In his metaphysical summa of 1986, The Plurality of Worlds, David Lewis famously defends a doctrine he calls ‘modal realism’, the idea that to account for the fact that some things are possible and some things are necessary we must postulate an infinity possible worlds, concrete entities like our own universe, but cut off from us in space and time. Possible worlds are required to account for the facts of modality without assuming that modality is primitive – that there (...) are irreducibly modal facts. We argue that on one reading, Lewis’s theory licenses us to assume maverick possible worlds which spread through logical space gobbling up all the rest. Because they exclude alternatives, these worlds result in contradictions, since different spread worlds are incompatible with one another. Plainly Lewis’s theory must be amended to exclude these excluders. But, we maintain, this cannot be done without bringing in modalprimitives. And once we admit modalprimitives, bang goes the rationale for Lewis’s modal realism. (shrink)
In Pantsar (2014), an outline for an empirically feasible epistemological theory of arithmetic is presented. According to that theory, arithmetical knowledge is based on biological primitives but in the resulting empirical context develops an essentially a priori character. Such contextual a priori theory of arithmetical knowledge can explain two of the three characteristics that are usually associated with mathematical knowledge: that it appears to be a priori and objective. In this paper it is argued that it can also explain (...) the ... (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)
This collection highlights the new trend away from rationalism and toward empiricism in the epistemology of modality. Accordingly, the book represents a wide range of positions on the empirical sources of modal knowledge. Readers will find an introduction that surveys the field and provides a brief overview of the work, which progresses from empirically-sensitive rationalist accounts to fully empiricist accounts of modal knowledge. Early chapters focus on challenges to rationalist theories, essence-based approaches to modal knowledge, and the (...) prospects for naturalizing modal epistemology. The middle chapters present positive accounts that reject rationalism, but which stop short of advocating exclusive appeal to empirical sources of modal knowledge. The final chapters mark a transition toward exclusive reliance on empirical sources of modal knowledge. They explore ways of making similarity-based, analogical, inductive, and abductive arguments for modal claims based on empirical information. Modal epistemology is coming into its own as a field, and this book has the potential to anchor a new research agenda. (shrink)
In this chapter, it is suggested that our epistemic access to metaphysical modality generally involves rationalist, a priori elements. However, these a priori elements are much more subtle than ‘traditional’ modal rationalism assumes. In fact, some might even question the ‘apriority’ of these elements, but I should stress that I consider a priori and a posteriori elements especially in our modal inquiry to be so deeply intertwined that it is not easy to tell them apart. Supposed metaphysically necessary (...) identity statements involving natural kind terms are a good example: the fact that empirical input is crucial in establishing their necessity has clouded the role and content of the a priori input, as I have previously argued. For instance, the supposed metaphysically necessary identity statement involving water and its microstructure can only be established with the help of a controversial a priori principle concerning the determination of chemical properties by microstructure. The Kripke-Putnam framework of modal epistemology fails precisely because it is unclear whether the required a priori element is present. My positive proposal builds on E. J. Lowe’s work. Lowe holds that our knowledge of metaphysical modality is based on our knowledge of essence. Lowe’s account strives to offer a uniform picture of modal epistemology: essence is the basis of all our modal knowledge. This is the basis of Lowe’s modal rationalism. I believe that Lowe’s proposal is on the right lines in the case of abstract objects, but I doubt that it can be successfully applied to the case of natural kinds. Accordingly, the case of natural kinds will be my main focus and I will suggest that modal rationalism, at least as it is traditionally understood, falls short of explaining modal knowledge concerning natural kinds. Yet, I think that Lowe has identified something of crucial importance for modal epistemology, namely the essentialist, a priori elements present in our modal inquiry. The upshot is that rather than moving all the way from modal rationalism to modal empiricism, a type of hybrid approach, ‘empirically-informed modal rationalism ’, can be developed. (shrink)
I propose that we approach the epistemology of modality by putting modal metaphysics first and, specifically, by investigating the metaphysics of essence. Following a prominent Neo-Aristotelian view, I hold that metaphysical necessity depends on the nature of things, namely their essences. I further clarify that essences are core properties having distinctive superexplanatory powers. In the case of natural kinds, which is my focus in the paper, superexplanatoriness is due to the fact that the essence of a kind is what (...) causes all the many properties and behaviors that are typically shared by all the instances of the kind. Accordingly, we know what is necessarily true of kinds by knowing what is essential to them in the sense of actually playing such causal-explanatory roles. Modal reasoning aimed at discovering metaphysical necessity thus proceeds via essentialist deduction: we move from essentialist truths to reach necessary truths. (shrink)
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)
My topic is moderate modal skepticism in the spirit of Peter van Inwagen. Here understood, this is a conservative version of modal empiricism that severely limits the extent to which an ordinary agent can reasonably believe “exotic” possibility claims. I offer a novel argument in support of this brand of skepticism: modal skepticism grounds an attractive (and novel) reply to Humean skepticism. Thus, I propose that modal skepticism be accepted on the basis of its theoretical utility (...) as a tool for dissolving philosophical paradox. (shrink)
We propose a generalization of Sahlqvist formulae to polyadic modal languages by representing modal polyadic languages in a combinatorial style and thus, in particular, developing what we believe to be the right approach to Sahlqvist formulae at all. The class of polyadic Sahlqvist formulae PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.
We study the general problem of axiomatizing structures in the framework of modal logic and present a uniform method for complete axiomatization of the modal logics determined by a large family of classes of structures of any signature.
This paper explains and defends the idea that metaphysical necessity is the strongest kind of objective necessity. Plausible closure conditions on the family of objective modalities are shown to entail that the logic of metaphysical necessity is S5. Evidence is provided that some objective modalities are studied in the natural sciences. In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal logic. (...) Those assumptions arguably include some necessitist principles. -/- Too often, philosophers have discussed ‘metaphysical’ modality — possibility, contingency, necessity — in isolation. Yet metaphysical modality is just a special case of a broad range of modalities, which we may call ‘objective’ by contrast with epistemic and doxastic modalities, and indeed deontic and teleological ones (compare the distinction between objective probabilities and epistemic or subjective probabilities). Thus metaphysical possibility, physical possibility and immediate practical possibility are all types of objective possibility. We should study the metaphysics and epistemology of metaphysical modality as part of a broader study of the metaphysics and epistemology of the objective modalities, on pain of radical misunderstanding. Since objective modalities are in general open to, and receive, natural scientific investigation, we should not treat the metaphysics and epistemology of metaphysical modality in isolation from the metaphysics and epistemology of the natural sciences. -/- In what follows, Section 1 gives a preliminary sketch of metaphysical modality and its place in the general category of objective modality. Section 2 reviews some familiar forms of scepticism about metaphysical modality in that light. Later sections explore a few of the many ways in which natural science deals with questions of objective modality, including questions of quantified modal logic. (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.
Actualists of a certain stripe—dispositionalists—hold that metaphysical modality is grounded in the powers of actual things. Roughly: p is possible iff something has, or some things have, the power to bring it about that p. Extant critiques of dispositionalism focus on its material adequacy, and question whether there are enough powers to account for all the possibilities we intuitively want to countenance. For instance, it seems possible that none of the actual contingent particulars ever existed, but it is impossible to (...) explain this by appealing to the powers of some actual thing or things to bring it about. I argue instead that dispositionalism, in the simple form championed by its proponents, is formally inadequate. Dispositionalists interpret the modal operators as simple existential claims about powers, but if we interpret the operators that way, the resulting system of modal logic is too weak to capture metaphysical modality. I argue that we can modify the standard dispositionalist interpretations of the operators to secure formal adequacy, but at the cost of accepting that not all modality is grounded in powers. This, I shall suggest, is not a bad thing—the resulting theory still has powers at its core and has certain attractive features, in addition to formal adequacy, that the standard theory lacks. (shrink)
Primitives are both important and unavoidable, and which set of primitives we endorse will greatly shape our theories and how those theories provide solutions to the problems that we take to be important. After introducing the notion of a primitive posit, I discuss the different kinds of primitives that we might posit. Following Cowling (2013), I distinguish between ontological and ideological primitives, and, following Benovsky (2013) between functional and content views of primitives. I then propose (...) that these two distinctions cut across each other leading to four types of primitive posits. I then argue that theoretical virtues should be taken to be meta-theoretical ideological primitives. I close with some reflections on the global nature of comparing sets of primitives. (shrink)
This paper provides a categorization of cross-modal experiences. There are myriad forms. Doing so allows us to think clearly about the nature of different cross-modal experiences and allows us to clearly formulate competing hypotheses about the kind of experiences involved in different cross-modal phenomena.
We outline a neo-Meinongian framework labeled as Modal Meinongian Metaphysics (MMM) to account for the ontology and semantics of fictional discourse. Several competing accounts of fictional objects are originated by the fact that our talking of them mirrors incoherent intuitions: mainstream theories of fiction privilege some such intuitions, but are forced to account for others via complicated paraphrases of the relevant sentences. An ideal theory should resort to as few paraphrases as possible. In Sect. 1, we make this explicit (...) via two methodological principles, called the Minimal Revision and the Acceptability Constraint. In Sect. 2, we introduce the standard distinction between internal and external fictional discourse. In Sects. 3–5, we discuss the approaches of (traditional) Meinongianism, Fictionalism, and Realism—and their main troubles. In Sect. 6 we propose our MMM approach. This is based upon (1) a modal semantics including impossible worlds (Subsect. 6.1); (2) a qualified Comprehension Principle for objects (Subsect. 6.2); (3) a notion of existence-entailment for properties (Subsect. 6.3). In Sect. 7 we present a formal semantics for MMM based upon a representation operator. And in Sect. 8 we have a look at how MMM solves the problems of the three aforementioned theories. (shrink)
In his book Worlds and Individuals, Possible and Otherwise (2010), Takashi Yagisawa presents and argues for a novel and imaginative version of modal realism. It differs both from Lewis’s modal realism (Lewis 1986) and from actualists’ ersatz accounts (Adams 1974; Sider 2002). In this paper, I’ll present two arguments, each of which shows that Yagisawa’s metaphysics is incoherent. The first argument shows that the combination of Yagisawa’s metaphysics with impossibilia leads to triviality: every sentence whatsoever comes out true. (...) This is so even if Yagisawa accepts a paraconsistent notion of logical consequence, on which contradictions do not entail arbitrary conclusions. The second argument is independent of Yagisawa’s acceptance of impossibilia. It shows that Yagisawa’s metaphysics of possible worlds is incoherent. Using ordinary modal reasoning, I derive a contradiction from Yagisawa’s account of possible worlds. (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 this work we propose an encoding of Reiter’s Situation Calculus solution to the frame problem into the framework of a simple multimodal logic of actions. In particular we present the modal counterpart of the regression technique. This gives us a theorem proving method for a relevant fragment of our modal logic.
A fundamental entity is an entity that is ‘ontologically independent’; it does not depend on anything else for its existence or essence. It seems to follow that a fundamental entity is ‘modally free’ in some sense. This assumption, that fundamentality entails modal freedom (or ‘FEMF’ as I shall label the thesis), is used in the service of other arguments in metaphysics. But as I will argue, the road from fundamentality to modal freedom is not so straightforward. The defender (...) of FEMF should provide positive reasons for believing it, especially in light of recent views that are incompatible with it. I examine both direct and indirect routes to FEMF. (shrink)
This paper examines "moderate modal skepticism", a form of skepticism about metaphysical modality defended by Peter van Inwagen in order to blunt the force of certain modal arguments in the philosophy of religion. Van Inwagen’s argument for moderate modal skepticism assumes Yablo's (1993) influential world-based epistemology of possibility. We raise two problems for this epistemology of possibility, which undermine van Inwagen's argument. We then consider how one might motivate moderate modal skepticism by relying on a different (...) epistemology of possibility, which does not face these problems: Williamson’s (2007: ch. 5) counterfactual-based epistemology. Two ways of motivating moderate modal skepticism within that framework are found unpromising. Nevertheless, we also find a way of vindicating an epistemological thesis that, while weaker than moderate modal skepticism, is strong enough to support the methodological moral van Inwagen wishes to draw. (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)
I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that only (...) the cardinalities of these sets matters, and that not all pairs of infinite sets determine the same logic. I use so-called two-cardinal theorems from model theory to investigate the space of logics and consequence relations determined by pairs of infinite sets, and show how to eliminate the assumption that worlds are individuals from Williamson’s argument. (shrink)
An intuitive objection to modal realism is that merely possible worlds and their inhabitants seem to be irrelevant to an analysis of modality. Kripke originally phrased the objection in terms of being concerned about one’s modal properties without being concerned about the properties one’s other-worldly counterparts have. The author assesses this objection in a variety of forms, and then provides his own formulation that does not beg the question against the modal realist. Finally, the author considers two (...) potential answers to the objection so understood and concludes that only one of them has a chance of succeeding. (shrink)
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)
In this paper we reply to arguments of Kroon (“Characterization and Existence in Modal Meinongianism”. Grazer Philosophische Studien 86, 23–34) to the effect that Modal Meinongianism cannot do justice to Meinongian claims such as that the golden mountain is golden, and that it does not exist.
According to the canonical formulation of the modal account of luck [e.g. Pritchard ], an event is lucky just when that event occurs in the actual world but not in a wide class of the nearest possible worlds where the relevant conditions for that event are the same as in the actual world. This paper argues, with reference to a novel variety of counterexample, that it is a mistake to focus, when assessing a given event for luckiness, on events (...) distributed over just the nearest possible worlds. More specifically, our objection to the canonical formulation of the modal account of luck reveals that whether an event is lucky depends crucially on events distributed over all possible worlds–viz., across the modal universe. It is shown that an amended modal account of luck which respects this point has the additional virtue of avoiding a notable kind of counterexample to modal accounts of luck proposed by Lackey. (shrink)
The paper compares the suitability of two different epistemologies of counterfactuals—(EC) and (W)—to elucidate modal knowledge. I argue that, while both of them explain the data on our knowledge of counterfactuals, only (W)—Williamson’s epistemology—is compatible with all counterpossibles being true. This is something on which Williamson’s counterfactual-based account of modal knowledge relies. A first problem is, therefore, that, in the absence of further, disambiguating data, Williamson’s choice of (W) is objectionably biased. A second, deeper problem is that (W) (...) cannot satisfactorily elucidate modal knowledge. Third, from a naturalistic perspective, the nature of this second problem favours (EC) against (W). (shrink)
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.
We argue that genuine modal realism can be extended, rather than modified, so as to allow for the possibility of nothing concrete, a possibility we term ‘metaphysical nihilism’. The issue should be important to the genuine modal realist because, not only is metaphysical nihilism itself intuitively plausible, but also it is supported by an argument with pre-theoretically credible premises, namely, the subtraction argument. Given the soundness of the subtraction argument, we show that there are two ways that the (...) genuine modal realist can accommodate metaphysical nihilism: (i) by allowing for worlds containing only spatiotemporal points and (ii) by allowing for a world containing nothing but the null individual. On methodological grounds, we argue that the genuine modal realist should reject the former way but embrace the latter way. (shrink)
The paper argues against Peacocke's moderate rationalism in modality. In the first part, I show, by identifying an argumentative gap in its epistemology, that Peacocke's account has not met the Integration Challenge. I then argue that we should modify the account's metaphysics of modal concepts in order to avoid implausible consequences with regards to their possession conditions. This modification generates no extra explanatory gap. Yet, once the minimal modification that avoids those implausible consequences is made, the resulting account cannot (...) support Peacocke's moderate rationalism. (shrink)
To solve the problem of counterpossibles, many philosophers have been arguing that one needs to invoke impossible worlds. This extension of the ontology of modality should save the analysis of counterfactuals from being insensitive to the problem of counterpossibles. Since theories of impossible worlds are extensions of original accounts of modalities, it is worth stressing that proper analyses of counterpossibles should not weaken the latter.In this paper I argue that these theories of impossible wolrds, which are based on D. Lewis' (...)modal realism - Extended Modal Realism and Hybrid Modal Realism - might be consider as either an unattractive for modal realists or insufficient for analyzing counterpossibles. (shrink)
The subject of this article is Modal-Epistemic Arithmetic (MEA), a theory introduced by Horsten to interpret Epistemic Arithmetic (EA), which in turn was introduced by Shapiro to interpret Heyting Arithmetic. I will show how to interpret MEA in EA such that one can prove that the interpretation of EA is MEA is faithful. Moreover, I will show that one can get rid of a particular Platonist assumption. Then I will discuss models for MEA in light of the problems of (...) logical omniscience and logical competence. Awareness models, impossible worlds models and syntactical models have been introduced to deal with the first problem. Certain conditions on the accessibility relations are needed to deal with the second problem. I go on to argue that those models are subject to the problem of quantifying in, for which I will provide a solution. (shrink)
It is a commonsense thesis that unactualized possibilities are not parts of actuality. To keep his modal realism in line with this thesis, David Lewis employed his indexical account of the term “actual.” I argue that the addition of counterpart theory to Lewis’s modal realism undermines his strategy for respecting the commonsense thesis. The case made here also reveals a problem for Lewis’s attempt to avoid haecceitism.
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)
Pace Necessitism – roughly, the view that existence is not contingent – essential properties provide necessary conditions for the existence of objects. Sufficiency properties, by contrast, provide sufficient conditions, and individual essences provide necessary and sufficient conditions. This paper explains how these kinds of properties can be used to illuminate the ontological status of merely possible objects and to construct a respectable possibilist ontology. The paper also reviews two points of interaction between essentialism and modal logic. First, we will (...) briefly see the challenge that arises against S4 from flexible essential properties; as well as the moves available to block it. After this, the emphasis is put on the Barcan Formula (BF), and on why it is problematic for essentialists. As we will see, Necessitism can accommodate both (BF) and essential properties. What necessitists cannot do at the same time is to continue to understanding essential properties as providing necessary conditions for the existence of individuals; against what might be for some a truism. (shrink)
We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's (...) and Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions. (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)
This paper outlines a formal account of tensed sentences that is consistent with Ockhamism, a view according to which future contingents are either true or false. The account outlined substantively differs from the attempts that have been made so far to provide a formal apparatus for such a view in terms of some expressly modified version of branching time semantics. The system on which it is based is the simplest quantified modal logic.
In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new proof (...) of S4 as being "the logic of topological spaces", but now under the perspective of paraconsistency. (shrink)
ABSTRACT: The modal systems of the Stoic logician Chrysippus and the two Hellenistic logicians Philo and Diodorus Cronus have survived in a fragmentary state in several sources. From these it is clear that Chrysippus was acquainted with Philo’s and Diodorus’ modal notions, and also that he developed his own in contrast of Diodorus’ and in some way incorporated Philo’s. The goal of this paper is to reconstruct the three modal systems, including their modal definitions and (...) class='Hi'>modal theorems, and to make clear the exact relations between them; moreover, to elucidate the philosophical reasons that may have led Chrysippus to modify his predessors’ modal concept in the way he did. It becomes apparent that Chrysippus skillfully combined Philo’s and Diodorus’ modal notions, with making only a minimal change to Diodorus’ concept of possibility; and that he thus obtained a modal system of modalities (logical and physical) which fit perfectly fit into Stoic philosophy. (shrink)
Modal rationalists uphold a strong constitutive relationship between a priori cognition and modal cognition. Since both a priori cognition and modal cognition have been taken to be characteristic of philosophical insights, I will critically assess an ambitious modal rationalism and an associated ambitious methodological rationalism. I begin by examining Kripkean cases of the necessary a posteriori in order to characterize the ambitious modal rationalism that will be the focus of my criticism. I then argue that (...) there is a principled association between this view in the epistemology of modality and an ambitious methodological rationalist picture of the nature of philosophical insights. On the basis of this discussion, I criticize ambitious modal rationalism and argue that the critique indicates some principled limits of generating philosophical insights by a priori modal cognition. Hence, my central diagnosis is that ambitious methodological rationalists are overly ambitious in the role that they assign a priori modal cognition in philosophical methodology. -/-. (shrink)
A new (sound and complete) proof style adequate for modal logics is defined from the polynomial ring calculus (PRC). The new semantics not only expresses truth conditions of modal formulas by means of polynomials, but also permits to perform deductions through polynomial handling. This paper also investigates relationships among the PRC here defined, the algebraic semantics for modal logics, equational logics, the Dijkstra–Scholten equational-proof style, and rewriting systems. The method proposed is throughly exemplified for S5, and can (...) be easily extended to other modal logics. (shrink)
A major criticism of David Lewis’ counterfactual theory of causation is that it allows too many things to count as causes, especially since Lewis allows, in addition to events, absences to be causes as well. Peter Menzies has advanced this concern under the title “the problem of profligate causation.” In this paper, I argue that the problem of profligate causation provides resources for exposing a tension between Lewis’ acceptance of absence causation and his modal realism. The result is a (...) different problem of profligate causation—one that attacks the internal consistency of Lewisian metaphysics rather than employing common sense judgments or intuitions that conflict with Lewis’ extensive list of causes. (shrink)
The subject of the first section is Carnapian modal logic. One of the things I will do there is to prove that certain description principles, viz. the ''self-predication principles'', i.e. the principles according to which a descriptive term satisfies its own descriptive condition, are theorems and that others are not. The second section will be devoted to Carnapian modal arithmetic. I will prove that, if the arithmetical theory contains the standard weak principle of induction, modal truth collapses (...) to truth. Then I will propose a different formulation of Carnapian modal arithmetic and establish that it is free of collapse. Noteworthy is that one can retain the standard strong principle of induction. I will occupy myself in the third section with Carnapian epistemic logic and arithmetic. Here too it is claimed that the standard weak principle of induction is invalid and that the alternative principle is valid. In the fourth and last section I will get back to the self-predication principles and I will point to some of the consequences if one adds them to Carnapian Epistemic arithmetic. The interaction of self-predication principles and the strong principle of induction results in a collapse of de re knowability. (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)
The paper investigates the link between the theory of modal occurrents (where individuals are allowed to stretch across possible worlds) and Lewis’s counterpart theory (where all individuals are world-bound but have counterparts in other worlds). First I show how to interpret modal talk extensionally within the theory of modal occurrents. Then I show that the assumption that worlds be pairwise discrete is all that is needed to reconstruct the bulk of counterpart theory (i.e., to define the concept (...) of a counterpart and to derive the standard postulates governing that concept) in terms of the theory of modal occurrents. Finally, I argue that this reconstruction allows us to view the indeterminacy of our modal intuitions as being part and parcel with the indeterminacy of our criteria for individuating modal occurrents, and that this indeterminacy is naturally explained in terms of linguistic (as opposed to ontic) vagueness. (shrink)
We introduce and study a variety of modal logics of parallelism, orthogonality, and affine geometries, for which we establish several completeness, decidability and complexity results and state a number of related open, and apparently difficult problems. We also demonstrate that lack of the finite model property of modal logics for sufficiently rich affine or projective geometries (incl. the real affine and projective planes) is a rather common phenomenon.
In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic, or multiple-conclusion calculi for classical logic). -/- The sequent derivations and proofnets are both simple extensions of sequents and proofnets for classical propositional logic, in which the new machinery—to take account of the modal vocabulary—is directly motivated (...) in terms of the simple, universal Kripke semantics for S5. The sequent system is cut-free and the circuit proofs are normalising. (shrink)
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