_Possible Worlds_ presents the first up-to-date and comprehensive examination of one of the most important topics in metaphysics. John Divers considers the prevalent philosophical positions, including realism, antirealism and the work of important writers on possibleworlds such as David Lewis, evaluating them in detail.
This article includes a basic overview of possible world semantics and a relatively comprehensive overview of three central philosophical conceptions of possibleworlds: Concretism (represented chiefly by Lewis), Abstractionism (represented chiefly by Plantinga), and Combinatorialism (represented chiefly by Armstrong).
David Lewis holds that a single possible world can provide more than one way things could be. But what are possibleworlds good for if they come apart from ways things could be? We can make sense of this if we go in for a metaphysical understanding of what the world is. The world does not include everything that is the case—only the genuine facts. Understood this way, Lewis's “cheap haecceitism” amounts to a kind of metaphysical anti-haecceitism: (...) it says there aren't any genuine facts about individuals over and above their qualitative roles. (shrink)
In this chapter, I survey what I call Lewisian approaches to modality: approaches that analyze modality in terms of concrete possibleworlds and their parts. I take the following four theses to be characteristic of Lewisian approaches to modality. (1) There is no primitive modality. (2) There exists a plurality of concrete possibleworlds. (3) Actuality is an indexical concept. (4) Modality de re is to be analyzed in terms of counterparts, not transworld identity. After an (...) introductory section in which I motivate analyzing modality in terms of possibleworlds, I devote one section to each of these four theses. For each thesis, I take Lewis’s interpretation and defense as my starting point. I then consider and endorse alternative ways of accepting the thesis, some of which disagree substantially with Lewis’s interpretation or defense. There is more than one way to be a Lewisian about modality. (shrink)
The canonical version of possibleworlds semantics for story prefixes is due to David Lewis. This paper reassesses Lewis's theory and draws attention to some novel problems for his account.
Adams’s Thesis, the claim that the probabilities of indicative conditionals equal the conditional probabilities of their consequents given their antecedents, has proven impossible to accommodate within orthodox possible-world semantics. This essay proposes a modification to the orthodoxy that removes this impossibility. The starting point is a proposal by Jeffrey and Stalnaker that conditionals take semantic values in the unit interval, interpreting these (à la McGee) as their expected truth-values at a world. Their theories imply a false principle, namely, that (...) the probability of a conditional is independent of any proposition inconsistent with its antecedent. But they also point to something important, namely, that our uncertainty about conditionals is not confined to uncertainty about the facts (what the actual world is like) but also expresses uncertainty about the counterfacts (what the world would be like if one or another supposition were true). To capture this observation, this essay proposes that the semantic contents of conditionals be treated as sets of vectors of possibleworlds, not singleton worlds, with the coordinates of each specifying the world that is or would be true under the supposition that it represents. The probabilities of truth for conditionals will then depend on the joint probabilities of the facts and counterfacts, the latter in turn depending on the mode of supposition. The implication of this treatment is that the probabilities of conditionals are conditional probabilities whenever the mode of supposition is evidential. (shrink)
The standard semantics for counterfactuals ensures that any counterfactual with a true antecedent and true consequent is itself true. There have been many recent attempts to amend the standard semantics to avoid this result. I show that these proposals invalidate a number of further principles of the standard logic of counterfactuals. The case against the automatic truth of counterfactuals with true components does not extend to these further principles, however, so it is not clear that rejecting the latter should be (...) a consequence of rejecting the former. Instead I consider how one might defuse putative counterexamples to the truth of true-true counterfactuals. (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 □ $\ulcorner A \ulcorner$ holds at a world ᵆ ∊ W if and only if A holds at every world $\upsilon$ ∊ W such that ᵆR $\upsilon$ . 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 ω-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)
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)
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)
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)
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)
This chapter provides an introduction to possibleworlds semantics in both logic and the philosophy of language, including a discussion of some of the advantages and challenges for possibleworlds semantics.
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)
Metaphysically possibleworlds have many uses. Epistemically possibleworlds promise to be similarly useful, especially in connection with propositions and propositional attitudes. However, I argue that there is a serious threat to the natural accounts of epistemically possibleworlds, from a version of Russell’s paradox. I contrast this threat with David Kaplan’s problem for metaphysical possible world semantics: Kaplan’s problem can be straightforwardly rebutted, the problems I raise cannot. I argue that although there (...) may be coherent accounts of epistemically possibleworlds with fruitful applications, any such an account must fundamentally compromise the basic idea behind epistemic possibility. (shrink)
The article investigates the sceptical challenge from an informationtheoretic 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 Borei numbers as a convenient way to refer uniformly to (the data that individuate) (...) different possibleworlds. Section 3 adopts the Hamming distance between Borei numbers as a metric to calculate the distance between possibleworlds. In Sects. 4 and 5, radical and moderate informational scepticism are analysed using Borei 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)
... 112 ROBERT STALNAKER example Alvin Plantinga and Robert Adams) define possibleworlds in terms of states of affairs or propositions ; others (for example Max Cresswell) use a strategy quite similar to that of situation semantics, defining possibleworlds as constructs out of ..
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)
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)
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)
Ever since Saul Kripke and others developed a semantic interpretation for modal logic, 'possibleworlds' has been a much debated issue in contemporary metaphysics. To propose the idea of a possible world that differs in some way from our actual world - for example a world where the grass is red or where no people exist - can help us to analyse and understand a wide range of philosophical concepts, such as counterfactuals, properties, modality, and of course, (...) the notions of possibility and necessity. This book examines the ways in which possibleworlds have been used as a framework for considering problems in logic and argument analysis. The book begins with a non-technical introduction to the basic ideas of modal logic in terms of Kripke's possibleworlds and then moves on to a discussion of 'possible for' and 'possible that'. The central chapters examine questions of meaning, epistemic possibility, temporal logic, metaphysics, and impossibility. Girle also investigates how the idea of a possible world can be put to use in different areas of philosophy, the problems it may raise, and the benefits that can be gained. (shrink)
Conditional structures lie at the heart of the sciences, humanities, and everyday reasoning. It is hence not surprising that conditional logics – logics specifically designed to account for natural language conditionals – are an active and interdisciplinary area. The present book gives a formal and a philosophical account of indicative and counterfactual conditionals in terms of Chellas-Segerberg semantics. For that purpose a range of topics are discussed such as Bennett’s arguments against truth value based semantics for indicative conditionals.
The goal of this paper is to argue for the fruitfulness for linguistic theory of an approach to semantics that has been developed primarily by logicians and philosophers. That the theory of possibleworlds semantics has been extremely fruitful for logic and philosophy is widely if not universally accepted, and I will not try to convince remaining skeptics on that score. But the goals of linguistics are sufficiently different from those of philosophy and logic that there are independent (...) and highly reasonable grounds for skepticism about the appropriateness of such a theory for linguistics, and I will address what seem to me the most important of these in addition to offering positive evidence in favor of such an approach to semantics. (shrink)
Ever since Saul Kripke and others developed a semantic interpretation for modal logic, 'possibleworlds' has been a much debated issue in contemporary metaphysics. To propose the idea of a possible world that differs in some way from our actual world - for example a world where the grass is red or where no people exist - can help us to analyse and understand a wide range of philosophical concepts, such as counterfactuals, properties, modality, and of course, (...) the notions of possibility and necessity. This book examines the ways in which possibleworlds have been used as a framework for considering problems in logic and argument analysis. The book begins with a non-technical introduction to the basic ideas of modal logic in terms of Kripke's possibleworlds and then moves on to a discussion of 'possible for' and 'possible that'. The central chapters examine questions of meaning, epistemic possibility, temporal logic, metaphysics, and impossibility. Girle also investigates how the idea of a possible world can be put to use in different areas of philosophy, the problems it may raise, and the benefits that can be gained. (shrink)
In the tech report Artemov and Yavorskaya [4] an elegant formulation of the first-order logic of proofs was given, FOLP. This logic plays a fundamental role in providing an arithmetic semantics for first-order intuitionistic logic, as was shown. In particular, the tech report proved an arithmetic completeness theorem, and a realization theorem for FOLP. In this paper we provide a possible-world semantics for FOLP, based on the propositional semantics of Fitting [5]. We also give an Mkrtychev semantics. Motivation and (...) intuition for FOLP can be found in Artemov and Yavorskaya [4], and are not fully discussed here.This paper is dedicated to Sergei Artemov, an honored colleague and friend, who has made wonderful things for the rest of us to play with. (shrink)
Offers a psychological approach to literature, examines the connection between language and reality, and discusses education and intellectual development.
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)
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)
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 a recent article Mark Ian Thomas Robson argues that there is a clear contradiction between the view that possibleworlds are a part of God's nature and the theologically pivotal, but philosophically neglected, claim that God is perfectly beautiful. In this article I show that Robson's argument depends on several key assumptions that he fails to justify and as such that there is reason to doubt the soundness of his argument. I also demonstrate that if Robson's argument (...) were sound then this would be a problem for all classical theists and not just those who hold the possibleworlds view. (shrink)
Actualism is the doctrine that the only things there are, that have being in any sense, are the things that actually exist. In particular, actualism eschews possibilism, the doctrine that there are merely possible objects. It is widely held that one cannot both be an actualist and at the same time take possible world semantics seriously — that is, take it as the basis for a genuine theory of truth for modal languages, or look to it for insight (...) into the modal structure of reality. For possible world semantics, it is supposed, commits one to possibilism. In this paper I take issue with this view. To the contrary, I argue that one can take possible world semantics seriously without any commitment to possibleworlds or possibilism and hence remain in full compliance with actualist scruples. Moreover, one can do so without without invoking either "ersatz" worlds or haecceities. (shrink)
object an item which does not have a position in space and time but which exists. (Philosophers have nominated such things as numbers, sets, and propositions to this category. The need to posit such entities has been discussed and disputed for at least 2400 years.).
The puzzle of petitionary prayer: if we ask for the best thing, God was already going to do it, and if we ask for something that's not the best, God's not going to grant our request. In this paper, we give a new solution to the puzzle.
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 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)
A very common twofold view in contemporary philosophy is that classical logic is the correct view of logical consequence and that possibility conforms to classical logic in the sense that ‘possibleworlds’ — whatever else they may be — are closed under classical logic. These two views are assumed in this paper. My aim in this paper is to show that a very natural ‘paraconsistent’ consequence relation is involved in the given view of possibleworlds and (...) logical consequence. (shrink)
[Robert Stalnaker] Saul Kripke made a convincing case that there are necessary truths that are knowable only a posteriori as well as contingent truths that are knowable a priori. A number of philosophers have used a two-dimensional model semantic apparatus to represent and clarify the phenomena that Kripke pointed to. According to this analysis, statements have truth-conditions in two different ways depending on whether one considers a possible world 'as actual' or 'as counterfactual' in determining the truth-value of the (...) statement relative to that possible world. There are no necessary a posteriori or contingent a priori propositions: rather, contingent a priori and necessary a posteriori statements are statements that are necessary when evaluated one way, and contingent when evaluated the other way. This paper distinguishes two ways that the two-dimensional framework can be interpreted, and argues that one of them gives the better account of what it means to 'consider a world as actual', but that it provides no support for any notion of purely conceptual a priori truth. /// [Thomas Baldwin] Two-dimensional possible world semantic theory suggests that Kripke's examples of the necessary a posteriori and contingent a priori should be handled by interpreting names as implicitly indexical. Like Stalnaker, I reject this account of names and accept that Kripke's examples have to be accommodated within a metasemantic theory. But whereas Stalnaker maintains that a metasemantic approach undermines the conception of a priori truth, I argue that it offers the opportunity to develop a conception of the a priori aspect of stipulations, conceived as linguistic performances. The resulting position accommodates Kripke's examples in a way which is both intrinsically plausible and fits with Kripke's actual discussion of them. (shrink)
In this paper we discuss the notion of “possibleworlds” contrasting a philosophical idea due to Malebranche with a mathematical concept of modern logic due to Kripke from which many pseudo-philosophical discussions have arisen.
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)
This paper surveys recent "new actualist" approaches to modality that do without possibleworlds and locate modality squarely in the actual world. New actualist theories include essentialism and dispositionalism about modality, each of which can come in different varieties. The commonalities and differences between these views, as well as their shared motivations, are layed out.
Possible world semantics considers not only what an expression actually refers to but also what it might have referred to in counterfactual circumstances. This has proven exceptionally useful both inside and outside philosophy. The way this is achieved is by using intensions. An intension of an expression is a function that assigns to each possible world the reference of the expression in that world. However, the specific intension of terms has been subject to frequent disputes. How is one (...) to determine the intension of a term? Carnap has shown how the intension of a term depends on the type of that term. Two-dimensional semantics has shown how intensions also depend on the actual state of affairs. I will show how, in addition, intensions are no less dependent on metaphysical criteria of identity. Furthermore, I will reveal how these three factors interact to fix the exact intension of a term. In other words, I propose an outline of the overall mechanism by which intensions are being fixed. (shrink)
