The standard view about counterfactuals is that a counterfactual (A > C) is true if and only if the A-worlds most similar to the actual world @ are C-worlds. I argue that the worlds conception of counterfactuals is wrong. I assume that counterfactuals have non-trivial truth-values under physical determinism. I show that the possible-worlds approach cannot explain many embeddings of the form (P > (Q > R)), which intuitively are perfectly assertable, and which must be (...) true if the contingent falsity of (Q > R) is to be explained. If (P > (Q > R)) has a backtracking reading then the contingent facts that (Q > R) needs to be true in the closest P-worlds are absent. If (P > (Q > R)) has a forwardtracking reading, then the laws required by (Q > R) to be true in the closest P-worlds will be absent, because they are violated in those worlds. Solutions like lossy laws or denial of embedding won't work. The only approach to counterfactuals that explains the embedding is a pragmatic metalinguistic approach in which the whole idea that counterfactuals are about a modal reality, be it abstract or concrete, is given up. (shrink)
How do ordinary objects persist through time and across possibleworlds ? How do they manage to have their temporal and modal properties ? These are the questions adressed in this book which is a "guided tour of theories of persistence". The book is divided in two parts. In the first, the two traditional accounts of persistence through time (endurantism and perdurantism) are combined with presentism and eternalism to yield four different views, and their variants. The resulting views (...) are then examined in turn, in order to see which combinations are appealing and which are not. It is argued that the 'worm view' variant of eternalist perdurantism is superior to the other alternatives. In the second part of the book, the same strategy is applied to the combinations of views about persistence across possibleworlds (trans-world identity, counterpart theory, modal perdurants) and views about the nature of worlds, mainly modal realism and abstractionism. Not only all the traditional and well-known views, but also some more original ones, are examined and their pros and cons are carefully weighted. Here again, it is argued that perdurance seems to be the best strategy available. (shrink)
The most commonly heard proposals for reducing possibleworlds to language succumb to a simple cardinality argument: it can be shown that there are more possibleworlds than there are linguistic entities provided by the proposal. In this paper, I show how the standard proposals can be generalized in a natural way so as to make better use of the resources available to them, and thereby circumvent the cardinality argument. Once it is seen just what the (...) limitations are on these more general proposals, it can be clearly seen where the real difficulty lies with any attempt to reduce possibleworlds to language. Roughly, the difficulty is this: no actual language could have the descriptive resources needed to represent all the ways things might have been. I conclude by arguing that this same difficulty spells doom for any nominalist or conceptualist proposal for reducing possibleworlds. (shrink)
Among the most remarkable developments in metaphysics since the 1950’s is the explosion of philosophical interest in possibleworlds. This paper proposes an explanation of what possibleworlds are, and argues that this proposal, the interpreted models conception, should be attractive to anyone who thinks that modal facts are primitive, and so not to be explained in terms of some non-modal notion of “possible world.” I articulate three constraints on any acceptable primitivist explanation of the (...) nature of possibleworlds, and show that the interpreted models conception meets the three constraints. (shrink)
If realism about possibleworlds is to succeed in eliminating primitive modality, it must provide an 'analysis' of possible world: nonmodal criteria for demarcating one world from another. This David Lewis has done. Lewis holds, roughly, that worlds are maximal unified regions of logical space. So far, so good. But what Lewis means by 'unification' is too narrow, I think, in two different ways. First, for Lewis, all worlds are (almost) 'globally' unified: at any world, (...) (almost) every part is directly linked to (almost) every other part. I hold instead that some worlds are 'locally' unified: at some worlds, parts are directly linked only to "neighboring" parts. Second, for Lewis, each world is (analogically) 'spatio-temporally' unified; every world is 'spatio-temporally' isolated from every other. I hold instead: a world may be unified by nonspatio-temporal relations; every world is 'absolutely' isolated from every other. If I am right, Lewis's conception of logical space is impoverished: perfectly respectable worlds are missing. (shrink)
In this paper I explore the relationship between the idea of possibleworlds and the notion of the beauty of God. I argue that there is a clear contradiction between the idea that God is utterly and completely beautiful on the one hand and the notion that He contains within himself all possibleworlds on the other. Since some of the possibleworlds residing in the mind of the deity are ugly, their presence seems (...) to compromise God's complete and utter beauty. (shrink)
In this paper, an argument of Alvin Plantinga's for the existence of abstract possibleworlds is shown to be unsound. The argument is based on a principle Plantinga calls "Quasicompactness", due to its structural similarity to the notion of compactness in first-order logic. The principle is shown to be false.
We show that, given standard assumptions about classical dynamical systems, Lewis' conception of possibleworlds is incompatible with classical physics in that it would imply that all dynamical systems were integrable.
The question as to whether some objects are possibleworlds that have an initial segment in common, i.e. so that their fusion is a temporal tree whose branches are possibleworlds, arises both for those who hold that our universe has the structure of a temporal tree and for those who hold that what there is includes concrete universes of every possible variety. The notion of “possible world” employed in the question is seen to (...) be the notion of an object of a kind such that objects of that kind play a certain theoretical role. Lewis’s discussion of the question is thereby clarified but is nevertheless inadequate; his negative answer is correct but even from his combinatorialist viewpoint the rationale he provides for this answer is misguided. I explain why the combinatorialist advocate of concrete plenitude should hold that no object is a tree of possibleworlds. Then I explain that for a different reason the nomic essentialist advocate of concrete plenitude should hold this much too. (shrink)
David Lewis' modal counterpart theory falls prey to the famous Saul Kripke's objection, and this is mostly due to his 'static' ontology (divergence) of possibleworlds. This paper examines a genuinely realist but different, branching ontology of possibleworlds and a new definition of the counterpart relation, which attempts to provide us with a better account of de re modality, and to meet satisfactorily Kripke's claim, while being also ontologically more 'parsimonious'.
Accounts of modality in terms of fictional possibleworlds face an objection based on the idea that when modal claims are analysed in terms of fictions, the connection between analysans and analysandum seems artificial. Strong modal fictionalism, the theory according to which modal claims are analysed in terms of a fiction, has been defended by, among others, Seahwa Kim, who has recently claimed that the philosophical objection that the connection between modality and fictions is artificial can be met. (...) I propose a new way of spelling out the intuition of artificiality and show that strong modal fictionalism should be rejected. (shrink)
This chapter begins with a discussion of Kant's theory of judgment-forms. It argues that it is not true in Kant's logic that assertoric or apodeictic judgments imply problematic ones, in the manner in which necessity and truth imply possibility in even the weakest systems of modern modal logic. The chapter then discusses theories of judgment-form after Kant, the theory of quantification, Frege's Begriffsschrift, C. I. Lewis and the beginnings of modern modal logic, the proof-theoretic approach to modal logic, possible (...) world semantics, correspondence theory, and modality and quantification. (shrink)
There are ways in which the new tenseless theory of time is analogous to David Lewis’s modal realism. The new tenseless theory gives an indexical analysis of temporal terms such as ‘now’, while Lewis gives and indexical analysis of ‘actual’. For the new tenseless theory, all times are equally real; for Lewis, all worlds are equally real. In this paper I investigate this apparent analogy between these two theories, and ask whether a proponent of one is committed, by parity (...) of reasoning, to the other. I conclude that the analogy is merely apparent, and that independent reasons are needed to support each theory. (shrink)
In his early lecture note Versuch einiger Betrachtungen über den Optimismus (1759) a young supporter of metaphysical optimism called Immanuel Kant tested the Leibnizian optimism by posing some counter-arguments against it only to falsify them. His counter-arguments were very inventive and they feature often in modern scholarship on Leibniz. In this paper I will present Kant’s main arguments and evaluate them. I will argue that Kant’s understanding on Leibnizian optimism is little misguided and for this reason his own positive counter-argument (...) despite its ingeniousness is problematic. His second solution to the problem is comparable to the doctrine of metaphysical optimism, but fails also for the same reason as the first one. -/- . (shrink)
In the paper there is presented the semantic interpretation of idealism/ realism controversy which is one of the most essential issues in Ingarden’s phenomenological project of ontology. The procedure of semantic paraphrase which is contemporary developed by Wolen´ ski, is the main interpretative tool. In the central part of the paper, there is formulated the formal theory of the semantic framework underlying idealism/realism discourse. Finally, there are formulated some notes showing that intentional conception of negation may be used for defending (...) various idealistic positions. (shrink)
"Jim would still be alive if he hadn't jumped" means that Jim's death was a consequence of his jumping. "x wouldn't be a triangle if it didn't have three sides" means that x's having a three sides is a consequence its being a triangle. Lewis takes the first sentence to mean that Jim is still alive in some alternative universe where he didn't jump, and he takes the second to mean that x is a non-triangle in every alternative universe where (...) it doesn't have three sides. Why did Lewis have such obviously wrong views? Because, like so many of his contemporaries, he failed to grasp the truth that it is the purpose of the present paper to demonstrate, to wit: No coherent doctrine assumes that statements about possibleworlds are anything other than statements about the dependence-relations governing our world. The negation of this proposition has a number of obviously false consequences, for example: all true propositions are necessarily true (there is no modal difference between "2+2=4" and "Socrates was bald"); all modal terms (e.g. "possible," "necessary") are infinitely ambiguous; there is no difference between laws of nature (e.g. "metal expands when heated") and accidental generalizations (e.g. "all of the coins in my pocket are quarters"); and there is no difference between the belief that 1+1=2 and the belief that arithmetic is incomplete. Given that possibleworlds are identical with mathematical models, it follows that the concept of model-theoretic entailment is useless in the way of understanding how inferences are drawn or how they should be drawn. Given that the concept of formal-entailment is equally useless in these respects, it follows that philosophers and mathematicians have simply failed to shed any light on the nature of the consequence-relation. Q's being either a formal or a model-theoretic consequence of P is parasitic on its bearing some third, still unidentified relation to P; and until this relation has been identified, the discipline of philosophical logic has yet to begin. (shrink)
The development of possibleworlds semantics for modal claims has led to a more general application of that theory as a complete semantics for various formal and natural languages, and this view is widely held to be an adequate (philosophical) interpretation of the model theory for such languages. We argue here that this view generates a self-referential inconsistency that indicates either the falsity or the incompleteness of PWS.
In this paper it is argued that the conjunction of linguistic ersatzism, the ontologically deflationary view that possibleworlds are maximal and consistent sets of sentences, and possible world semantics, the view that the meaning of a sentence is the set of possibleworlds at which it is true, implies that no actual speaker can effectively use virtually any language to successfully communicate information. This result is based on complexity issues that relate to our finite (...) computational ability to deal with large bodies of information and a strong, but well motivated, assumption about the cognitive accessibility of meanings of sentences ersatzers seem to be implicitly committed to. It follows that linguistic ersatzism, possible world semantics, or both must be rejected. (shrink)
If a possible-worlds semantic theory for modal logics is pure, then the assertion of the theory, taken at face-value, can bring no commitment to the existence of a plurality of possibleworlds (genuine or ersatz). But if we consider an applied theory (an application of the pure theory) in which the elements of the models are required to be possibleworlds, then assertion of such a theory, taken at face-value, does appear to bring commitment (...) to the existence of a plurality of possibleworlds. Or at least that is so if the applied theory is adequate. For an applied possible-worlds semantic theory that is constrained to contain only one-world models is bound to deliver results on validity, soundness and completeness that are apt to seem disastrous. I attempt to steer a course between commitment to the existence of a plurality of possibleworlds and commitment to such a disastrous applied possible-worlds semantics by noting, and developing, the position of one who asserts such a theory at face-value but who remains agnostic about the existence of other (non-actualized) possibleworlds. Thus, a novel interpretation of applied possible-worlds semantics is offered on which we may lay claim to whatever benefits such a theory offers while avoiding realism about (other) possibleworlds. Thereby, the contention that applied possible-worlds semantics gives us reason to be realists about possibleworlds is (further) undermined. (shrink)
It is difficult to wander far in contemporary metaphysics without bumping into talk of possibleworlds. And reference to possibleworlds is not confined to metaphysics. It can be found in contemporary epistemology and ethics, and has even made its way into linguistics and decision theory. What are those possibleworlds, the entities to which theorists in these disciplines all appeal? This paper sets out and evaluates a leading contemporary theory of possible (...) class='Hi'>worlds, David Lewis's Modal Realism. I note two competing ambitions for a theory of possibleworlds: that it be reductive and user-friendly. I then outline Modal Realism and consider objections to the effect that it cannot satisfy these ambitions. I conclude that there is some reason to believe that Modal Realism is not reductive and overwhelming reason to believe that it is not user-friendly. (shrink)
Possibleworlds, concrete or abstract as you like, are irrelevant to the truthmakers for modality—or so I shall argue in this paper. First, I present the Neo-Humean picture of modality, and explain why those who accept it deny a common sense view of modality. Second, I present what I take to be the most pressing objection to the Neo-Humean account, one that, I argue, applies equally well to any theory that grounds modality in possibleworlds. Third, (...) I present an alternative, properties-based theory of modality and explore several specific ways to flesh the general proposal out, including my favored version, the Powers Theory. And, fourth, I offer a powers semantics for counterfactuals that each version of the properties-based theory of modality can accept, mutatis mutandis. Together with a definition of possibility and necessity in terms of counterfactuals, the powers semantics of counterfactuals generates a semantics for modality that appeals to causal powers and not possibleworlds. (shrink)
In his "Two Concepts of PossibleWorlds" (1986), Peter Van Inwagen explores two kinds of views about the nature of possibleworlds: abstractionism and concretism. The latter is the view defended by David Lewis, who claims that possibleworlds are concrete spatio-temporal universes, very much like our own, causally and spatio-temporally disconnected from each other. The former is the view of the majority, who claim that possibleworlds are some kind of abstract (...) objects – such as propositions, properties, states of affairs or sets of numbers. In this paper, I will develop this view in an "extreme abstractionist" way, appealing to a "modal bundle theory", and I will try to show that it is preferable to the standard abstractionist views. Finally, I will compare this kind of abstractionism to concretism, only to find that the difference between the two is minimal. (shrink)
It is difficult to wander far in contemporary metaphysics without bumping into talk of possibleworlds. And, reference to possibleworlds is not confined to metaphysics. It can be found in contemporary epistemology and ethics, and has even made its way into linguistics and decision theory. What are those possibleworlds, the entities to which theorists in these disciplines all appeal? Some have hoped that a theory of possibleworlds can be used (...) to reduce modality to non-modal terms. This paper sets reductive theories aside, and articulates and applies a framework for evaluating non-reductive theories of possibleworlds. I argue that, if we abjure reduction, we should aim for a theory of possibleworlds that is user-friendly. I then outline four leading contemporary theories and consider objections to each. My conclusions are negative: every theory we discuss fails to be user-friendly in some significant respect. (shrink)
Providing a possibleworlds semantics for a logic involves choosing a class of possibleworlds models, and setting up a truth definition connecting formulas of the logic with statements about these models. This scheme is so flexible that a danger arises: perhaps, any (reasonable) logic whatsoever can be modelled in this way. Thus, the enterprise would lose its essential tension. Fortunately, it may be shown that the so-called incompleteness-examples from modal logic resist possibleworlds (...) modelling, even in the above wider sense. More systematically, we investigate the interplay of truth definitions and model conditions, proving a preservation theorem characterizing those types of truth definition which generate the minimal modal logic. (shrink)
This book is a survey, fortified by original material, of metaphysical theories of modality set in terms of possibleworlds. Those theories include what Divers calls “genuine realism”, or “GR” — this is David Lewis’s “genuine modal realism” — and what Divers calls “actualist realism”, or “AR” — this seems to be the same as what Lewis called “ersatz modal realism”, which has also become widely know as “ersatzism”. Two important kinds of theory are not included: those that (...) treat modality by means not involving possibleworlds at all (for example, modalism, various kind of non-cognitivism, and Quinean eliminativism about modality); and those that, while treating modality by talking about possibleworlds, go on to deny that there are any possibleworlds in one way or another (for example, Rosen’s fictionalism, and Divers’ own agnosticism about possibleworlds). These get a short discussion towards the end of the introductory part of the book (sections 2.4–2.6), and Divers is planning to write a companion volume covering them. (shrink)
A possibleworlds treatment of the normal alethic modalities was, after classical model theory, logic’s most significant semantic achievement in the century just past. Kripke’s groundbreaking paper appeared in 1959 and, in the scant few succeeding years, its principal analytical tool, possibleworlds, was adapted to serve a range of quite different-seeming purposes – from nonnormal logics, to epistemic and doxastic logics, deontic and temporal logics and, not much later, the logic of counterfactual conditionals. In short (...) order, possibleworlds acquired a twofold reputation which has steadily enlarged to the present day. They were celebrated for both their mathematical power and their sheer versatility. This sets the stage for what I want to do here. I wish to explore the extent to which the supposed versatility of a possibleworlds semantics is justified. In so doing, I shall confine my attention to its role in (1) logics of counterfactual conditionals, and (2) logics of belief. The question I pose is, why and on what grounds should we think that the device of possibleworlds turns the semantic trick for these logics? My answer is that they do not turn the trick for them. Whereupon a further question presses for attention. If possibleworlds semantics don’t work there, why does virtually everyone think that they do? Answering this second question is risky. Who am I to say why virtually everyone thinks that the possibleworlds approach is more successful than I do? Who has vouchsafed me these powers? I shall try to mitigate the riskiness of my answer by contextualizing the evaluation of this approach in the following ways. First, the triumph of possibleworlds occurred in the midst of a powerful general trend in logical theory, especially, in the past 60 years. In that period, logical theory became aggressively and widely pluralistic. Second, the versatility – the sheer ubiquity – of possibleworlds as a tool of semantic and philosophical analysis, gives to possibleworlds a kind of hegemonic standing.. (shrink)
The possible-worlds semantics for modality says that a sentence is possibly true if it is true in some possible world. Given classical prepositional logic, one can easily prove that every consistent set of propositions can be embedded in a ‘maximal consistent set’, which in a sense represents a possible world. However the construction depends on the fact that standard modal logics are finitary, and it seems false that an infinite collection of sets of sentences each finite (...) subset of which is intuitively ‘possible’ in natural language has the property that the whole set is possible. The argument of the paper is that the principles needed to shew that natural language possibility sentences involve quantification over worlds are analogous to those used in infinitary modal logic. (shrink)
The possible-worlds analysis of propositions identifies a proposition with the set of possibleworlds where it is true. This analysis has the hitherto unnoticed consequence that a proposition depends for its existence on the existence of every proposition that entails it. This peculiar consequence places the possible-worlds analysis in conflict with the conjunction of two compelling theses. One thesis is that a phrase of the form ‘the proposition that S’ is a rigid designator. The (...) other thesis is that a proposition which is directly about an object – a singular proposition – depends for its existence on the existence of the object. I defend these theses and conclude that the cost of the possible-worlds analysis is prohibitively high. (shrink)
Various writers have proposed that the notion of a possible world is a functional concept, yet very little has been done to develop that proposal. This paper explores a particular functionalist account of possibleworlds, according to which pluralities of possibleworlds are the bases for structures which provide occupants for the roles which analyse our ordinary modal concepts. It argues that the resulting position meets some of the stringent constraints which philosophers have placed upon (...) accounts of possibleworlds, while also trivializing the question what possibleworlds are. The paper then discusses a range of problems facing the functionalist position. (shrink)
This thesis examines the alethic modal concepts of possibility and necessity. It is argued that one cannot do justice to all our modal talk without possibleworlds, i.e., complete ways that a cosmos might have been. I argue that not all of the proposed applications of possibleworlds succeed but enough remain to give one good theoretical reason to posit them. The two central problems now are: (1) What feature of reality makes correct alethic modal claims (...) true and (2) What are possibleworlds? (shrink)
This paper charts some early history of the possibleworlds semantics for modal logic, starting with the pioneering work of Prior and Meredith. The contributions of Geach, Hintikka, Kanger, Kripke, Montague, and Smiley are also discussed.
Possible-worlds talk obscures, rather than clariﬁes, the debate about haecceitism. In this paper I distinguish haecceitism and anti-haecceitism from other doctrines that sometimes go under those names. Then I defend the claim that there are no non-tendentious deﬁnitions of ‘haecceitism’ and ‘anti-haecceitism’ using possible-worlds talk. That is, any deﬁnition of ‘haecceitism’ using possible-worlds talk depends, for its correctness, on a substantive theory of the nature of possibleworlds. This explains why using (...) class='Hi'>possible-worlds talk when discussing haecceitism causes confusion: if the parties to the discussion presuppose different theories of the nature of possibleworlds, then they will mean diﬀerent things by ‘haecceitism’. (shrink)
I outline a neo-Fregean strategy in the debate on the existence of possibleworlds. The criterion of identity and the criterion of application are formulated. Special attention is paid to the fact that speakers do not possess proper names for worlds. A broadly Quinean solution is proposed in response to this difficulty.
God is traditionally taken to be a perfect being, and the creator and sustainer of all that is. So, if theism is true, what sort of world should we expect? To answer this question, we need an account of the array of possibleworlds from which God is said to choose. It seems that either there is (a) exactly one best possible world; or (b) more than one unsurpassable world; or (c) an infinite hierarchy of increasingly better (...)worlds. Influential arguments for atheism have been advanced on each hierarchy, and these jointly comprise a daunting trilemma for theism. In this paper, I argue that if theism is true, we should expect the actual world to be a multiverse comprised of all and only those universes which are worthy of creation and sustenance. I further argue that this multiverse is the unique best of all possibleworlds. Finally, I explain how his unconventional view bears on the trilemma for theism. (shrink)
This book discusses a range of important issues in current philosophical work on the nature of possibleworlds. Areas investigated include the theories of the nature of possibleworlds, general questions about metaphysical analysis and questions about the direction of dependence between what is necessary or possible and what could be.
Dispositional essentialism, a plausible view about the natures of (sparse or natural) properties, yields a satisfying explanation of the nature of laws also. The resulting necessitarian conception of laws comes in a weaker version, which allows differences between possibleworlds as regards which laws hold in those worlds and a stronger version that does not. The main aim of this paper is to articulate what is involved in accepting the stronger version, most especially the consequence that all (...)possible properties exist in all worlds. I also suggest that there is no particularly strong reason for preferring the weaker to the stronger version. For example, Armstrong's instantiation condition on universals entails that according to strong necessitarianism every property is instantiated in all possibleworlds. But first we do not need to accept Armstrong's instantiation condition, in part because his arguments for it are forceful only for a contingentist about laws and properties. Secondly, even if we do accept the condition, the consequence that all properties are instantiated is not itself contradictory, so long as any form of necessitarianism holds. Strong necessitarianism is prima facie counter-intuitive. But for that matter so is weak necessitarianism. Accepting either weak or strong necessitarianism requires denying the force of intuition in this area. And indeed we have every reason to deny the force of intuition and its primary source, imagination, concerning modal facts. (shrink)
The gist of these objections to the possible world account of necessity is that, for it to be true, ‘possible’ would have to be a name for an attribute. But to say that something is possible is not to describe it, but to say that there could be such a thing. And possibilities are not classes of entities. Possibleworlds have been described as ways, but a way of getting to London from Cambridge is not (...) an entity, and that there is a way is entailed by facts such as that if you travel south along the M3, you will get there. (shrink)
Timothy Williamson has defended the claim that any philosophically satisfying conception of modality that encompasses possibleworlds semantics (PWS) commits us to the Barcan Formula. His argument depends on the assumption that the domain of what there is (the domain of the actual world) has to be identified with the domain D(@), where @ is the index or possible world that in PWS represents , or stands for , the actual world. I work out an interpretation of (...) the relation between PWS and possibleworlds terminology that makes it plausible to reject that assumption. (shrink)
The role of possibleworlds in philosophy is hard to overestimate. Nevertheless, their nature and existence is very controversial. This is particularly serious, since their standard applications depend on there being sufficiently many of them. The paper develops an account of possibleworlds on which it is particularly easy to believe in their existence: an account of possibleworlds as pleonastic entities. Pleonastic entities are entities whose existence can be validly inferred from statements that (...) neither refer to nor quantify over them as a matter of conceptual necessity. Definitions are proposed that ensure that this is the case for possibleworlds. (shrink)
If is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for predicates of (...) sentences has not been developed very far. By introducing possible-worlds semantics for the language of arithmetic plus the unary predicate , we tackle both problems. Given a frame W,R> consisting of a set W of worlds and a binary relation R on W, we investigate whether we can interpret at every world in such a way that A holds at a world wW if and only if A holds at every world vW such that wRv. The arithmetical vocabulary is interpreted by the standard model at every world. Several paradoxes (like Montague's Theorem, Gödel's Second Incompleteness Theorem, McGee's Theorem on the -inconsistency of certain truth theories, etc.) show that many frames, e.g., reflexive frames, do not allow for such an interpretation. We present sufficient and necessary conditions for the existence of a suitable interpretation of at any world. Sound and complete semi-formal systems, corresponding to the modal systems K and K4, for the class of all possible-worlds models for predicates and all transitive possible-worlds models are presented. We apply our account also to nonstandard models of arithmetic and other languages than the language of arithmetic. (shrink)
The paper is a brief survey of the most important semantic constructions founded on the concept of possible world. It is impossible to capture in one short paper the whole variety of the problems connected with manifold applications of possibleworlds. Hence, after a brief explanation of some philosophical matters I take a look at possibleworlds from rather technical standpoint of logic and focus on the applications in formal semantics. In particular, I would like (...) to focus on the fruitful marriage of possible world semantics and algebra and its evolution leading to very general construction of Wójcicki called referential semantics and some of its refinements. The presentation is informal and sketchy; the main purpose is to put in one place a short, and readable I hope, description of the most important constructions and to point out the main sources of these solutions. (shrink)
This paper is about possibleworlds semantics for propositional attitude sentences. In particular I shall focus on belief reports in English such as "Lusina believes that tofu is nutritious." It is well-known that possibleworlds semantics for such reports suffers from the so-called _problem of equivalence_ . In this paper I shall examine some attempts to deal with this problem and argue that they are unsatisfactory.
This article opposes a view widely accepted in studies concerning the history of modal logic, according to which (i) the approach of C. I. Lewis towards constructing modern modal logic was purely syntactical (i.e. limited to the construction of axiomatic systems S1-S5 of propositional modal logic), and (ii) the notion of a possible world was incorporated into modern logic and philosophy mainly by authors such as Rudolf Carnap and Saul Kripke. The article presents Lewis' definition of a possible (...) world, and his formulation of the truth-conditions of statements containing strict implication as their main connective in terms of possibleworlds. The main question of the article is whether it is possible to consider Lewis' work in this area as an early stage of the development of possible world semantics, and if so, in what sense? The article concludes by answering affirmatively, due to soundness and completeness proofs with respect to S5 using Lewis' semantics. (shrink)
The Argument from Inferiority holds that our world cannot be the creation of an omnipotent and omnibenevolent being; for if it were, it would be the best of all possibleworlds, which evidently it is not. We argue that this argument rests on an implausible principle concerning which worlds it is permissible for an omnipotent being to create: roughly, the principle that such a being ought not to create a non-best world. More specifically, we argue that this (...) principle is plausible only if we assume that there is a best element in the set of all possibleworlds. However, as we show, there are conceivable scenarios in which that assumption does not hold. (shrink)
I argue that if a subject's acquaintance with an object is necessary for him to think about and refer to the object, then the content of his thought cannot be a set of metaphysically possibleworlds. Acquaintance resets what possibilities there are; it affects the powers of representation, and does not only limit the range of possibilities. If acquaintance restricts what a subject can think about, the theorist cannot specify what possibilities are open to the subject simply in (...) terms of possibleworlds. (shrink)
The article investigates the sceptical challenge from an information-theoretic perspective. Its main goal is to articulate and defend the view that either informational scepticism is radical, but then it is epistemologically innocuous because redundant; or it is moderate, but then epistemologically beneficial because useful. In order to pursue this cooptation strategy, the article is divided into seven sections. Section 1 sets up the problem. Section 2 introduces Borel numbers as a convenient way to refer uniformly to (the data that individuate) (...) different possibleworlds. Section 3 adopts the Hamming distance between Borel numbers as a metric to calculate the distance between possibleworlds. In Sects. 4 and 5, radical and moderate informational scepticism are analysed using Borel numbers and Hamming distances, and shown to be either harmless (extreme form) or actually fruitful (moderate form). Section 6 further clarifies the approach by replying to some potential objections. In the conclusion, the Peircean nature of the overall approach is briefly discussed. (shrink)
14. Forthcoming. 'The Best of All PossibleWorlds' (PDF file) (with Campbell Brown), Synthese (Kluwer). The Argument from Inferiority holds that our world cannot be the creation of an omnipotent and omnibenevolent being; for if it were, it would be the best of all possibleworlds, which evidently it is not. We argue that this argument rests on an implausible principle concerning which worlds it is permissible for an omnipotent being to create: roughly, the principle (...) that such a being ought not to create a non-best world. More specifically, we argue that this principle is plausible only if we assume that there is a best element in the set of all possibleworlds. However, as we show, there are conceivable scenarios in which that assumption does not hold. (shrink)
By "a possible world" philosophers mean a total state of affairs in the conception of which no contradiction is involved. Our own world - the real world, the actual one - is just one of many possibleworlds. Indeed, it is just one of infinitely many, since for any possible world containing say n atoms there is another logically possible world containing n+1 atoms, and so on ad infinitum. All possibleworlds other than (...) the actual world we inhabit are nonactual. (shrink)
Of late, evidentiality has received great attention in formal semantics. In this paper I develop ‘evidentiality-informed’ truth conditions for modal operators such as must and may . With language data drawn from Luoping Nase (a Tibeto-Burman language spoken in the P.R. of China and belonging to the Yi Nationality), I illustrate that epistemic modals clash with clauses articulating first-hand information. I then demonstrate that existing models such as Kratzer’s graded possible-worlds semantics fail to provide accurate truth conditions for (...) modals tagging clauses with first-hand information. As a remedy I propose a fuzzy version of possible-worlds semantics with various grades of belief and knowledge. In addition to preserving the expressive power of graded possible-worlds semantics, the fuzzy model will be shown to supply appropriate truth conditions for epistemic modals appended to evidential clauses (i.e. clauses expressing first-hand information). (shrink)
Possibleworlds semantics (PWS) is a family of methods that have been used to analyze a wide variety of intensional phenomena, including modality, conditionals, tense and temporal adverbs, obligation, and reports of informational and cognitive content. PWS spurred the development of philosophical logic and led to new applications of logic in computer science and artiﬁcial intelligence. It revolutionized the study of the semantics of natural languages. PWS has inspired analyses of many concepts of philosophical importance, and the concept (...) of a possible world has been at the heart of important philosophical systems. (See also POSSIBLEWORLDS, PHILOSOPHICAL ISSUES IN.. (shrink)
The paper puts forward a theory of historical modalities that is framed in terms of possible continuations rather than possibleworlds or histories. The proposal is tested as a semantic theory for a language with historical modalities, tenses, and indexicals.
A certain argument has been given in the literature to the effect that generalism (the view that all facts about all possibleworlds can (in principle) be given in general terms, that is, without resorting to nonqualitative thisnesses) excludes transworld identitism (the view that there are numerical identities through possibleworlds). It follows from this argument, among other things, that transworld identitism entails Scotistic haecceitism (acceptance of nonqualitative thisnesses), and that generalists subscribing to de reism (the (...) view that there are true modal statements de re) are committed to counterpartism (the view that sameness through worlds is not numerical identity). The purpose of this paper is to resist the argument in question by constructing generalist transworld identitism, that is, by providing an account involving identities through possibleworlds, without resorting to nonqualitative thisnesses. (shrink)
In recent years possibleworlds and individuals have been in philosophical vogue, playing an important role in logical semantics, analytic metaphysics, linguistic theory, and elsewhere. In the enthusiasm over this much-promising device people have lost sight of the fact that the actual identification and introduction of such possibilia is effectively impossible. For the prospect of ostensive confrontation is here lost, and the purely descriptive individuation of nonexistent individuals is an altogether impracticable project. The very most we can accomplish (...) here is to deal with schemata and scenarios-items whose element of generality is always present. We can indeed meaningfully operate a possibilism that is proportionately oriented (de dicto), but cannot succeed with one that is substantively oriented (de re). (shrink)
Those who object to David Lewis' modal realism express qualms about philosophical respectability of the Lewisian notion of a possible world and its correlate notion of an inhabitant of a possible world. The resulting impression is that these two notions either stand together or fall together. I argue that the Lewisian notion of a possible world is otiose even for a good Lewisian modal realist, and that one can carry out a good Lewisian semantics for modal discourse (...) without Lewisian possible worls. I do so by generalizing Lewis' own idea that restrictions on quantification come and go with the pragmatic wind and relativizing possibleworlds as shifting domains of discourse. I then suggest a way to soften the infamous incredulous stare. (shrink)
Leibniz has enjoyed a prominent place in the history of thought about possibleworlds.' I shall argue that on the feading interpretation of Leibniz's account of contingency Ã¢â¬â an ingenious interpretation with ample textual support Ã¢â¬â possibleworlds may be invoked by Leibniz only on pain of inconsistency. Leibnizian contingency, as reconstructed in detail by Robert C. Sleigh, Jr.,z will be shown to preclude propositions with different truth-values in different possibleworlds.
In the first section of this paper I discuss what Leibniz meant by a miracle and why Leibniz’s definition of the best of all possibleworlds implies that it is a world in which miracles are minimized. In the second part of the paper I argue that human happiness within the best of all possibleworlds also requires, on Leibniz’s principles, that miracles must there be minimized. In the third section of the paper I consider what, (...) if any, miracles actually remain possible for Leibniz within the best of all possibleworlds. In the final section I discuss one important kind of event upon which Leibniz vacillated whether it required miraculous intervention -- namely, the elevation of the sensitive soul to rationality -- and some speculation about the cause of this vacillation in Leibniz is offered. (shrink)
‘Adams worlds’ are possibleworlds that contain no creature whose life is not worth living or whose life is overall worse than in any other possible world in which it would have existed. Creating an Adams world involves no wrongdoing or unkindness towards creatures on the part of the creator. I argue that the notion of an Adams world is of little value in theodicy. Theists are not only committed to thinking that this world was created (...) without wrongdoing or unkindness but also must rule out the possibility that the world might have been better had God not existed. Nor is there much reason, independent of the availability of a satisfactory theodicy, for believing that the actual world is an Adams world. The need for a theodicy constructed along Leibnizian lines, incorporating the claim that this world is the best possible, is thus reinforced. (shrink)
A century ago, Charles S. Peirce proposed a logical approach to modalities that came close to possible-worlds semantics. This paper investigates his views on modalities through his diagrammatic logic of Existential Graphs (EGs). The contribution of the gamma part of EGs to the study of modalities is examined. Some ramifications of Peirce’s remarks are presented and placed into a contemporary perspective. An appendix is included that provides a transcription with commentary of Peirce’s unpublished manuscript on modality from 1901.
God is traditionally understood to be a perfect being who is the creator and sustainer of all that is. God's creative and sustaining activity is often thought to involve choosing a possible world for actualization. It is generally said that either there is (a) exactly one best of all possibleworlds, or there are (b) infinitely many increasingly better worlds, or else there are (c) infinitely many unsurpassable worlds within God's power to actualize. On each (...) view, critics have offered arguments for atheism that turn on God's choice of a world. In what follows, I first discuss some background issues, and I then survey the contemporary literature on these arguments. (shrink)
The paper has two main tasks: to trace the systematic connections between two recent pieces of epistemological work by David Henderson and Terry Horgan, and to criticize as unintelligible the concept of epistemically relevant possibleworlds, which is central to one of them. Iceberg Epistemology sketches a general account of the structure of our cognitive organisation, which can, by and large, be classified as an externalist, reliabilist account. I argue that Henderson & Horgan's new objective epistemic value (labelled (...) robustness of reliability and loosely defined as reliability across a wide range of epistemically relevant possibleworlds) is introduced to clarify the connection between reliability and the ideal of truth (and by that to remedy a standard shortcoming of externalist accounts). However, the concept of an epistemically relevant possible world seems to be unintelligible (at least on the basis of the introductory examples offered so far). Some concluding remarks address the status and the achievability of robustness of reliability as an epistemic ideal. (shrink)
Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quantification over histories, which is a second-order quantification over sets of possibleworlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as first-order counterparts of the original (...) semantics. (shrink)
An outline for a modal interpretation in terms of possibleworlds is presented. The so-called Schmidt histories are taken to correspond to the physically possibleworlds. The decoherence function defined in the histories formulation of quantum theory is taken to prescribe a non-classical probability measure over the set of the possibleworlds. This is shown to yield dynamics in the form of transition probabilities for occurrent events in each world. The role of the consistency (...) condition is discussed. (shrink)
In modal subordination, a modal sentence is interpreted relative to a hypothetical scenario introduced in an earlier sentence. In this paper, I argue that this phenomenon reﬂects the fact that the interpretation of modals is an ANAPHORIC process. Modal morphemes introduce sets of possibleworlds, representing alternative hypothetical scenarios, as entities into the discourse model. Their interpretation depends on evoking sets of worlds recording described and reference scenarios, and relating such sets to one another using familiar notions (...) of restricted, preferential quantiﬁcation. This proposal relies on an extended model of environments in dynamic semantics to keep track of associations between possibleworlds and ordinary individuals; it assumes that modal meanings and other lexical meanings encapsulate quantiﬁcation over possibleworlds. These two innovations are required in order for modals to refer to sets of possibleworlds directly as static objects in place of the inherently dynamic objects—quite different from the referents of pronouns and tenses—used in previous accounts. The simpler proposal that results offers better empirical coverage and suggests a new parallel between modal and temporal interpretation. (shrink)
I defend a neo-logicist approach in the debate over the metaphysics of possibleworlds. I start by examining a series of proposals put forward by Robert Stalnaker. All of them have a shared theme of deriving ontological commitment to problematic abstract objects from the commitment to the practice quantifying over them. These general proposals ﬁnd a crisper formulation in Frege’s context principle. I build the case for the employment of a modal analogue of Hume’s Principle: possible (...) class='Hi'>worlds are to be identiﬁed by the statements true on them. The analogy with arithmetic is limited, as we lack singular terms for possibleworlds. The preferred solution is to take Quine’s criterion of ontological commitment on board. I ﬁnish by formulating the criterion of application for the sortal concept of possible world. (shrink)
The Argument from Inferiority holds that our world cannot be the creation of an omnipotent and omnibenevolent being; for if it were, it would be the best of all possibleworlds, which evidently it is not. We argue that this argument rests on an implausible principle concerning which worlds it is permissible for an omnipotent being to create: roughly, the principle that such a being ought not to create a non-best world. More specifically, we argue that this (...) principle is plausible only if we assume that there is a best element in the set of all possibleworlds. However, as we show, there are conceivable scenarios in which that assumption does not hold. (shrink)
There are three possible situations regarding createable possibleworlds: (1) there is a best possible world of that sort; (2) there are two or more unsurpassably good worlds of that sort; (3) there is an infinite series of significantly and increasingly better possible createable worlds. Rowe argues that if (1) is true then, if God exists, he does not deserve our praise or gratitude for doing what he could not fail to do, namely, (...) create the best possible world. With this I agree. He argues that if (2) is true, then God does not deserve our praise or gratitude either, because it did not matter which of these worlds he created. I disagree with Rowe here arguing that we can be grateful for being alive even if there is an equally good possible world where we do not exist. Rowe also argues that if (3) were true, God could not exist, for (3) would allow that there is some being greater than God, which is impossible. I also disagree with Rowe about what follows from (3): God could not create the worst of the best worlds in the infinite series of increasingly better worlds, but he could create some extremely good world in that series without that possibility implying that there could be some being greater than God. (shrink)
Kripke has noted that possibleworlds are stipulated, not discovered, and that the stipulation of these worlds allows us to separate accidental from essential properties. In this paper I argue that possibleworlds theory gives us an important tool for analyzing what Descartes is doing in the Meditations. The first Meditation becomes a thought experiment in which possible realities are stipulated in a search for one or more essential properties. Viewing the doubt in this (...) manner sheds new light on the cogito and sum res cogitans and shows the limitations of some contemporary discussion of the cogito, namely, the positions taken by Ayer and Hintikka. (shrink)
After presenting Apostels views on scientific realism, I present definitions of the concepts of ontology and metaphysics. I then proceed to develop Apostels basic ontology and his metaphysics. Apostel proposed a particular understanding of existence based on his views on causation. He also developed a view of the universe as a causal self-explaining system. I discuss and illustrate three kinds of what he calls metaphysical deductions that aim to deliver such a view of the universe. The most important one is (...) the Leibnizian variational method, that should allow us to deduce the existing universe as the best of all possibleworlds. (shrink)
In the logic of theory change, the standard model is AGM, proposed by Alchourrón et al. (J Symb Log 50:510–530, 1985 ). This paper focuses on the extension of AGM that accounts for contractions of a theory by a set of sentences instead of only by a single sentence. Hansson (Theoria 55:114–132, 1989 ), Fuhrmann and Hansson (J Logic Lang Inf 3:39–74, 1994 ) generalized Partial Meet Contraction to the case of contractions by (possibly non-singleton) sets of sentences. In this (...) paper we present the possibleworlds semantics for partial meet multiple contractions. (shrink)
In several works on modality, G. H. von Wright presents tree structures to explain possibleworlds. Worlds that might have developed from an earlier world are possible relative to it. Actually possibleworlds are possible relative to the world as it actually was at some point. Many logically consistent worlds are not actually possible. Transitions from node to node in a tree structure are probabilistic. Probabilities are often more useful than similarities (...) between worlds in treating counterfactual conditionals. (shrink)
The goal of theodicy is to show how God could create our world with all its evil. This paper argues that the theodicist can achieve her goal only if she gives up one of these three propositions: (1) evil does not exist in heaven; (2) heaven is better than the present world; (3) heaven is a possible world. Second, it is argued that the theodicist can reject (3) without giving up her belief that heaven exists, so that (3) is (...) her best alternative. (shrink)
According to David Lewis, a realist about possibleworlds must hold that actuality is relative: the worlds are ontologically all on a par; the actual and the merely possible differ, not absolutely, but in how they relate to us. Call this 'Lewisian realism'. The alternative, 'Leibnizian realism', holds that actuality is an absolute property that marks a distinction in ontological status. Lewis presents two arguments against Leibnizian realism. First, he argues that the Leibnizian realist cannot account (...) for the contingency of actuality. Second, he argues that the Leibnizian realist cannot explain why skepticism about one's own actuality is absurd. In this paper, I mount a defense of Leibnizian realism. (shrink)
Bringsjord (1985) argues that the definition W of possibleworlds as maximal possible sets of propositions is incoherent. Menzel (1986a) notes that Bringsjord’s argument depends on the Powerset axiom and that the axiom can be reasonably denied. Grim (1986) counters that W can be proved to be incoherent without Powerset. Grim was right. However, the argument he provided is deeply flawed. The purpose of this note is to detail the problems with Grim’s argument and to present a (...) sound alternative argument for his conclusion – basically the argument Russell gave to establish a well-known paradox in The Principles of Mathematics. (shrink)
The possibility of Junk is the possibility that something exists and everything is a proper part. Just as we might imagine that there are no simples—that everything has a proper part, all the way down—we might imagine that there are no caps—that everything is a proper part, all the way up. It is not obvious that this apparent possibility can be accommodated within a Lewisian modal framework. For Lewis, every possibility involves the existence of a possible world, and a (...)possible world is just is a maximal sum, and so a cap. But the Lewisian can accommodate Junk, if she wishes, by allowing parts of possibleworlds to represent complete possibilities. (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 possibleworlds, concrete entities like our own universe, but cut off from us in space and time. Possibleworlds 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 possibleworlds 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)
A Leibnizian semantics proposed by Becker in 1952 for the modal operators has recently been reviewed in Copeland’s paper The Genesis of Possible World Semantics (Copeland in J Philos Logic 31:99–137, 2002 ), with a remark that “neither the binary relation nor the idea of proving completeness was present in Becker’s work”. In light of Frege’s celebrated Sense-Determines-Reference principle, we find, however, that it is Becker’s semantics, rather than Kripke’s semantics, that has captured the true spirit of Frege’s semantic (...) program. Furthermore, for Kripke’s possible world semantics to fit in Frege’s framework of senses , worlds and referents , it will have to be thoroughly reformulated. By introducing the notion of a hi-world into the picture, we manage to keep the key ingredients of Becker’s semantics intact, while at the same time solve a fatal problem that used to shadow Becker’s original semantics—it had not been able to make sense of inhomogeneous modality. The resulting generalized Beckerian semantics provides, in effect, a Beckerian analysis of the Kripkean possibleworlds. It reveals the subtle hierarchical internal structure of a Kripkean world that has not been discovered before. (shrink)
This book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the (...)possible-world semantics of quantum counterfactuals using David Lewis's famous approach as a starting point but modifying it significantly in order to achieve compatibility with the demands of the special theory of relativity as well as quantum mechanics. There have been several attempts to use counterfactuals semantics to strengthen Bell's theorem and its cognates such as the GHZ and Hardy theorems. These are critically evaluated in the book. Finally, a counterfactual reconstruction of the EPR argument and Bell's theorem is proposed that sheds a new light on their philosophical consequences regarding the relations between realism and local causation. (shrink)
Leibniz argued that God would not create a world unless it was the best possible world. I defend Leibniz’s argument. I then consider whether God could refrain from creating if there were no best possible world. I argue that God, on pain of contradiction, could not refrain from creating in such a situation. I conclude that either this is the best possible world or God is not our creator.
The quantitative argument against the notion of a best possible world claims that, no matter how many worthwhile lives a world contains, another world contains more and is, other things being equal, better. Parfit’s ‘ Mere Addition Paradox ’ suggests that defenders of this argument must accept his ‘ Repugnant Conclusion ’ : that outcomes containing billions upon billions of lives barely worth living are better than outcomes containing fewer lives of higher quality. Several responses to the Paradox are (...) discussed and rejected as either inadequate or unavailable in a theistic context. The quantitative argument fails if some world is such that addition to it is not possible, i.e., if it is intensively infinite, as Liebniz claimed. If the notion of such a world is incoherent, then no world is quantitatively best and the quantitative argument succeeds, but only at the cost of embracing the Repugnant Conclusion. (shrink)
In his paper, "The Two Main Problems of Philosophy"[Note 1], Professor N.L. Wilson offers an inductive argument for the thesis "that there is only one possible world … possibility, actuality and necessity collapse into each other."[p. 200].
The aim of this paper is to show that the definition of a possible world in the actualist tradition of A. Plantinga, R.M. Adams, R. Chisholm, J. Pollock and N . Wolterstorff is unable to accomodate tensed states of affairs. An example of a tensed state of affairs is the transiently obtaining state of affairs that the storm is present, which obtains only if its negation, it is not the case that the storm is present also obtains but at (...) different times. A possible world that includes tensed states of affairs and their negations cannot be defined in the traditional way, which states that a possible world is a state of affairs S that includes every state of affairs S' or (exclusive disjunction) the negation of S'. Rather, it must be defined in a new way: A possible world is a state of affairs S that includes every state of affairs S' or (inclusive disjunction) the negation of S', such that for every pair P of mutually contradictory tensed states of affairs entailed by S, the members of P obtain nonsimultaneously in S. (shrink)
Las nociones epistémicas modales se definen como aquellos conceptos epistémicos que, como el de cognoscibilidad o el de indudabilidad, incluyen una nota modal. Segun se defiende en este trabajo, la semántica de mundos posibles y algunas de sus extensiones (especialmente las llevadas a cabo para logica temporal, logica epistemica y logica condicional) son instrumentos adecuados para deshacer el nudo de las intensionalidades superpuestas en estas nociones especialmente esquivas al análisis. Para mostrarlo, se proporcionan una serie de análisis sucesivos de la (...) nocion de cognoscibilidad que a partir de una interpretación naif van salvando una serie de presuposiciones, problemas y paradojas hasta dar con una analisis que se presume satisfactorio.“Modal epistemic notions” are those epistemic concepts which in some way or another has a modal element. These modal epistemic notions, although they could appear intuitively clear, they turn out to be particularly obscure, slippery, when one subjects them to a formal analysis. In this paper we will try to show that possible world semantics (and its extensions for epistemic, temporal and conditional logic) is an appropriate instrument for the explanation ofthese notions. Four successive analysis of the notion of “knowability” are given, ranging from a naive account to an analysis that gets to the bottom ofthe problem. (shrink)
In this article I explore Leibniz's claim in the Theodicy that on the essential points Malebranche's theodicy "reduces to" his own view. This judgment may seem to be warranted given that both thinkers emphasize that evils are justified by the fact that they follow from the simple and uniform laws that govern that world which is worthy of divine creation. However, I argue that Leibniz's theodicy differs in several crucial respects from Malebranche's. I begin with a qualified endorsement of Charles (...) Larmore's recent claim that remarks in Malebranche's correspondence with Leibniz indicate that their theodicies rely on incompatible conceptions of the moral rationality of divine action. I also attempt to go beyond Larmore's discussion in highlighting further differences concerning the sort of freedom involved in the divine act of creation. My conclusion is that these differing conceptions of divine morality and divine freedom reveal that in contrast to the case of Leibniz, Malebranche's theodicy not only does not require that God create anything at all, but also is compatible with the result that the world he decides to create is not uniquely the best possible. (shrink)
Modal realism -- Time, space, world -- Existence -- Actuality -- Modal realism and modal tense -- Transworld individuals and their identity -- Existensionalism -- Impossibility -- Proposition and relief -- Fictional worlds -- Epistemology.
The fundamental principle of the theory of possibleworlds is that a proposition p is possible if and only there is a possible world at which p is true. In this paper we present a valid derivation of this principle from a more general theory in which possibleworlds are defined rather than taken as primitive. The general theory uses a primitive modality and axiomatizes abstract objects, properties, and propositions. We then show that this (...) general theory has very small models and hence that its ontological commitments — and, therefore, those of the fundamental principle of world theory — are minimal. (shrink)
One very popular kind of semantics for subjunctive conditionals is aclosest-worlds account along the lines of theories given by David Lewisand Robert Stalnaker. If we could give the same sort of semantics forindicative conditionals, we would have a more unified account of themeaning of ``if ... then ...'' statements, one with manyadvantages for explaining the behaviour of conditional sentences. Such atreatment of indicative conditionals, however, has faced a battery ofobjections. This paper outlines a closest-worlds account of indicativeconditionals that (...) does better than some of its cousins in explaining thebehaviour of such conditionals. The paper then discusses objectionsoffered by Dorothy Edgington and Frank Jackson to closest-worldsaccounts of indicative conditionals, and shows that these objections canbe met by the account outlined. (shrink)
Possibleworlds are maximal possibilities. But what kind of thing is a maximal possibility? Not a maximal individual: there are maximal possibilities that are not maximal individuals, because each maximal individual could have any one of several maximal properties. And not a maximal property: there are maximal possibilities that are not maximal properties, because each maximal property could be had by any one of many possible maximal individuals. So if you like your worlds concrete, you should (...) say that they are maximal facts, and if you like your worlds abstract, you should say that they are maximal propositions. (shrink)
give a proof of the existence of nonlocal influences acting on correlated spin-1/2 particles in the singlet state which does not require any particular interpretation of quantum mechanics (QM). (Except Stapp holds that the proof fails under a many-worlds interpretation of QM—a claim we analyse in 1.2.) Recently, in responding to Redhead's (, pp. 90-6) criticism that the Stapp 1 proof fails under an indeterministic interpretation of QM, Stapp  (henceforth Stapp 2), has revised the logical structure of his (...) proof including its crucial locality assumption. Our main aim is to show that this revision is a step in the wrong direction because it faces two difficulties which undermine the resulting proof's significance (3.1) and validity (3. 2). We also clarify and extend the Stapp 1 proof (1. 1) with the aid of Lewis' analysis of counterfactuals (1. 2) and causal dependence (2. 2 and 2. 3). In so doing, we are able to identify two new defects in the Stapp 1 proof (1. 3 and 2. 1) in addition to corroborating Redhead's criticism (2. 2). Also, the additional assumptions which save the Stapp 1 proof's validity are detailed (2. 3) and some new difficulties for the determinist are pointed out by exploiting a slightly extended version of the proof (2. 4). In providing this full analysis of the Stapp 1 proof, we also construct the necessary framework within which to provide a critique of Stapp 2's proof (3). *Portions of this paper were presented by R. K. Clifton to the 1988 British Society for the Philosophy of Science Conference at the University of Southampton. R. K. Clifton wishes to thank the Natural Sciences and Engineering Research Council of Canada, the Royal Commission for the Exhibition of 1851, and the Governing Body of Peterhouse at Cambridge University for support during this work. (shrink)
In this paper non-normal worlds semantics is presented as a basic, general, and unifying approach to epistemic logic. The semantical framework of non-normal worlds is compared to the model theories of several logics for knowledge and belief that were recently developed in Artificial Intelligence (AI). It is shown that every model for implicit and explicit belief (Levesque), for awareness, general awareness, and local reasoning (Fagin and Halpern), and for awareness and principles (van der Hoek and Meyer) induces a (...) non-normal worlds model validating precisely the same formulas (of the language in question). (shrink)
Suppose the members of a group (e.g., committee, jury, expert panel) each form a judgment on which worlds in a given set are possible, subject to the constraint that at least one world is possible but not all are. The group seeks to aggregate these individual judgments into a collective judgment, subject to the same constraint. I show that no judgment aggregation rule can solve this problem in accordance with three conditions: “unanimity,” “independence” and “non-dictatorship,” Although the (...) result is a variant of an existing theorem on “group identification” (Kasher and Rubinstein, Logique et Analyse 160:385–395, 1997), the aggregation of judgments on which worlds are possible (or permissible, desirable, etc.) appears not to have been studied yet. The result challenges us to take a stance on which of its conditions to relax. (shrink)
Four questions are raised about the semantics of Quantified Modal Logic (QML). Does QML admit possible objects, i.e. possibilia? Is it plausible to admit them? Can sense be made of such objects? Is QML committed to the existence of possibilia?The conclusions are that QML, generalized as in Kripke, would seem to accommodate possibilia, but they are rejected on philosophical and semantical grounds. Things must be encounterable, directly nameable and a part of the actual order before they may plausibly enter (...) into the identity relation. QML is not committed to possibiha in that the range of variables may be restricted to actual objects.Support of the conclusions requires some discussion of substitution puzzles; also, the semantical distinction between proper names which are directly referring, and descriptions even where the latter are "rigid designators".Views of W.V. Quine, B. Russell, K. Donnellan, D. Kaplan as well as S. Kripke are invoked or evaluated in conjunction with these issues. (shrink)