Logical monism is the view that there is ‘One True Logic’. This is the default position, against which pluralists react. If there were not ‘One True Logic’, it is hard to see how there could be one true theory of anything. A theory is closed under a logic! But what is logical monism? In this article, I consider semantic, logical, modal, scientific, and metaphysical proposals. I argue that, on no ‘factualist’ analysis (according to which ‘there is One True Logic’ expresses (...) a factual claim, rather than an attitude like approval), does the doctrine have both metaphysical and methodological import. Metaphysically, logics abound. Methodologically, what to infer from what is not settled by the facts, even the normative ones. I conclude that the only interesting sense in which there could be One True Logic is noncognitive. The same may be true of monism about normative areas, like moral, epistemic, and prudential ones, generally. (shrink)

This book is about the idea that some true statements would have been true no matter how the world had turned out, while others could have been false. It develops and defends a version of the idea that we tell the difference between these two types of truths in part by reflecting on the meanings of words. It has often been thought that modal issues—issues about possibility and necessity—are related to issues about meaning. In this book, the author defends the (...) view that the analysis of meaning is not just a preliminary to answering modal questions in philosophy; it is not merely that before we can find out whether something is possible, we need to get clear on what we are talking about. Rather, clarity about meaning often brings with it answers to modal questions. In service of this view, the author analyzes the notion of necessity and develops ideas about linguistic meaning, applying them to several puzzles and problems in philosophy of language. Meaning and Metaphysical Necessity will be of interest to scholars and advanced students working in metaphysics, philosophy of language, and philosophical logic. [See my homepage for a sample chapter.]. (shrink)

Talk of metaphysical modality as “absolute” is ambiguous, as it appears to convey multiple ideas. Metaphysical possibility is supposedly completely unrestricted or unqualified; metaphysical necessity is unconditional and exceptionless. Moreover, metaphysical modality is thought to be absolute in the sense that it’s real or genuine and the most objective modality: metaphysical possibility and necessity capture ways things could and must have really been. As we disentangle these ideas, certain talk of metaphysical modality qua “absolute” turns out to be misguided. Metaphysical (...) possibility isn't completely unrestricted or most inclusive compared to the other modalities; metaphysical necessity, like all kinds of necessities, is relative to or conditional upon a specific framework of reference. Still, metaphysical modality captures how things could and must have really been most generally because it deals with reality and the nature of things or their essence. That’s the chief interest of metaphysics. Arguments against the alleged absoluteness of metaphysical modality may not thereby undermine its philosophical significance. (shrink)

In this article, we discuss a simple argument that modal metaphysics is misconceived, and responses to it. Unlike Quine's, this argument begins with the simple observation that there are different candidate interpretations of the predicate ‘could have been the case’. This is analogous to the observation that there are different candidate interpretations of the predicate ‘is a member of’. The argument then infers that the search for metaphysical necessities is misguided in much the way the ‘set-theoretic pluralist’ claims that the (...) search for the true axioms of set theory is. We show that the obvious responses to this argument fail. However, a new response has emerged that purports to prove, from higher-order logical principles, that metaphysical possibility is the broadest kind of possibility applying to propositions, and is to that extent special. We distill two lines of reasoning from the literature, and argue that their import depends on premises that any ‘modal pluralist’ should deny. Both presuppose that there is a unique typed hierarchy, which is what the modal pluralist, in the context of higher-order logic, should disavow. In other words, both presupposes that there is a unique candidate for what higher-order claims could mean. We consider the worry that, in a higher-order setting, modal pluralism faces an insuperable problem of articulation, collapses into modal monism, is vulnerable to the Russell-Myhill paradox, or even contravenes the truism that there is a unique actual world, and argue that these worries are misplaced. We also sketch the bearing of the resulting ‘Higher-Order Pluralism’ on the theory of content. One theme of the discussion is that, if Higher-Order Pluralism is correct, then there is no fixed metatheory from which to characterize higher-order reality. (shrink)

⦿ In my dissertation I introduce, motivate and take the first steps in the implementation of, the project of naturalising modal metaphysics: the transformation of the field into a chapter of the philosophy of science rather than speculative, autonomous metaphysics. -/- ⦿ In the introduction, I explain the concept of naturalisation that I apply throughout the dissertation, which I argue to be an improvement on Ladyman and Ross' proposal for naturalised metaphysics. I also object to Williamson's proposal that modal metaphysics (...) --- or some view in the area --- is already a quasi-scientific discipline. -/- ⦿ Recently, some philosophers have argued that the notion of metaphysical modality is as ill defined as to be of little theoretical utility. In the second chapter I intend to contribute to such skepticism. First, I observe that each of the proposed marks of the concept, except for factivity, is highly controversial; thus, its logical structure is deeply obscure. With the failure of the "first principles" approach, I examine the paradigmatic intended applications of the concept, and argue that each makes it a device for a very specific and controversial project: a device, therefore, for which a naturalist will find no use for. I conclude that there is no well-defined or theoretically useful notion of objective necessity other than logical or physical necessity, and I suggest that naturalising modal metaphysics can provide more stable methodological foundations. -/- ⦿ In the third chapter I answer a possible objection against the in-principle viability of the project: that the concept of metaphysical modality cannot be understood through the philosophical analysis of any scientific theory, since metaphysical necessity "transcends'' natural necessity, and science only deals with the latter. I argue that the most important arguments for this transcendence thesis fail or face problems that, as of today, remain unsolved. -/- ⦿ Call the idea that science doesn't need modality, "demodalism''. Demodalism is a first step in a naturalistic argument for modal antirealism. In the fourth chapter I examine six versions of demodalism to explain why a family of formalisms, that I call "spaces of possibility'', are (i) used in a quasi-ubiquitous way in mathematised sciences (I provide examples from theoretical computer science to microeconomics), (ii) scientifically interpreted in modal terms, and (iii) used for at least six important tasks: (1) defining laws and theories; (2) defining important concepts from different sciences (I give several examples); (3) making essential classifications; (4) providing different types of explanations; (5) providing the connection between theory and statistics, and (6) understanding the transition between a theory and its successor (as is the case with quantisation). -/- ⦿ In fifth chapter I propose and defend a naturalised modal ontology. This is a realism about modal structure: my realism about constraints. The modal structure of a system are the relationships between its possible states and between its possible states and those of other systems. It is given by the plurality of restrictions to which said system is subject. A constraint is a factor that explains the impossibility of a class of states; I explain this concept further. First, I defend my point of view by rejecting some of its main rivals: constructive empiricism, Humean conventionalism, and wave function realism, as they fail to make sense of quantum chaos. This is because the field requires the notion of objective modal structure, and the mentioned views have trouble explaining the modal facts of quantum dynamics. Then, I argue that constraint realism supersedes these views in the context of Bohm's standard theory and mechanics, and underpins the study of quantum chaos. Finally, I consider and reject two possible problems for my point of view. -/- ⦿ A central concern of modal metaphysicians has been to understand the logical system that best characterises necessity. In the sixth chapter I intend to recover the logical project applied to my naturalistic modal metaphysics. Scientists and philosophers of science accept different degrees of physical necessity, ranging from purely mathematically necessary facts that restrict physical behaviour, to kinetic principles, to particular dynamical constraints. I argue that this motivates a multimodal approach to modal logic, and that the time dependence of dynamics motivates a logic of historical necessity. I propose multimodal propositional (classical) logics for Bohmian mechanics and the Everettian theory of many divergent worlds, and I close with a criticism of Williamson's approach to the logic of state spaces of dynamic systems. (shrink)

The aim of this paper is to argue in favor of the view that some counterpossibles are false. This is done indirectly by showing that accepting the opposite view, i.e., one that ascribes truth to each and every counterpossible, results in the claim that every necessarily false theory has exactly the same consequences. Accordingly, it is shown that taking every counterpossible to be true not only undermines the value of debates over various alternative theories and their consequences, but also puts (...) into question the very possibility of such debates. In order to explicate this thesis, the close bond between counterpossibles and the so-called story prefix is explored. A number of possible responses to this criticism are also presented, and it is argued that none of them address the main problem. (shrink)

Abstract Impossible fictions have lessons to teach us about linguistic representation, about mental content and concepts, and about uses of conceivability in epistemology. An adequate theory of impossible fictions may require theories of meaning that can distinguish between different impossibilities; a theory of conceptual truth that allows us to make useful sense of a variety of conceptual falsehoods; and a theory of our understanding of necessity and possibility that permits impossibilities to be conceived. After discussing these questions, strategies for resisting (...) the picture of impossible fictions presented here and in Part I are discussed. Perhaps apparently impossible fictions describe possibilities after all; or perhaps impossible fictions are all trivial; or perhaps some apparently intelligible impossible fictions are unintelligible after all. (shrink)

Readers of fictions sometimes resist taking certain kinds of claims to be true according to those fictions, even when they appear explicitly or follow from applying ordinary principles of interpretation. This "imaginative resistance" is often taken to be significant for a range of philosophical projects outside aesthetics, including giving us evidence about what is possible and what is impossible, as well as the limits of conceivability, or readers' normative commitments. I will argue that this phenomenon cannot do the theoretical work (...) that has been asked of it. Resistance to taking things to be fictional is often best explained by unfamiliarity with kinds of fictions than any representational, normative, or cognitive limits. With training and experience, any understandable proposition can be made fictional and be taken to be fictional by readers. This requires a new understanding both of imaginative resistance, and what it might be able to tell us about topics like conceivability or the bounds of possibility. (shrink)

Logical nihilism is the view that the relation of logical consequence is empty: there are counterexamples to any putative logical law. In this paper, I argue that the nihilist threat is illusory. The nihilistic arguments do not work. Moreover, the entire project is based on a misguided interpretation of the generality of logic.

We explore a ‘Neo-Cartesian’ account of divine ultimacy that raises the concept of God to its ultimate level of abstraction so that we can do away with even the question of his existence. Our starting point is God’s relation to the logical and metaphysical order of reality and the views of Descartes and Leibniz on this topic. While Descartes held the seemingly bizarre view that the eternal truths are freely created by God, Leibniz stands for the mainstream view that the (...) eternal truths are grounded in God’s nature. We argue that the implausibility of Descartes’ doctrine stems mainly from the assumption that there is a non-epistemic notion of absolute necessity that constitutes the ultimate court of appeal for all modal questions and that this assumption is questionable. We also question the assumption that God’s ultimacy merely requires that all reality be grounded in God in the sense of mere explanation, so that it suffices if the necessary truths are grounded in God’s nature but not in God’s will. This will lead us to a reassessment of Descartes’ position. In the final and main part of the paper, we push Descartes’ doctrine of the creation of the eternal truths to its ‘logical’ conclusion with the aim of getting to a novel conception of ‘God.’. (shrink)

It is widely alleged that metaphysical possibility is “absolute” possibility Conceivability and possibility, Clarendon, Oxford, 2002, p 16; Stalnaker, in: Stalnaker Ways a world might be: metaphysical and anti-metaphysical essays, Oxford University Press, Oxford, 2003, pp 201–215; Williamson in Can J Philos 46:453–492, 2016). Kripke calls metaphysical necessity “necessity in the highest degree”. Van Inwagen claims that if P is metaphysically possible, then it is possible “tout court. Possible simpliciter. Possible period…. possib without qualification.” And Stalnaker writes, “we can agree (...) with Frank Jackson, David Chalmers, Saul Kripke, David Lewis, and most others who allow themselves to talk about possible worlds at all, that metaphysical necessity is necessity in the widest sense.” What exactly does the thesis that metaphysical possibility is absolute amount to? Is it true? In this article, I argue that, assuming that the thesis is not merely terminological, and lacking in any metaphysical interest, it is an article of faith. I conclude with the suggestion that metaphysical possibility may lack the metaphysical significance that is widely attributed to it. (shrink)

It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If there were nothing otherwise “uniquely metaphysically significant” about (...) metaphysical necessity, then paradigmatic metaphysical necessities would be necessary in one sense of “necessary”, not necessary in another, and that would be it. The question of whether they were necessary simpliciter would be like the question of whether the Parallel Postulate is true simpliciter – understood as a pure mathematical conjecture, rather than as a hypothesis about physical spacetime. In a sense, the latter question has no objective answer. In this article, I argue that paradigmatic questions of modal metaphysics are like the Parallel Postulate question. I then discuss the deflationary ramifications of this argument. I conclude with an alternative conception of the space of possibility. According to this conception, there is no objective boundary between possibility and impossibility. Along the way, I sketch an analogy between modal metaphysics and set theory. (shrink)

Possible worlds have found many applications in contemporary philosophy: from theories of possibility and necessity, to accounts of conditionals, to theories of mental and linguistic content, to understanding supervenience relationships, to theories of properties and propositions, among many other applications. Almost as soon as possible worlds started to be used in formal theories in logic, philosophy of language, philosophy of mind, metaphysics, and elsewhere, theorists started to wonder whether impossible worlds should be postulated as well. In many applications, possible worlds (...) face limitations that can be dealt with through postulating impossible worlds as well. This chapter examines some of the uses of impossible worlds, and philosophical challenges theories of impossible worlds face. (shrink)

It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If there were nothing otherwise “uniquely metaphysically significant” about (...) metaphysical necessity, then paradigmatic metaphysical necessities would be necessary in one sense of “necessary”, not necessary in another, and that would be it. The question of whether they were necessary simpliciter would be like the question of whether the Parallel Postulate is true simpliciter – understood as a pure mathematical conjecture, rather than as a hypothesis about physical spacetime. In a sense, the latter question has no objective answer. In this article, I argue that paradigmatic questions of modal metaphysics are like the Parallel Postulate question. I then discuss the deflationary ramifications of this argument. I conclude with an alternative conception of the space of possibility. According to this conception, there is no objective boundary between possibility and impossibility. Along the way, I sketch an analogy between modal metaphysics and set theory. (shrink)

This paper explores a special kind of loop of grounding: cosmic loops. A cosmic loop is a loop that intuitively requires us to go "around" the entire universe to come back to the original ground. After describing several kinds of cosmic loop scenarios, I will discuss what we can learn from these scenarios about constraints on grounding; the conceivability of cosmic loops; the possibility of cosmic loops; and the prospects for salvaging local reflexivity, asymmetry and transitivity of grounding in a (...) world containing a cosmic loop of ground. The considerations raised in this paper also bear on what we should think about relations that are meant to support grounding relations: in particular, revisions to theories of the part-whole relation are discussed. (shrink)

A lot of philosophers engage in debates about what claims are “metaphysically necessary”, and a lot more assume with little argument that some classes of claims have the status of “metaphysical necessity”. I think we can usefully replace questions about metaphysical necessity with five other questions which each capture some of what people may have had in mind when talking about metaphysical necessity. This paper explains these five other questions, and then discusses the question “how much of metaphysics is metaphysically (...) necessary?”, and each of its five replacements. (shrink)

Lewisian Genuine Realism about possible worlds is often deemed unable to accommodate impossible worlds and reap the benefits that these bestow to rival theories. This thesis explores two alternative extensions of GR into the terrain of impossible worlds. It is divided in six chapters. Chapter I outlines Lewis’ theory, the motivations for impossible worlds, and the central problem that such worlds present for GR: How can GR even understand the notion of an impossible world, given Lewis’ reductive theoretical framework? Since (...) the desideratum is to incorporate impossible worlds into GR without compromising Lewis’ reductive analysis of modality, Chapter II defends that analysis against objections. The rest of the thesis is devoted to incorporating impossible worlds into GR. Chapter III explores GR-friendly impossible worlds in the form of set-theoretic constructions out of genuine possibilia. Then, Chapters IV-VI venture into concrete impossible worlds. Chapter IV addresses Lewis’ objection against such worlds, to the effect that contradictions true at impossible worlds amount to true contradictions tout court. I argue that even if so, the relevant contradictions are only ever about the non-actual, and that Lewis’ argument relies on a premise that cannot be nonquestion- beggingly upheld in the face of genuine impossible worlds in any case. Chapter V proposes that Lewis’ reductive analysis can be preserved, even in the face of genuine impossibilia, if we differentiate the impossible from the possible by means of accessibility relations, understood non-modally in terms of similarity. Finally, Chapter VI counters objections to the effect that there are certain impossibilities, formulated in Lewis’ theoretical language, which genuine impossibilia should, but cannot, represent. I conclude that Genuine Realism is still very much in the running when the discussion turns to impossible worlds. (shrink)

It is a venerable slogan due to David Hume, and inherited by the empiricist tradition, that the impossible cannot be believed, or even conceived. In Positivismus und Realismus, Moritz Schlick claimed that, while the merely practically impossible is still conceivable, the logically impossible, such as an explicit inconsistency, is simply unthinkable. -/- An opposite philosophical tradition, however, maintains that inconsistencies and logical impossibilities are thinkable, and sometimes believable, too. In the Science of Logic, Hegel already complained against “one of the (...) fundamental prejudices of logic as hitherto understood”, namely that “the contradictory cannot be imagined or thought” (Hegel 1931: 430). Our representational capabilities are not limited to the possible, for we appear to be able to imagine and describe also impossibilities — perhaps without being aware that they are impossible. -/- Such impossibilities and inconsistencies are what this entry is about... (shrink)

I am grateful to Sean Carroll, Paul Horwich, and Sarah McGrath for their stimulating responses to Morality and Mathematics (M&M). Their arguments concern the reality of unapplied mathematics, the practical import of moral facts, and the deliberative and explanatory roles of evaluative theories. In what follows, I address their responses, as well as some broader issues.

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)

En este trabajo examino el argumento de McFetridge a favor de la necesidad de la creencia en la necesidad. El argumento pretende establecer un dilema fatal para el “nihilista” modal, aquel que no cree que al menos alguna proposición es necesaria. Mi objetivo principal es mostrar que el dilema que presenta el argumento de McFetridge no es sólido, pues tiene una limitación muy importante con respecto al segundo de sus cuernos, el cual es el más interesante. El segundo cuerno del (...) dilema plantea una especie de argumento trascendental: es necesario creer en la necesidad si es que vamos a ser capaces de razonar confiablemente bajo suposiciones contrafácticas. Sin embargo, este argumento asume que la suposición contrafáctica es una actividad esencial en nuestras vidas, lo cual señala, sostengo, un punto central alrededor del cual el nihilista modal intentaría reafirmar su posición. Así, pretendo mostrar que el segundo cuerno del dilema de McFetridge revela que el quid de la discusión entre creyentes y nihilistas modales debe moverse propiamente de la cuestión del rol de la creencia en la necesidad a la cuestión del rol de la suposición contrafáctica. (shrink)

Logical monists and pluralists disagree about how many correct logics there are; the monists say there is just one, the pluralists that there are more. Could it turn out that both are wrong, and that there is no logic at all?

In this paper I probe the idea that neither possibilism nor trivialism could be ruled out on a purely logical basis. I use the apparatus of relational structures used in the semantics for modal logics to engineer some models of possibilism and trivialism and I discuss a philosophical stance about logic, truth values and the meaning of connectives underlying such analysis.

We outline a theory of the cognitive role of belief in absolute necessity that is normative and intended to be metaphysically neutral. We take this theory to be unique in scope since it addresses simultaneously the questions of how such belief is (properly) acquired and of how it is (properly) manifest. The acquisition and manifestation conditions for belief in absolute necessity are given univocally, in terms of complex higher-order attitudes involving two distinct kinds of supposition (A-supposing and C-supposing). It is (...) subsequently argued that the proposed acquisition and manifestation conditions are rationally interdependent, and that such harmony affords explanations of connections between different facets of belief in necessity that otherwise remain mysterious. (shrink)

The article looks at the structure of impossible worlds, and their deployment in the analysis of some intentional notions. In particular, it is argued that one can, in fact, conceive anything, whether or not it is impossible. Thus a semantics of conceivability requires impossible worlds.

According to logical non-necessitarianism, every inference may fail in some situation. In his defense of logical monism, Graham Priest has put forward an argument against non-necessitarianism based on the meaning of connectives. According to him, as long as the meanings of connectives are fixed, some inferences have to hold in all situations. Hence, in order to accept the non-necessitarianist thesis one would have to dispose arbitrarily of those meanings. I want to show here that non-necessitarianism can stand, without disposing arbitrarily (...) of the meanings of connectives, based on a minimalist view on the meanings of connectives. (shrink)

Impossible worlds are regarded with understandable suspicion by most philosophers. Here we are concerned with a modal argument which might seem to show that acknowledging their existence, or more particularly, the existence of some hypothetical (we do not say “possible”) world in which everything was the case, would have drastic effects, forcing us to conclude that everything is indeed the case—and not just in the hypothesized world in question. The argument is inspired by a metaphysical (rather than modal-logical) argument of (...) Paul Kabay’s which would have us accept this unpalatable conclusion, though its details bear a closer resemblance to a line of thought developed by Jc Beall, in response to which Graham Priest has made some philosophical moves which are echoed in our diagnosis of what goes wrong with the present modal argument. Logical points of some interest independent of the main issue arise along the way. (shrink)

_T__S_ is a logic that has no valid inferences. But, could there be a logic without valid metainferences? We will introduce _T__S_ _ω_, a logic without metainferential validities. Notwithstanding, _T__S_ _ω_ is not as empty—i.e., uninformative—as it gets, because it has many antivalidities. We will later introduce the two-standard logic [_T__S_ _ω_, _S__T_ _ω_ ], a logic without validities and antivalidities. Nevertheless, [_T__S_ _ω_, _S__T_ _ω_ ] is still informative, because it has many contingencies. The three-standard logic [ \(\mathbf {TS}_{\omega (...) }, \mathbf {ST}_{\omega }, [{\overline {\emptyset }}{\emptyset }, {\emptyset } {\overline {\emptyset }}]\) ] that we will further introduce, has no validities, no antivalidities and also no contingencies whatsoever. We will also present two more validity-empty logics. The first one has no supersatisfiabilities, unsatisfabilities and antivalidities ∗. The second one has no invalidities nor non-valid-nor-invalid (meta)inferences. All these considerations justify thinking of logics as, at least, three-standard entities, corresponding, respectively, to what someone who takes that logic as correct, accepts, rejects and suspends judgement about, just because those things are, respectively, validities, antivalidities and contingencies of that logic. Finally, we will present some consequences of this setting for the monism/pluralism/nihilism debate, and show how nihilism and monism, on one hand, and nihilism and pluralism, on the other hand, may reconcile—at least according to how Gillian Russell understands nihilism, and provide some general reasons for adopting a multi-standard approach to logics. (shrink)

A world is trivial if it makes every proposition true all at once. Such a world is impossible, an absurdity. Our world, we hope, is not an absurdity. It is important, nevertheless, for semantic and metaphysical theories that we be able to reason cogently about absurdities—if only to see that they are absurd. In this note we describe methods for ‘observing’ absurd objects like the trivial world without falling in to incoherence, using some basic techniques from modal logic. The goal (...) is to begin to locate the trivial world’s relative position in modal space; the outcome is that the less we assume about relative possibility, the more detail we can discern at the edge of reason. (shrink)

The paradoxes of self reference have to be dealt with by anyone seeking to give a satisfactory account of the logic of truth, of properties, and even of sets of numbers. Unfortunately, there is no widespread agreement as to how to deal with these paradoxes. Some approaches block the paradoxical inferences by rejecting as invalid a move that classical logic counts as valid. In the recent literature, this deviant logic analysis of the paradoxes has been called into question.This disagreement motivates (...) a re-examination of the philosophy of formal logic and the status of logical truths and rules. In this paper I do some of this work, and I show that this gives us the means to defend the deviant approaches against such criticisms. As a result I hope to show that these analyses of the paradoxes are worthy of more serious consideration than they have so far received. (shrink)

While knowledge of mere possibilities is difficult to understand, knowledge of possibilities that are actual seems unproblematic (as far as we know the actual world). The principle that what is actual is possible has been near-universally accepted. After summarizing some sporadic dissent, I present a proposal for how the validity of the principle might be restricted. While the principle certainly holds for sufficiently inclusive objective and epistemic possibilities, it may not hold when the accessibility of possibilities is contextually restricted.

This note is an analysis of the paradox given by Myers. It is shown, assuming that the resources available in paraconsistent logic may be applied, how the conclusion of the paradox may be perfectly acceptable, but that the argument is, nonetheless, invalid. This provides a dialethic solution to the paradox.

A simple, bivalent semantics is defined for Łukasiewicz’s 4-valued modal logic Łm4. It is shown that according to this semantics, the essential presupposition underlying Łm4 is the following: A is a theorem iff A is true conforming to both the reductionist and possibilist theses defined as follows: rt: the value of modal formulas is equivalent to the value of their respective argument iff A is true, etc.); pt: everything is possible. This presupposition highlights and explains all oddities arising in Łm4.

Beall has given more or less convincing arguments to the effect that neither classical logic, nor K3, nor LP, nor S3 can play the role he expects from logic: to be the basement theory for all true theories, including true theology. However, he has not considered all the pertinent competitors, and he has not given any reassurance that he has not gone too low in the hierarchy of logics to find his desired “universal closure of all true theories”. In this (...) paper, I put forward those additional arguments to show the superiority of FDE with respect to logics that include a detachable conditional but that are very much like FDE otherwise. I also discuss the problem that theological consequence might not contrapose even if theological consequence is supposed to extend FDE consequence and the latter does contrapose. (shrink)

One of Arthur Prior’s constructions of the relational calculus for times within tense logic plus propositional quantifiers is considered using Malcolm Rennie’s multimodal semantics and found wantin...