We show that—unlike products of ‘transitive’ modal logics which are usually undecidable—their ‘expanding domain’ relativisations can be decidable, though not in primitive recursive time. In particular, we prove the decidability and the finite expanding product model property of bimodal logics interpreted in two-dimensional structures where one component—call it the ‘flow of time’—is • a finite linear order or a finite transitive tree and the other is composed of structures like • transitive trees/partial orders/quasi-orders/linear orders or only finite such structures (...) expanding over time. The decidability proof is based on Kruskal’s tree theorem, and the proof of non-primitive recursiveness is by reduction of the reachability problem for lossy channel systems. The result is used to show that the dynamic topological logic interpreted in topological spaces with continuous functions is decidable if the number of function iterations is assumed to be finite. (shrink)

This paper develops an account of the meaning of `ought', and the distinction between weak necessity modals (`ought', `should') and strong necessity modals (`must', `have to'). I argue that there is nothing specially ``strong'' about strong necessity modals per se: uses of `Must p' predicate the (deontic/epistemic/etc.) necessity of the prejacent p of the actual world (evaluation world). The apparent ``weakness'' of weak necessity modals derives from their bracketing whether the necessity of the prejacent is verified in the actual world. (...) `Ought p' can be accepted without needing to settle that the relevant considerations (norms, expectations, etc.) that actually apply verify the necessity of p. I call the basic account a modal-past approach to the weak/strong necessity modal distinction (for reasons that become evident). Several ways of implementing the approach in the formal semantics/pragmatics are critically examined. The account systematizes a wide range of linguistic phenomena: it generalizes across flavors of modality; it elucidates a special role that weak necessity modals play in discourse and planning; it captures contrasting logical, expressive, and illocutionary properties of weak and strong necessity modals; and it sheds light on how a notion of `ought' is often expressed in other languages. These phenomena have resisted systematic explanation. In closing I briefly consider how linguistic inquiry into differences among necessity modals may improve theorizing on broader philosophical issues. (shrink)

This paper explores the prospects of a combinatorial account of modality. We argue against David M. Armstrong’s version of combinatorialism, which seeks to do without modal primitives, on the grounds, among other things, that Armstrong’s basic ontological categories are themselves subject to non-contingent constraints on recombination. We outline an alternative version, which acknowledges the necessity of modal primitives, at the level of ontology, and not just of our concepts.

This paper sets out a number of reasons for thinking that the framework of possible worlds, even when construed non-reductively, does not provide an adequate basis for an explanation of modality. I first consider a non-reductive version of Lewis' modal realism, and then move on to consider the ersatzist approach of Plantinga et al. My main complaint is that the framework of possible worlds gets the semantics and metaphysics of ordinary modal discourse wrong. That is, possible worlds do (...) not give us an adequate answer to the semantic question of what ordinary modal claims mean, nor do they give us an adequate answer to the metaphysical question of what makes such claims true. (shrink)

Explicit axioms relating ◊ϕand □ϕ appear to be needed if ◊ is taken to be primitive. We prove that such axioms are in fact indispensable.

Draws attention to some unexpected consequences of using a zero-ary connective in modal propositional logic.

In the present paper we give the first proof-theoretical example of an embedding of classical logic into a quantum-like logic. This is performed in the framework of basic logic, where a proof-theoretical approach to quantum logic is convenient. We consider basic orthologic, that corresponds to a sequential formulation of paraconsistent quantum logic, and which is given by basic orthologic added with weakening and contraction, in a language with Girard's negation. In the paper we first consider a convenient cut-free calculus for (...) classical logic, in the same language; then, in a language enriched with a new kind of literals, we introduce basic orthologic with a primitive modality, where classical logic is embeddable. Similarly to Girard's negation, our modality is not a connective but conceivable as an operator defined inductively on the set of formulae. This allows us to obtain a calculus which enjoys cut-elimination. (shrink)

Ignoring primitive terms leads to an infinite regress. The alternative is to account for an intuitive understanding into the meaning of such terms. The current investigation proceeds on the basis of an idea of the structure of the various modes of being within which concrete entities function. Examples of primtive terms are given from disciplines such as mathematics, physics and logic and they are related to the general idea of a modal aspect. It is argued that primitive terms are (...) not isolated but reveal their meaning only through their interconnections with other primitive terms that are embedded in other modal aspects. However, although primitive terms are found within the various aspects, the meaning of an aspect only comes to expression through its coherence with other aspects, evinced in modal analogies that are qualified by the core meaning of an aspect. There appears to be two options, either reduce what is irreducible or merely provide synonymous terms for given primitives. The former happens when other unique terms are used to define a specific one and the latter when the attempted ‘definitions’ revert to terms with which the original terms could be meaningfully replaced. It is been pointed out that the coherence between primitives invites every academic discipline to account for the meaning attached to the analogies of primitive terms it is employing, without exploring this additional theme any further. (shrink)

Modality and Anti-Metaphysics critically examines the most prominent approaches to modality among analytic philosophers in the twentieth century, including essentialism. Defending both the project of metaphysics and the essentialist position that metaphysical modality is conceptually and ontologically primitive, Stephen McLeod argues that the logical positivists did not succeed in banishing metaphysical modality from their own theoretical apparatus and he offers an original defence of metaphysics against their advocacy of its elimination. -/- Seeking to assuage the sceptical worries which underlie (...) class='Hi'>modal anti-realism, McLeod provides an original contribution to essentialist epistemology, engaging with current debates about modality and suggesting that standard essentialist approaches to some issues in the philosophies of logic and language require revision. -/- This book offers valuable insights to professional philosophers, postgraduates and advanced undergraduates interested in metaphysics, philosophy of logic or the history of twentieth-century analytic philosophy. (shrink)

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 modal primitives. And once we admit modal primitives, bang goes the rationale for Lewis’s modal realism. (shrink)

In the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic,supposingthat someone were capable to compile it, would?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancient and Medieval times? no (...) one could have foreseen that in a short time modal logic would become a lively source of ideas and methods for analytical philosophers,historians of philosophy,linguists, epistemologists and computer scientists. The aim which oriented the composition of this book was not to write a new manual of modal logic buttoo?ertoeveryreader,evenwithnospeci?cbackground in logic, a conceptually linear path in the labyrinth of the current panorama of modal logic. The notion which in our opinion looked suitable to work as a compass in this enterprise was the notion of multimodality, or, more speci?cally, the basic idea of grounding systems on languages admitting more than one primitive modal operator. (shrink)

This book is collection of the the author’s previously published papers on the philosophy of modality and tense and it also includes three unpublished papers. The author provides an exposition and defence of certain positions for which he is well-known: the intelligibility of modality de re; the primitiveness of the modal; and the primacy of the actual over the possible. He also argues for some less familiar positions: the existence of distinctive forms of natural and normative necessity, not reducible (...) to any form of metaphysical necessity; the need to make a distinction between the worldly and unworldly, analogous to the distinction between the tensed and the tenseless; and the viability of a nonstandard form of realism about tense, which recognizes the tensed character of reality without conceding there is any privileged standpoint from which it is to be viewed. (shrink)

The aim of this paper is to provide an analysis of modality by means of the existence of concrete impossible worlds. In particular, I pursue a strategy according to which logical impossibility is analyzed as logical inaccessibility. I then consider whether it makes sense to think of logical models in isolation from the concrete world but without their being divorced from all spatiotemporal totalities. The metaphysics of structure developed in this paper assumes that structural properties of possible and impossible worlds (...) are primitive and objective. However, I provide some characterizations of their logical and metaphysical behavior, as well as guidelines for talking about them. (shrink)

Aesthetics, like other philosophical subjects, has historically made use of «top down» methods. Recent discoveries in genetics, evolutionary psychology, paleoarchaeology, and neuroscience call for a new «naturalistic» or «bottom up» perspective. Combining these fields with behavioral biology and ethnoarts studies, I offer seven premises that underlie a new understanding of evolved predispositions of the brain/mind that all artists use to attract attention, sustain interest, and create, mold, and shape emotion. I describe aesthetic «primitives» in somatic and behavioral modalities, suggesting (...) that these were present in early sapiens and continue to influence human art making and aesthetic response today. Keywords: Aesthetic Mind; Neuroaesthetics, evolutionary aesthetics, cognitive aesthetics, evolution of art. (shrink)

Modal Dimensionalism is a metaphysical theory about possible worlds that is naturally suggested by the often-noted parallelism between modal logic and tense logic. It says that the universe spreads out not only in spatiotemporal dimensions but also in a modal dimension. It regards worlds as nothing more or less than indices in the modal dimension in the way analogous to the way in which Temporal Dimensionalism regards temporal points and intervals as indices in the temporal dimension. (...) Despite its naturalness and intuitive appeal. Modal Dimensionalism has been largely ignored while the debates between David Lewis and his critics have dominated the discourse on the nature of possible worlds. It is high time that we took Modal Dimensionalism seriously as a viable alternative. (shrink)

This paper is about avoiding commitment to an ontology of possible worlds with two primitives: a hyperintensional connective like ‘in virtue of’, and primitive quantification into predicate position. I argue that these tools (which some believe can be independently motivated) render dispensable the ontology of possible worlds needed by traditional anaylses of modality. They also shed new light on the notion of truth-at-a-world.

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

This thesis is a study on the nature of modality in Hegel’s Logic and contemporary modal metaphysics. The thesis has two aims: Firstly, it examines Lewisian modal realism, as well as the post-Lewisian modal metaphysical accounts of modal actualism and modal essentialism in order to reveal that each position appeals to a non-modal foundation to make modal concepts explicit. Each position thus falls under what Hegel regards as pre-critical metaphysics by suggesting a modally (...) unaccountable ground for modal concepts. The very idea of a foundation to modality is problematic because as a foundation, it is necessarily assumed without further justification, and it directs our attention away from the nature of modality itself to its supposed foundations. These non-modal foundational take the form of possible worlds for modal realism, the form of properties for modal actualism and the form of essence for modal essentialism. To eschew foundationalism in modal metaphysics and provide a less questionable basis for modality, the thesis suggests Hegel’s treatment of modality as a viable alternative in virtue of its being free from the concerns stemming from the pre-critical way of doing metaphysics. The thesis situates Hegel in contemporary modal metaphysics by undertaking two types of exposition. By examining Hegel's treatment of essence and property, the thesis will show negatively that essence and property cannot be a foundation for modality, while by examining Hegel’s treatment of modality, the thesis positively proves that modal concepts are analysable and explainable within the domain of actuality, a domain that can only be made explicit by modal determinations. These two expositions provide an idea of a self-sustaining and self-explanatory modal metaphysics without appealing to non-modal foundationalist metaphysical commitments. More precisely, I argue that Hegel’s logical derivation of modal concepts constitutes a Hegelian modal metaphysics, which contains a comprehensive account of modal concepts that does not rely on any non-modal primitive. (shrink)

We present the propositional logic LEC for the two epistemic modalities of current and stable knowledge used by an agent who system-atically enriches his language. A change in the linguistic resources of an agent as a result of certain cognitive processes is something that commonly happens. Our system is based on the logic LC intended to formalize the idea that the occurrence of changes induces the passage of time. Here, the primitive operator C read as: it changes that, defines the (...) temporal succession of states of the world. The notion of current knowledge concerns variable components of the world and it may change over time. We represent it by the primitive operator k read as: the agent currently knows that, and assume that it has S5 properties. The second type of knowledge, symbolized by the primitive operator K read as: the agent stably knows that, relates to constant components of the world and it does not change. As a result of the axiomatic entanglement of C, K and k we show that stable knowledge satisfies axioms of S4.3. K and k modalities are not mutually definable, stable knowledge implies the current one and if the latter never changes, then it comes to be stable. The combination of K and k with the idea of an expanding language allows questioning of the so-called perfect recall principle. It cannot be maintained for both types of knowledge just because of changes in the vocabulary of the agent and possibly the growing spectrum of possible states of the world. We interpret LEC in the semantics of histories of epistemic changes and show that it is complete. Finally, we compare our logic with selected epistemic logics based on the concept of linear discrete time. (shrink)

We present a general approach to quantified modal logics that can simulate most other approaches. The language is based on operators indexed by terms which allow to express de re modalities and to control the interaction of modalities with the first-order machinery and with non-rigid designators. The semantics is based on a primitive counterpart relation holding between n-tuples of objects inhabiting possible worlds. This allows an object to be represented by one, many, or no object in an accessible world. (...) Moreover by taking as primitive a relation between n-tuples we avoid some shortcoming of standard individual counterparts. Finally, we use cut-free labelled sequent calculi to give a proof-theoretic characterisation of the quantified extensions of each first-order definable propositional modal logic. In this way we show how to complete many axiomatically incomplete quantified modal logics. (shrink)

Laws of nature are sometimes said to govern their instances. Spelling out what governance is, however, is an important task that has only recently received sustained philosophical attention. In the first part of this paper, I argue against the two prominent reductive views of governance—modal views and grounding views. Ruling out the promising candidates for reduction supports the claim that governance is sui generis. In the second part of this paper, I argue that governance is subject to a contingency (...) requirement. Laws govern their instances only if those instances are metaphysically contingent. I end by defending the resulting account of governance from two potential objections. (shrink)

According to modalism, modality is primitive. In this paper, we examine the implications of this view for modal epistemology, and articulate a modalist account of modal knowledge. First, we discuss a theoretical utility argument used by David Lewis in support of his claim that there is a plurality of concrete worlds. We reject this argument, and show how to dispense with possible worlds altogether. We proceed to account for modal knowledge in modalist terms.

It is surprisingly difficult to determine what modal strength Leibniz wants to ascribe to his principle of the identity of indiscernibles (PII). I consider this question by examining (i) some direct textual evidence, (ii) Leibniz's main arguments for PII, (iii) Leibniz's presumable response to a prominent contemporary defense of the necessity of PII against Max Black style counterexamples, and (iv) Leibniz's views about the possibility of primitive haecceities. I conclude that Leibniz probably takes PII to be necessary.

Ontic structural realism is the view that structures are what is real in the first place in the domain of fundamental physics. The structures are usually conceived as including a primitive modality. However, it has not been spelled out as yet what exactly that modality amounts to. This paper proposes to fill this lacuna by arguing that the fundamental physical structures possess a causal essence, being powers. Applying the debate about causal vs categorical properties in analytic metaphysics to ontic structural (...) realism, I show that the standard argument against categorical and for causal properties holds for structures as well. Structural realism, as a position in the metaphysics of science that is a form of scientific realism, is committed to causal structures. The metaphysics of causal structures is supported by physics, and it can provide for a complete and coherent view of the world that includes all domains of empirical science. (shrink)

The relationships between various modal logics based on Belnap and Dunn’s paraconsistent four-valued logic FDE are investigated. It is shown that the paraconsistent modal logic \, which lacks a primitive possibility operator \, is definitionally equivalent with the logic \, which has both \ and \ as primitive modalities. Next, a tableau calculus for the paraconsistent modal logic KN4 introduced by L. Goble is defined and used to show that KN4 is definitionally equivalent with \ without the (...) absurdity constant. Moreover, a tableau calculus is defined for the modal bilattice logic MBL introduced and investigated by A. Jung, U. Rivieccio, and R. Jansana. MBL is a generalization of BK that in its Kripke semantics makes use of a four-valued accessibility relation. It is shown that MBL can be faithfully embedded into the bimodal logic \ over the non-modal vocabulary of MBL. On the way from \ to MBL, the Fischer Servi-style modal logic \ is defined as the set of all modal formulas valid under a modified standard translation into first-order FDE, and \ is shown to be characterized by the class of all models for \. Moreover, \ is axiomatized and this axiom system is proved to be strongly sound and complete with respect to the class of models for \. Moreover, the notion of definitional equivalence is suitably weakened, so as to show that \ and \ are weakly definitionally equivalent. (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)

Modal primitivists hold that some modal truths are primitively true. They thus seem to face a special epistemological problem: how can primitive modal truths be known? The epistemological objection has not been adequately developed in the literature. I undertake to develop the objection, and then to argue that the best formulation of the epistemological objection targets all realists about modality, rather than the primitivist alone. Furthermore, the moves available to reductionists in response to the objection are also (...) available to primitivists. I conclude by suggesting that extant theories of the epistemology of modality are not sensitive to the question of primitivism versus reductionism. (shrink)

This paper introduces a new framework, based on the notion of compatibility space, obtained by adding a primitive incompatibility relation to a state space in the sense of Fine. The key idea inspiring the framework is to modify Fine's truthmaker semantics by taking the notion of incompatibility as primitive, and use it to define other notions. We discuss some interesting features of the framework and explore its advantages over the standard framework of state spaces. We review some applications of the (...) framework, including proofs of soundness and completeness theorems for a number of logics, one way to use compatibility states to mirror Kripke frames, and an exploration of a way to use the new framework to provide truthmaking clauses for modal formulas. (shrink)

A generalized inclusion frame consists of a set of points W and an assignment of a binary relation $R\sb{w}$ on W to each point w in W. Generalized inclusion frames whose $R\sb{w}$ are partial orders are called comparison frames. Conditional logics of various comparative notions, for example, Lewis's V-logic of comparative possibility and utilitarian accounts of conditional obligation, model the dyadic modal operator $>$ on comparison frames according to the following truth condition: $\alpha > \beta$ "holds at w" iff (...) every point in the truth set of $\alpha$ bears $R\sb{w}$ to some point where $\beta$ holds. ;In this essay I provide a relational frame theory which embraces both accessibility semantics and g.i. semantics as special cases. This goal is achieved via a philosophically significant generalization of universal strict implication which does not assume accessibility as a primitive. Within this very general setting, I provide the first axiomatization of the dyadic modal logic corresponding to the class of all g.i. frames. Various correspondences between dyadic logics and first order definable subclasses of the class of g.i. frames are established. Finally, some general model constructions are developed which allow uniform completeness proofs for important sublogics of Lewis' V. (shrink)

This book concerns the philosophical analysis of modal sentences. David Lewis' Modal Translation Scheme 'translates' sentences of quantified modal logic into sentences of predicate logic supplemented by counterpart theory. A number of theoretical advantages are thereby secured. One component of the translation scheme makes reference to non-actual but possible worlds i.e. the primitive predicate "at a world(s), w". The author addresses the problem of advanced modal sentences which threaten this predicate and so the ability of genuine (...) realism to secure the aforementioned theoretical benefits. The problem of advanced modal sentences is a relatively new field of philosophical research. This ground-breaking book will primarily be of interest to researchers in modality, particularly those working in this field. (shrink)

Modal primitivism is the view that there are modal features of the world which cannot be reduced to the non-modal. Theories which embrace primitive modality are often rejected for reasons of ideological simplicity: the fewer primitive notions a theory invokes, the better. Furthermore, modal primitivism is often associated with the view that all modal features of the world are irreducibly modal, which appears unsystematic and unexplanatory. As a result, many prefer modal reductionism. This (...) work is an articulation and defense of a modal primitivist theory of modality which requires minimal ideology and is systematic and explanatory. On this version of modal primitivism, only some modal features of the world are irreducibly modal—namely, incompatibilities between certain properties or relations. Other modal features of the world are reducible to a combination of primitive incompatibilities and the non-modal features of the world. In chapter 1, I introduce various issues in the metaphysics of modality, giving appropriate background for what follows. My modal primitivist theory of modality is introduced in chapters 2 and 3. In chapter 2, I argue that a well-known modal reductionist theory of modality is not as ideologically innocent as it’s thought to be: modal primitivism has the upper hand with respect to primitive notions. I then introduce the primitive notion of incompatibility and show how this notion can be used to account for de dicto modality, which concerns purely qualitative modal claims. In chapter 3, I present a theory of de re modality, that which concerns modal claims involving particular individuals. Since on this theory the de re is reducible to the de dicto, it requires no more primitive modality than that which appears at the level of the de dicto. I end in chapter 4 by arguing against a rival modal primitivist theory, showing that the primitive notion that it countenances, dispositionality, cannot account for all modal claims. (shrink)

The description of resources in game semantics has never achieved the simplicity and precision of linear logic, because of the misleading conception that linear logic is more primitive than game semantics. Here, we defend the opposite view, and thus advocate that game semantics is conceptually more primitive than linear logic. This revised point of view leads us to introduce tensor logic, a primitive variant of linear logic where negation is not involutive. After formulating its categorical semantics, we interpret tensor logic (...) in a model based on Conway games equipped with a notion of payoff, in order to reflect the various resource policies of the logic: linear, affine, relevant or exponential. (shrink)

Gideon Rosen proposes a view called "modal fictionalism" which Rosen thinks has all the benefits of modal realism without its ontological costs. Whereas modal realists have a paraphrase r(0) of a modal claim "0", modal fictionalists claim that the correct translation of "0" is rather the result of prefixing "according to the hypothesis of a plurality of worlds" to r(0). Rosen takes the prefix to be primitive and defines other modal notions in terms of (...) it. Bob Hale, however, thinks the fictionalist's project suffers from a "simple" dilemma. The purpose of this paper is to show that Rosen is right in taking the prefix as primitive and Hale is wrong in thinking fictionalism as being threatened by the dilemma. (shrink)

Fine (J Philos Logic 46(6):625–674, 2017) develops a unilateral and a bilateral truthmaker semantics for propositional logic. The unilateral approach trades off the primitive exact falsification relation of the bilateral approach for a primitive exclusion relation between states, thereby raising the question if exclusion serves any purpose other than to avoid exact falsification. We argue that exclusion is motivated independently of its use in avoiding exact falsification, namely as a foundation for the reconstruction of modal notions such as possibility (...) and necessity. This reconstruction in turn motivates what we call _emergent exclusion_: an atomic state can exclude a sum of atomic states collectively without excluding any of these atomic states individually. Emergent exclusion is banned in Fine (2017a) in order to maintain exact equivalence in de Morgan’s law \(\lnot (P \wedge Q) \Leftrightarrow \lnot P \vee \lnot Q\) ; we argue that the two sides of this law are not exactly equivalent and discuss a variety of state spaces that feature emergent exclusion. This paper aims to be accessible to linguists without prior exposure to truthmaker semantics. We highlight points of contact with natural language semantics, such as event semantics and algebraic semantics of plurals and conjunction. (shrink)

The article sets out a primitive ontology of the natural world in terms of primitive stuff—that is, stuff that has as such no physical properties at all—but that is not a bare substratum either, being individuated by metrical relations. We focus on quantum physics and employ identity-based Bohmian mechanics to illustrate this view, but point out that it applies all over physics. Properties then enter into the picture exclusively through the role that they play for the dynamics of the primitive (...) stuff. We show that such properties can be local, as well as holistic, and discuss two metaphysical options to conceive them, namely, Humeanism and modal realism in the guise of dispositionalism. 1 Introduction2 Primitive Ontology: Primitive Stuff3 The Physics of Matter as Primitive Stuff4 The Humean Best System Analysis of the Dynamical Variables5 Modal Realism about the Dynamical Variables6 Conclusion. (shrink)

In this paper thecanonicalmodal logics, a kind of complete modal logics introduced in K. Fine [4] and R. I. Goldblatt [5], will be characterized semantically using the concept of anultrafilter extension, an operation on frames inspired by the algebraic theory of modal logic. Theorem 8 of R. I. Goldblatt and S. K. Thomason [6] characterizing the modally definable Σ⊿-elementary classes of frames will follow as a corollary. A second corollary is Theorem 2 of [4] which states that any (...) complete modal logic defining a Σ⊿-elementary class of frames is canonical.The main tool in obtaining these results is the duality between modal algebras and general frames developed in R. I. Goldblatt [5]. The relevant notions and results from this theory will be stated in §2. The concept of a canonical modal logic is introduced and motivated in §3, which also contains the above-mentioned theorems. In §4, a kind of appendix to the preceding discussion, preservation of first-order sentences under ultrafilter extensions is discussed.The modal language to be considered here has an infinite supply of proposition letters, a propositional constant ⊥, the usual Boolean operators ¬, ∨, ∨, →, and ↔ —with ¬ and ∨ regarded as primitives—and the two unary modal operators ◇ and □ — ◇ being regarded as primitive. Modal formulas will be denoted by lower case Greek letters, sets of formulas by Greek capitals. (shrink)

On what I call absolutist essentialism about modality (AE), the metaphysical necessities are the propositions that are true in virtue of the essence (i.e. Aristotelian, absolute essence) of some entities. Other kinds of necessity can then be defined by restriction – e.g. the conceptual necessities are the propositions that are true in virtue of the essence of conceptual entities specifically. As an account of metaphysical modality and some other kinds (e.g. logical, conceptual), AE may have important virtues. However, when it (...) comes to accounting for further important kinds, like natural or normative necessity, it faces a challenge. Three main options have been defended: treat those kinds as further restricted forms of metaphysical necessity; define them as conditional forms of metaphysical necessity; treat them as primitive kinds. -/- In this paper, I propose a new option, which combines the main idea of AE (reducing necessities to essences) with an idea which has been developed largely independently: that of relative essence. On the proposed view, those kinds (e.g. natural necessity) that cannot be grounded in the essences (i.e. absolute essences) of the relevant entities (e.g. natural entities) may be grounded in their relative essences instead. Thus, I propose a generalized, or extended, version of AE, which I call relativized essentialism about modality (RE). In particular, RE offers prospects for a general framework for kinds of modality which is flexible enough to cover a large range of kinds (both absolute and relative ones) while remaining parsimonious and unified. (shrink)

1. Anderson and Belnap's most explicit characterization of the fallacy of modality is as follows: "Modal fallacies arise when it is claimed that entailments follow from, or are entailed by, contingent propositions." The view which Nelson attributes to Anderson and Belnap, on the other hand, is "that necessary propositions are entailed only by necessary ones, never by contingent ones." Anderson and Belnap speak of "entailments," whereas Nelson generalizes to "necessary propostitions." The move is far from innocent, as we shall (...) see. For though Anderson and Belnap hold that every true entailment is a necessary proposition, not every necessary proposition is an entailment. In order to grasp the implications of this distinction more clearly, let us see how Anderson and Belnap's statement of the modal fallacy might legitimately be restated in terms of necessity. To that end we must draw a related distinction between necessary propositions and necessity propositions. A expresses a necessary proposition iff A → A → A holds. A expresses a necessity proposition iff A is of the form B → C. The particular form of these definitions is dependent on the fact that entailment rather than necessity is primitive in Anderson and Belnap's system; the forms in parentheses are the equivalents in terms of necessity. Now it follows from these definitions that every entailment is a necessity proposition and that every necessity proposition is an entailment. The modal fallacy may thus be equivalently characterized as the claim that a necessity proposition is entailed by a contingent proposition. That this is different from Nelson's formulation is clear from the following considerations. First, not every necessary proposition is a necessity proposition; example: "Either it is raining or it is not raining." Second, not every necessity proposition is a necessary proposition; example: any false necessity proposition. Thus the possibility is left open that some necessary proposition might be entailed by a contingent one. This is exactly the case with Nelson's example 2, "That every polychromatic surface is red entails that every polychromatic surface is colored." This might well be a theorem in a suitable extension of E. Such cases do not, however, arise among the theorems of EI. In that limited system, all that a contingent proposition can entail is itself. (shrink)

An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its negation are satisfied. Paraconsistent logics are negation-inconsistent yet non-overcomplete; paracomplete logics are negation-incomplete yet non-overcomplete. A paranormal logic (...) is simply a logic that is both paraconsistent and paracomplete. -/- Despite being perfectly consistent and complete with respect to classical negation, nearly every normal modal logic, in its ordinary language and interpretation, admits to some latent paranormality: It is paracomplete with respect to a negation defined as an impossibility operator, and paraconsistent with respect to a negation defined as non-necessity. In fact, as it will be shown here, even in languages without a primitive classical negation, normal modal logics can often be alternatively characterized directly by way of their paranormal negations and related operators. So, instead of talking about ‘necessity’, ‘possibility’, and so on, modal logics could be seen just as devices tailored for the study of (modal) negation. This paper shows how and to what extent this alternative characterization of modal logics can be realized. (shrink)

Hossack (2007) defends what he calls the rationalist thesis: the thesis that necessity reduces to (or at least always coincides with) a priori knowledge. In this paper I discuss some features of Hossack’s rationalist account of necessity. In the first half, I attempt to fill in a missing link in the rationalist thesis, connecting the notions of primitiveness of facts and a priori modes of presentation. In the second half, I complain that the strategy of dissolving counterexamples is not enough, (...) and that a general principle connecting necessity and a prioricity is needed. I suggest further kinds of counterexamples that might arise, but rather than demand a response to each counterexample, I suggest that they highlight the need for a general argument for the rationalist thesis. (shrink)

Brandom’s reading of Hegel’s metaphysics offers an excitingly rich interpretation within the context of contemporary modal metaphysics. Brandom reads Hegel’s determinate negation in the way that the concepts of material incompatibility and material consequence relations operate. Brandom recognizes incompatibility as a modal concept and places it as a primitive in the foundation of Hegel’s metaphysics. This paper examines of Brandom’s modal foundationalist claim in comparison to how Hegel conceives of modality in his Logic. Upon this examination, the (...) paper suggests that Brandom’s interpretation remains problematically indifferent to the anti-foundationalist aspect of Hegel’s Logic and Hegel’s understanding of modality. (shrink)

In the past three decades there has been a rapid development of the formal machinery for modal logic. Quantified modal logic has developed along with a semantics and model theory that is appropriate to it. With this technical development there has been relatively little discussion of what modality is all about. There are two fundamental questions that have gone unanswered. First, to what does necessity amount? Is this a new logical notion, or is it something that can be (...) further analyzed in terms of other notions that we already have at our disposal? The second question is what makes truths involving necessity true? What is their ontological grounding in the world? This essay is directed at the first of these questions. ;There are three possible reductions of metaphysical modality. First, there is the reduction suggested by the semantics for modal logic: a reduction in terms of possible worlds. Second, there is the reduction in terms of cognition. What is possible is what is conceivable. Third, there is the reduction in terms of language. Necessities arise from the structures of language and/or language use. ;I argue that none of these is successful. All of them suffer either from presupposing some form of metaphysical necessity in the reductive base, rendering them circular and not truly reductive, or they do not do justice to the modality being reduced. ;Since necessity is not reducible to any non-modal features of the world, we need to determine whether we ought to reject it as unacceptable on this basis, or whether we ought to retain it, but treat is as a new primitive that is introduced into a philosophical or logical theory. I urge the latter course is the one that we ought to take because without it too many things will likewise be deemed unacceptable. Causal necessity and explanation, normally accepted theories or knowledge and perception, logic and logical validity, and one common manner of distinguishing sets from properties will be deemed unacceptable if de re necessity is unacceptable. All of these presuppose de re metaphysical necessity in some way. I conclude that de re metaphysical necessity ought to be retained in our theory as primitive, unanalyzable notion. (shrink)

Four progressively ambitious systems of modal propositional logic are set forth, together with decision procedures. The simultaneous employment of parenthesis notation and parenthesis-free notation, the dual use of symbols as primitive and defined, and the introduction of a new modal operator (the truth operator) are the principal devices used to effect the development of these logics. The first two logics turn out to be "the same" as two of von Wright's systems.