosophical theorizing about sense experience. The most common interpretation of the indistinguishability claim is modal: that it is impossible to distinguish perfect hallucination from perception through introspection alone. I run through various models of introspection and show that none of them can accommodate the modal interpretation. Rejecting the modal interpretation opens up two alternative interpretations of the indistinguishability claim. According to the generic (...) interpretation, hallucination is indistinguishable from perception despite the existence of possible exceptions, while according to the actuality interpretation, the indistinguishability of hallucination from perception consists in the actual failure to distinguish hallucination from perception. These alternative understandings of the indistinguishability claim have a number of significant implications for the problem of perception, including the rejection of perfect hallucination and illusion in favour of our ordinary, non-philosophical concepts of these states. (shrink)

The modality of normality distinguishes states of affairs which are normal from those which are abnormal. Existing work on the modality of normality assumes that it is a restriction of metaphysical modality. In this paper, we argue that this assumption is inappropriate and explore the consequences of abandoning it. -/- After preliminary discussion (§1), we introduce the dominant framework for reasoning about normality (§2) and argue that it ascribes implausibly strong structural properties to the modality. In its place, we propose (...) a new framework, which avoids this commitment (§§3-5). This account has a number of interesting features, which we explore in both an informal and formal setting. If correct, it implies that the modality of normality occupies a distinctive place in the space of modalities. Before concluding, we consider some of the wider implications of our account (§6), focusing on the role normality has played in epistemic theorizing. (shrink)