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)

My main purpose in this article is to present an argument for the idea that necessity qua truth in all possible worlds, without other qualifications, leads us to contradiction. If we do not want to accept the contradiction, we will face a dilemma: or accepting that everything we take as contingent is in fact necessary, or accepting that we cannot translate some sentences – at least the indexed to worlds sentences – to the possible worlds (...) vocabulary. We have an intuition – and we develop an argument for it – that if “P”, evaluated in w*, is a contingent truth, so it cannot be the case that “P in w*” is a necessary truth. Generally, the argument tries to show that “P”, evaluated in w*, and “P in w*” are made true by the same contingent fact. If we suppose that “P in w*” is necessary, we would have to suppose that the fact that makes it true is also necessary, which would be contradictory with the fact that makes “P” true in w*, if we accept that what makes “P” in w* and “P in w*” true is the same fact. I attain such an aim by presenting an argument that is divided in two parts, one to imply the contradiction and the other to show that there is no relevant difference between the indicated sentences, by showing how the dilemma arises, and by answering some possible objections. This is an important objective because the possible worlds vocabulary is the default vocabulary to treat the modalities of necessity and possibility. And if it is flawed, it is important that we identify the flaw and fix it – which is exactly what we intend to do at the end of this article, by suggesting some qualification at the necessity notion, that the necessity is the native truth in all possible worlds. And this would save the possible worlds vocabulary from the presented objection. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public (...) domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The negation constitutes one of the main troubles for attempts to naturalise the semantics of the logical vocabulary, as shown by the problems related to the interpretation of disjunction in the treatment of error (Fodor) or to the definition of contraries in the analysis of reidentification abilities (Millikan). There seems to be no way out between “no (naturalized) negation, no grip of logic on the world” and “no (truth-functional) negation, no logic”. Unexpected help may come from the cognitive phenomenology (...) of negation. For three reasons: • Firstly, because it allows a distinction to be made between semantic analysis, identification of the possession conditions and psychology of the acquisition of the notion of negation, a distinction whose absence produces many misunderstandings between those who support a naturalization of semantics and those who oppose it. • Then because it places negation at the level of the contrast between beliefs, a terrain that is hostile to some naturalizers. • Finally, because it makes it possible to define a peculiar type of liberalised naturalization of semantics and, consequently, to present a hypothesis for the naturalization of cognitive phenomenology. (shrink)

In Rapture some mad shit happens: there are Plasmids that allow players to fire bees out of their hands, generate electricity bolts, set enemies on fire, pick stuff up using telekinetic powers, and much more. One theory is that physical things are those that can be completely described by the vocabulary of the best possible theory of physics. Physicalism would thus be the view that this theory of physics would completely specify all the fundamental categories, all the ingredients (...) we need to make the world. Another theory is that the physical properties are the ones needed to account for the objects we accept as physical; for example, Andrew Ryan's putter. The physicalist's claim would be that these properties are the only ones we need to account for the rest of the world. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Evaluation, Standards, Normalization: Historico-philosophical Formations and the Conditions of Possibility for Checklist Thought Bernadette Baker University of Wisconsin-Madison In education today a new vocabulary has emerged that is far more than just words. In the context of educational policy the setting of goals or objectives is now being subsumed under terms such as statewidestandards, child development is now being adjectivized by descriptors such as learning disability or emotionally (...) disturbed, and the evaluation ofclassroom-based performance is now being collated in aportfolio. These are more than just buzz words-at one level they are new ways of governing children and teachers, of organizing action, and of perceiving the world. What, for instance, does it tell us about ourselves when first-grade students Mikey, Enrique, Waldo, orDonal are introduced to visitors to the school by labels such as LD, ED, ADD, ADHD, and so forth, rather thanby their name? What does it tell us about ourselves when we say a curriculum or program of study is in line with the standards established somewhere else? And what story do we think is being narratedin the documentation of a child's performance in portfolio form across a semester or year? In consideringwhyterms suchasstandards, child development, or even evaluation have such contemporary currency I am necessarily drawn into a study of the timespaces in which they did not have such currency at all. This paper maps four moves into a moment that I think of as a rather long present-day-a present that is not simply this morning, yesterday, or the daybefore, but one that links the subjectivities ofthose now living in educational workto those made available about one hundred years ago. The four moves that I analyze here can be thought of as conditions of possibility for the operation of contemporary educational mies of reasoning, especially those that have formed around the resurgent popularity of"checklist thought" in reform efforts. The four moves collectively historicize how notions of standards, child development, and evaluation can pop up as commonsensical tropes through which to gather and degather action in the educational field. The first ofthese moves is that which flows from the operation ofan ideal to the operation of a norm. The second move is that which flows between the advent of statistics and the advent of eugenics. The third move is that which flows between the appearance ofnovels and fiction and the novel ficticityoffacts. And the fourth move is that which flows from the fictions of child development narratives to the stories that standards tell us. Collectively, these historico-philosophical moves will enable reconsideration of what we think evaluation, standards, and norms for child development actually narrate, lending food for thought to the specificityoftheir uptake in music education. From Ideal to Norm One way inwhichto examinethe shift from a seventeenth-century concept of the ideal to the nineteenth-century concept of the norm is by telling a story that was told in the early twentieth century. At this time when the educational field was formalizing, there was great care taken to record discussions held at conferences. When conferenceproceedings werepublished, theywere usually structured so that the presenter's paper©Philosophy ofMusic Education ReviewlO, no. 1 (Fall, 2002): 92-101. Bernadette Baker 93 was followed by a transcript of the conversation held after it. Like today, in the discussion time, audience members asked questions or made comments. Unlike today, the names of such participating audience members were typed into the proceedings and their specific questions or comments were written up as part ofreporting on the paper presented. In a discussion held at a conference in 1 905 on the topic of methods for training children labeledas feebleminded, apresenterhadspokenof the positive uses of a vegetable garden in the disciplining of feebleminded girls. The audience members relayed their own versions of experimenting with gardening and gathering, some complaining oftoo little space and others indicating the effects of having too many fields from which to gather. Dr. Dunlap was one such participant, indicatingimplicitlytheeffectsofhavingtoo many choices. In the spirit ofthe hunter/gatherer dichotomy, thegirlslabeledas feeblemindedatthe institutionwhereDr. Dunlap worked weresentout to pick com. The following story emerged. Dr. Dunlap: Our girls go out under an attendant and gather vegetables... (shrink)

The aim of this article is to provide a discussion of scholarly ‘crisis of modernity’ discourses that have developed in the field of social philosophy. Re-visiting past and present discourses can be illuminating in at least three ways: it can reveal the broader picture of the present financialized and technologized world and the rise of financial technologies; it can provide scholars with new vocabularies, concepts, and metaphors to comprehend present-day phenomena and developments; and it can reveal the variety of commitments (...) that are possible, today, too. This article starts with a discussion of the original ‘crisis of modernity’ discourses, in which the clashing arguments of Comte and Tocqueville are featured, and a discussion of a second ‘crisis of modernity’ that developed in the context of the ‘Great Depression.’ A third ‘crisis of modernity’ discourse emerged in the wake of the financial crises of the 1970s. Such crises are still ongoing and discussed within the boundaries of the third ‘crisis of modernity’ discourse. How financial technologies do and do not fit within this third discourse is discussed in the remainder of this article. (shrink)

Proposing a new interpretation of Being or, which amounts to the same, of the history of philosophy, is among the most difficult tasks a philosopher can set for himself. It is much easier to describe a particular philosopher’s understanding of Being or a theme in a particular epoch in the history of philosophy, because other established interpretations are available upon which one may rely to justify his own contribution, if only by contrasting it to others. This, after all, is what (...) distinguishes a philosopher from a professor of philosophy and, again, a thinker from an academic: while the latter is anxious to describe as clearly as possible, the former is interested in shedding new light.Although Lee Braver’s text seems to belong to the latter category, it actually fits into the former, as the ordering of the title and the subtitle of his work indicates. If this order were reversed, the text itself would, perhaps, be poorer, in that it would indicate a simple reconstruction of the history of continental anti-realism; although such history is also one of Braver’s objectives, it is not the most significant feature of his book. Braver’s main contribution lies in analyzing “in a newly created vocabulary” (i.e. the vocabulary of Hegel. (shrink)

Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form $$p\wedge \Diamond \lnot p$$ (‘p, but it might be that not p’) appears to be a contradiction, $$\Diamond \lnot p$$ does not entail $$\lnot p$$, which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. (...) Some theories predict that $$ p\wedge \Diamond \lnot p$$, a so-called epistemic contradiction, is a contradiction only in an etiolated sense, under a notion of entailment that does not always allow us to replace $$p\wedge \Diamond \lnot p$$ with a contradiction; these theories underpredict the infelicity of embedded epistemic contradictions. Other theories savage classical logic, eliminating not just rules that intuitively fail, like distributivity and disjunctive syllogism, but also rules like non-contradiction, excluded middle, De Morgan’s laws, and disjunction introduction, which intuitively remain valid for epistemic modals. In this paper, we aim for a middle ground, developing a semantics and logic for epistemic modals that makes epistemic contradictions genuine contradictions and that invalidates distributivity and disjunctive syllogism but that otherwise preserves classical laws that intuitively remain valid. We start with an algebraic semantics, based on ortholattices instead of Boolean algebras, and then propose a possibility semantics, based on partial possibilities related by compatibility. Both semantics yield the same consequence relation, which we axiomatize. We then show how to lift an arbitrary possible worlds model for a non-modal language to a possibility model for a language with epistemic modals. The goal throughout is to retain what is desirable about classical logic while accounting for the non-classicality of epistemic vocabulary. (shrink)

This chapter provides an introduction to possible worlds semantics in both logic and the philosophy of language, including a discussion of some of the advantages and challenges for possible worlds semantics.

The role of possible worlds 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 possible worlds on which it is particularly easy to believe in their existence: an account of possible worlds 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 possible worlds. (shrink)

This article includes a basic overview of possible world semantics and a relatively comprehensive overview of three central philosophical conceptions of possible worlds: Concretism (represented chiefly by Lewis), Abstractionism (represented chiefly by Plantinga), and Combinatorialism (represented chiefly by Armstrong).

We take Carnap’s problem to be to what extent standard consequence relations in various formal languages fix the meaning of their logical vocabulary, alone or together with additional constraints on the form of the semantics. This paper studies Carnap’s problem for basic modal logic. Setting the stage, we show that neighborhood semantics is the most general form of compositional possible worlds semantics, and proceed to ask which standard modal logics (if any) constrain the box operator to be (...) interpreted as in relational Kripke semantics. Except when restricted to finite domains, no modal logic characterizes all the Kripkean interpretation of P. Moreover, we show that, in contrast with the case of first-order logic, the obvious requirement of permutation invariance is not adequate in the modal case. After pointing out some known facts about modal logics that nevertheless force the Kripkean interpretation, we focus on another feature often taken to embody the gist of modal logic: locality. We show that invariance under point-generated subframes (properly defined) does single out the Kripkean interpretations, but only among topological interpretations, not in general. Finally, we define a notion of bisimulation invariance — another aspect of locality — that, together with a reasonable closure condition, gives the desired general result. Along the way, we propose a new perspective on normal neighborhood frames as filter frames, consisting of a set of worlds equipped with an accessibility relation, and a free filter at every world. (shrink)

_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 possible worlds such as David Lewis, evaluating them in detail.

David Lewis holds that a single possible world can provide more than one way things could be. But what are possible worlds 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 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 possible worlds semantics for partial meet multiple contractions. (shrink)

The conditional interpretation of general categorical statements like ‘All men are animals’ as universally quantified material conditionals ‘For all x, if x is F, then x is G’ suggests that the logical structure of law statements is conditional rather than categorical. Disregarding the problem that the universally quantified material conditional is trivially true whenever there are no xs that are F, there are some reasons to be sceptical of Frege’s equivalence between categorical and conditional expressions. -/- Now many philosophers will (...) claim that the material conditional interpretation of laws statements, dispositions ascriptions, or any causal claim is generally accepted as wrong and outdated. Still, there seem to be some basic logical assumptions that are shared by most of the participants in the debate on causal matters which at least stems from the traditional truth functional interpretation of conditionals. This is indicated by the vocabulary in the philosophical debate on causation, where one often speaks of ‘counterfactuals’, ‘possible worlds’ and ‘necessity’ without being explicit on whether or to what extent one accepts the logical-technical definition of these notions. To guarantee a non-Humean and non-extensional approach to causal relations, it is therefore important to be aware of the logical and metaphysical implications of the technical vocabulary. -/- In this paper we want to show why extensional logic cannot deal with causal relations. Via a logical analysis of law-like statements ‘All Fs are Gs’ we hope to throw some new light on interrelated notions like causation, laws, induction, hypotheticality and modality. If successful, our analysis should be of relevance for a deeper understanding of any type of causal relations, whether we understand them to be laws, dispositions, singulars or categoricals. (shrink)

In this chapter, I survey what I call Lewisian approaches to modality: approaches that analyze modality in terms of concrete possible worlds 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 possible worlds. (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 possible worlds, 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)

In the paper we will study the notions of possible-worlds semantics, fiction, and creativity. The intention is to show how the notion of possible-worlds semantics allows us to generate a fresh interpretation of the notions of fiction and creativity. To do this, we have to consider the philosophy of logic. Possible-worlds semantics can be used in interpreting modal notions. The intention is to interpret the notions of fiction and creativity as modal notions. However, the (...) analysis shows that the notions of fiction and creativity are multimodal notions. (shrink)

Gyula begins with a contrast between contemporary scare-quotes essentialism and Aristotelian full-blooded essentialism. The former is a semantic thesis couched in the vocabulary of possible-worlds semantics, holding that some terms are rigid designators, while the latter is a metaphysical thesis, couched in a more ancient vocabulary, holding that things have essences. Gyula argues that the more traditional metaphysical framework deserves reconsideration, both because it can help us with problems arising from the contemporary approach, and because it (...) possesses greater expressive power than the contemporary approach. He presents a fragmentary formal semantics for the traditional approach, and argues that this semantics enables us to see how the problems of contemporary essentialism can be avoided while at the same time other properly metaphysical issues, which are unapproachable from within the contemporary model due to its expressive weakness, become available for investigation. The semantics that he presents seems intended to establish the intelligibility of the traditional vocabulary, and so of the thesis of Aristotelian essentialism which is couched in it. Gyula then argues that this thesis is in fact true, using the vocabulary which the semantics has rendered legitimate. (shrink)

Most compatibilists have sought to defend their view by means of an analysis of the concept of ‘can’ in terms of subjunctive conditionals. Keith Lehrer opposes this analysis; he nevertheless embraces compatibilism. In a recent paper he has proposed a novel analysis of the concept of ‘can’ within the framework of possible-world semantics. The paper has provoked considerable discussion. In it Lehrer claims that he demonstrates the truth of compatibilism. Others have claimed that this is not so, but at (...) least one commentator has asserted that Lehrer's analysis strongly supports compatibilism. In this section I shall give a brief exposition of relevant portions of Lehrer's account of ‘can’ and then in the next section I shall seek to show that it fails to render compatibilism any more plausible than incompatibilism. Indeed, I shall seek to show that, if one of Lehrer's primitive concepts is understood as it seems it should be understood, then there would seem to be good reason to believe that his analysis supports not compatibilism but incompatibilism. (shrink)

The canonical version of possible worlds 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.

Among the most remarkable developments in metaphysics since the 1950’s is the explosion of philosophical interest in possible worlds. This paper proposes an explanation of what possible worlds 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 possible worlds, and show that the interpreted models conception meets the three constraints. (shrink)

The most commonly heard proposals for reducing possible worlds to language succumb to a simple cardinality argument: it can be shown that there are more possible worlds 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 possible worlds 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 possible worlds. (shrink)

The main objective of the paper is to give initial answers to three important questions. Why did Leibniz visit Spinoza? Why did his preparation for this meeting include a modification of the ontological proof of God? What is the philosophical result of the meeting and what do possible worlds have to do with it? In order to provide answers, three closely related manuscripts by Leibniz from November 1676 have been compared and the slow conceptual change of his philosophical (...) apparatus has been analyzed. The last of these manuscripts was presented and read in front of Spinoza. Around that time Leibniz abandoned the idea of plurality of worlds (cf. Tschirnhaus) and instead proposed the idea of possible worlds, thus introducing possibility into the (onto/theo)logical structure itself in order to avoid the “precipice” of Spinoza’s necessity. What is interesting, however, is how exactly this conceptual change occurred at the end of 1676 and what its philosophical and methodological implications are. (shrink)

The issue of reduction of propositions to sets of possible worlds is addressed. It is shown that, under some natural assumptions, there always exist recursive propositions, i.e. decidable sets of possible worlds, which are not assigned to any sentence of a language. Some consequences of this result are discussed.

Providing a possible worlds semantics for a logic involves choosing a class of possible worlds 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 possible worlds 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)

As part of an ongoing study of causal models in the history of science, a counterfactual scenario in the history of modern astronomy is explored with the aid of computer simulations. After the definition of “linking advance”, a possible world involving technological antecedence is described, branching out in 1510, in which the telescope is invented 70 years before its actual construction, at the time in which Fracastoro actually built the first prototelescope. By using the principle of the closest (...) class='Hi'>possible world, we estimate that in this scenario the discovery of the elliptical orbit of Mars would by anticipated by only 28 years. The second part of the paper involves an estimate of the probability of the previous scenario, guided by the principle that the actual world is the mean and using computer simulations to create possible worlds in which the time spans between advances is varied according to a gamma distribution function. Taking into account the importance of the use of the diaphragm for the invention of the telescope, the probability that the telescope were built by 1538 for a branching time at 1510 is found to be smaller than 1%. The work shows that one of the important features of computational simulations in philosophy of science is to serve as a consistency check for the intuitions and speculations of the philosopher. (shrink)

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)

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 possible worlds 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)

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 possible worlds. Section 3 adopts the Hamming distance between Borei numbers as a metric to calculate the distance between possible worlds. 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)

Well‐known arguments for atheism have been grounded on the alleged lack of morally justifying reasons to permit particular moral and natural evils and on the thesis that God would have to create the best possible world. After discussing obstacles to the suggestion that there is a best of all possible worlds, I examine the prospects for responding to these atheistic arguments by exploring the case for our own world's being the best of all possible worlds (...) against the backdrop of the multiverse hypothesis – an intriguing claim about the partitioned structure of reality that has been receiving serious and recent attention in philosophy and physics. (shrink)

In this paper, a novel experimental task is developed for testing the highly influential, but experimentally underexplored, possible worlds account of conditionals (Stalnaker, 1968; Lewis, 1973). In Experiment 1, this new task is used to test both indicative and subjunctive conditionals. For indicative conditionals, five competing truth tables are compared, including the previously untested, multi-dimensional possible worlds semantics of Bradley (2012). In Experiment 2, these results are replicated and it is shown that they cannot be accounted (...) for by an alternative hypothesis proposed by our reviewers. In Experiment 3, individual variation in truth assignments of indicative conditionals is investigated via Bayesian mixture models that classify participants as following one of several competing models. As a novelty of this study, it is found that a possible worlds semantics of Lewis and Stalnaker is capable of accounting for participants’ aggregate truth value assignments in this task. Applied to indicative conditionals, we show across three experiments, that the theory both captures participants’ truth values at the aggregate level (Experiments 1 and 2) and that it makes up the largest subgroup in the analysis of individual variation in our experimental paradigm (Experiment 3). (shrink)

The role of possible worlds 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 possible worlds on which it is particularly easy to believe in their existence: an account of possible worlds 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 possible worlds. (shrink)

In this paper I explore the relationship between the idea of possible worlds 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 possible worlds on the other. Since some of the possible worlds 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 possible worlds 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 possible worlds view. (shrink)

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 possible worlds, 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)

Possible world semantics has been gradually fine-grained over the years. First, simple extensional semantics was fine-grained by relativizing it to worlds considered as counterfactual, thus generating standard possible-world semantics, which was later further fine-grained by relativizing it to worlds considered as actual, thus generating two-dimensional semantics. However, worlds considered as actual were only considered with respect to the empirical facts obtaining in such worlds. This paper shows that no less of an important role is (...) played by another feature of actual worlds, namely, the criteria of identity that obtain in such worlds. (shrink)

Metaphysically possible worlds have many uses. Epistemically possible worlds 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 possible worlds, 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 possible worlds with fruitful applications, any such an account must fundamentally compromise the basic idea behind epistemic possibility. (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 possible worlds 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 possible worlds. Finally, I explain how his unconventional view bears on the trilemma for theism. (shrink)

I outline a neo-Fregean strategy in the debate on the existence of possible worlds. 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.

Saul Kripke did more than anyone else to bring possible worlds into the contemporary philosophical discourse, first with his more formal work on the model theory for modal logic in the 1960s, and then with his more philosophical lectures on reference and modality, delivered in January 1970, that used the possible worlds apparatus informally to clarify the relations between semantic issues about names and metaphysical issues about individuals and kinds. Possible worlds semantics have been (...) widely applied since then, both in philosophy and in other fields such as linguistic semantics and pragmatics, theoretical computer science, and game theory. Kripke’s work, along with that of David Lewis, stimulated an ongoing debate about the nature and metaphysical status of possible worlds. Kripke himself has had little to say about the issues raised in this debate, in print, beyond what he said in Naming and Necessity and in brief remarks in a preface to a later edition of the lectures, published in 1980. But there is a clear view of the nature of possible worlds, and of the status of an explanation of modality in terms of possible worlds, implicit in the lectures and the preface. -/- The central focus of the post–Naming and Necessity debate about possible worlds has been a contrast between David Lewis’s modal realism and various versions of actualism. On this general issue, it is clear enough where Kripke stands: His criticisms of what he describes as the “other countries” picture of possible worlds are an explicit rejection of Lewis’s realism about possible worlds. But the rejection of modal realism raises a range of further questions: What exactly are possible worlds (or possible states of the world, which Kripke suggests would be less misleading terminology)? What contribution do they make to the explanation of modal discourse, and of the distinctive facts that modal discourse is used to state? Does the slogan “necessity is truth in all possible worlds” provide, or point to, a reductive analysis of necessity? Are possible worlds, in some sense, prior to modal operators and modal auxiliaries? If not, in what sense are they explanatory? How are possible worlds, or counterfactual situations, specified? How do they contribute to our understanding of specific meta- physical questions about the relations between particular individuals and their qualitative characteristics, the kinds to which they belong, and the matter of which they are constituted? How are we to understand the possible existence of individuals that do not actually exist? What is the status of the domains of individuals in merely possible worlds? -/- My aim in this chapter is to spell out the views about some of these foundational questions that are expressed or at least implicit in Kripke’s lectures. In Section 2, I discuss the general contrast between modal realism and actualism and questions about the kind of explanation that possible worlds provide for modal discourse and modal facts. In Section 3, I look at Kripke’s views about how possible worlds are specified, in particular at the role of individuals in specifying possible worlds. In Section 4, I consider the problems about merely possible individuals. (shrink)

This paper is about possible worlds 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 possible worlds 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.

In lieu of an abstract, here is a brief excerpt of the content:Possible Worlds in the Tahâfut al-tahâfut:Averroes on Plenitude and PossibilityTaneli Kukkonen1.It has become customary to credit John Duns Scotus with having first systematically laid out the basis for treating the modal terms as referring to synchronic alternative states of affairs. This has been viewed as constituting a genuine shift in modal paradigms, as no former model had included the idea of genuine synchronic alternative possibilities. Historians of (...) modal logic and contemporary logicians alike have found it interesting that certain key features of Duns Scotus's theory and subsequent late medieval work markedly resemble the so-called possible worlds semantics approach of modern modal theory.1Duns Scotus' innovations were not completely without precedent. Several key elements in Scotus' theory were foreshadowed by twelfth-century developments. Perhaps somewhat amusingly, one of the most important forerunners to the Latin discussion was one in whose context the expression "possible worlds" would have made sense in a very special way.2 This is the medieval Arabic debate on the eternity of the world and its modal status. In this paper I propose to take stock of the positions the Arabs reached, and to do so by way of [End Page 329] consulting one of the documents central to the debate, the Tahâfut al-tahâfut or the "Incoherence of the Incoherence," by Abû al-Walîd Ibn Rushd (the Latin "Averroes," 1126-1198). In the first part I examine Averroes' exposition of the received Aristotelian tradition; in the second I assess the revisions to modal theory suggested by al-Ghazâlî (1058-1111), in the latter's comprehensive critique of philosophical doctrine. Though the two inquiries are obviously complementary, they can be accomplished independently of each other.It will be seen that Averroes' and his formidable adversary's views on the interpretation of the modal concepts differ quite fundamentally. What makes the ensuing debate, often fraught with misunderstandings and misrepresentation, so engaging is that both parties, in spite of their differences, refer to a common Aristotelian backdrop in questions of terminology and mode of argumentation. Both Averroes and al-Ghazâlî are well-placed to present a considered and balanced account of what they take to be crucial in the issues involved. It is on account of this that the complex interplay between the old and the new comes to the fore with exceptional force and clarity in the Tahâfut debates.2.The Tahâfut al-tahâfut, first published in 1180, is a philosophical rejoinder to an attack on philosophy, Abû Hâmid al-Ghazâlî's Tahâfut al-falâsifa or "The Incoherence of the Philosophers" (1095). In that celebrated work al-Ghazâlî had claimed to expose certain philosophical doctrines as not only contrary to orthodox Muslim belief, but also internally incoherent.3 Averroes' reply in turn was written in order "to show the different degrees of assent and conviction attained by the assertions in The Incoherence of the Philosophers, and to prove that the greater part has not reached the degree of evidence and of truth."4 The work is thus of a doubly dialectical nature. Whereas al-Ghazâlî tries to show the philosophers' reasoning to be defective, Averroes has to show both that al-Ghazâlî is likewise lacking in intellectual rigor and that philosophy, properly understood, is innocent of the charges leveled at it. If the Islamic philosophers (al-Fârâbî and, above all, Avicenna) have in fact erred, this is only to the extent that they have misrepresented correct Aristotelian doctrine. [End Page 330]Averroes' presentation is appropriately delicate considering the complexity of the task at hand. Averroes quotes al-Ghazâlî exclusively in full, lengthy passages, with the result of incorporating almost all of the Tahâfut al-falâsifa in his own work. In so doing he gives us an adequate and comparably fair representation of al-Ghazâlî's views. Averroes then goes on to discuss what al-Ghazâlî says both in the philosophers' name and in his own, and points out their respective deviations from Aristotelian doctrine. The text thus comes laid out in three successive layers, with Averroes' own... (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 possible worlds. Hence, after a brief explanation of some philosophical matters I take a look at possible worlds 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)

Ever since Saul Kripke and others developed a semantic interpretation for modal logic, 'possible worlds' 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 possible worlds 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 possible worlds 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)

Ever since Saul Kripke and others developed a semantic interpretation for modal logic, 'possible worlds' 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 possible worlds 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 possible worlds 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)

The question as to whether some objects are possible worlds that have an initial segment in common, i.e. so that their fusion is a temporal tree whose branches are possible worlds, 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 possible worlds. Then I explain that for a different reason the nomic essentialist advocate of concrete plenitude should hold this much too. (shrink)

Realists about possible worlds typically identify possible worlds with abstract objects, such as propositions or properties. However, they face a significant objection due to Lewis (1986), to the effect that there is no way to explain how possible worlds-as-abstract objects represent possibilities. In this paper, I describe a response to this objection on behalf of realists. The response is to identify possible worlds with propositions, but to deny that propositions are abstract objects, (...) or indeed objects at all. Instead, I argue that realists should follow Prior (1971) and others in treating higher-order quantification (e.g. quantification into predicate or sentence position) as a genuine form of quantification in its own right, and so in particular, not to be analysed in terms of first-order quantification over abstract objects. I argue that from this ‘higher-orderist’ perspective, there is a relatively straightforward answer to the question of how possible worlds-as-propositions succeed in representing possibilities. (shrink)