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Impossible Worlds

Edited by Barak Krakauer (University of California, Santa Cruz)
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Summary Impossible worlds are structures that have been proposed to make sense of certain kinds of modal phenomena. Unlike the possible worlds, impossible worlds are incomplete, inconsistent, or both; nonetheless, impossible worlds are employed in a similar way, intended to represent or model certain kinds of scenarios. A possible worlds theorist may attempt to give an account of propositions, properties, intentional attitudes, or various flavors of necessity and possibility, yet run into trouble in "hyperintensional" contexts: she might, for example, want to distinguish properties that are necessarily co-extensive (such as triangularity and trilateraltiy) or propositions that are true in the same set of worlds (such as <2 + 2 = 4> and ). Impossible worlds could be added to such a system to make the kinds of distinctions in modal space that seem to be required, since there would be impossible worlds where a figure has three sides but not three angles, or where all bachelors are male but 2 + 2 does not equal 4. Some impossible worlds theorists hold that these structures are sui generis entities, entities of the same kind as possible worlds, or entities constructed from the possible worlds.
Introductions Francesco Berto's Stanford Encyclopedia entry is a good introduction to some of the motivations for impossible worlds as well as their metaphysics. 
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  1. Sara Bernstein (forthcoming). Omission Impossible. Philosophical Studies.
    This paper gives a framework for understanding causal counterpossibles, statements in which a counterfactual imbued with causal content has an antecedent that appeals to a metaphysically impossible world. Such statements are generated by omissive causal claims that appeal to metaphysically impossible events. I give an account of impossible omissions, and argue for two claims: (i) impossible omissions are causally relevant to the actual world, and (ii) the analysis of causal counterpossibles provides further evidence for the nonvacuity of counterpossibles more generally.
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  2. Francesco Berto (2013). Impossible Worlds. Stanford Encyclopedia of Philosophy (2013).
    It is a venerable slogan due to David Hume, and inherited by the empiricist tradition, that the impossible cannot be believed, or even conceived. In Positivismus und Realismus, Moritz Schlick claimed that, while the merely practically impossible is still conceivable, the logically impossible, such as an explicit inconsistency, is simply unthinkable. -/- An opposite philosophical tradition, however, maintains that inconsistencies and logical impossibilities are thinkable, and sometimes believable, too. In the Science of Logic, Hegel already complained against “one of the (...)
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  3. Francesco Berto (2012). Existence as a Real Property. Synthèse Library, Springer.
    This book is both an introduction to and a research work on Meinongianism. “Meinongianism” is taken here, in accordance with the common philosophical jargon, as a general label for a set of theories of existence – probably the most basic notion of ontology. As an introduction, the book provides the first comprehensive survey and guide to Meinongianism and non-standard theories of existence in all their main forms. As a research work, the book exposes and develops the most up-to-date Meinongian theory (...)
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  4. Francesco Berto (2011). Modal Meinongianism and Fiction: The Best of Three Worlds. Philosophical Studies 152 (3):313-35.
    We outline a neo-Meinongian framework labeled as Modal Meinongian Metaphysics (MMM) to account for the ontology and semantics of fictional discourse. Several competing accounts of fictional objects are originated by the fact that our talking of them mirrors incoherent intuitions: mainstream theories of fiction privilege some such intuitions, but are forced to account for others via complicated paraphrases of the relevant sentences. An ideal theory should resort to as few paraphrases as possible. In Sect. 1, we make this explicit via (...)
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  5. Francesco Berto (2010). Impossible Worlds and Propositions: Against the Parity Thesis. Philosophical Quarterly 60 (240):471-486.
    Accounts of propositions as sets of possible worlds have been criticized for conflating distinct impossible propositions. In response to this problem, some have proposed to introduce impossible worlds to represent distinct impossibilities, endorsing the thesis that impossible worlds must be of the same kind; this has been called the parity thesis. I show that this thesis faces problems, and propose a hybrid account which rejects it: possible worlds are taken as concrete Lewisian worlds, and impossibilities are represented as set-theoretic constructions (...)
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  6. Francesco Berto (2008). Modal Meinongianism for Fictional Objects. Metaphysica 9 (2):205-218.
    Drawing on different suggestions from the literature, we outline a unified metaphysical framework, labeled as Modal Meinongian Metaphysics (MMM), combining Meinongian themes with a non-standard modal ontology. The MMM approach is based on (1) a comprehension principle (CP) for objects in unrestricted, but qualified form, and (2) the employment of an ontology of impossible worlds, besides possible ones. In §§1–2, we introduce the classical Meinongian metaphysics and consider two famous Russellian criticisms, namely (a) the charge of inconsistency and (b) the (...)
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  7. Jens Christian Bjerring (2013). On Counterpossibles. Philosophical Studies (2):1-27.
    The traditional Lewis–Stalnaker semantics treats all counterfactuals with an impossible antecedent as trivially or vacuously true. Many have regarded this as a serious defect of the semantics. For intuitively, it seems, counterfactuals with impossible antecedents—counterpossibles—can be non-trivially true and non-trivially false. Whereas the counterpossible "If Hobbes had squared the circle, then the mathematical community at the time would have been surprised" seems true, "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would (...)
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  8. Jens Christian Bjerring (2013). Impossible Worlds and Logical Omniscience: An Impossibility Result. Synthese 190 (13):2505-2524.
    In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents that (...)
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  9. Jens Christian Bjerring (2012). Problems in Epistemic Space. Journal of Philosophical Logic (1):1-18.
    When a proposition might be the case, for all an agent knows, we can say that the proposition is epistemically possible for the agent. In the standard possible worlds framework, we analyze modal claims using quantification over possible worlds. It is natural to expect that something similar can be done for modal claims involving epistemic possibility. The main aim of this paper is to investigate the prospects of constructing a space of worlds—epistemic space—that allows us to model what is epistemically (...)
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  10. Jens Christian Bjerring (2010). Non-Ideal Epistemic Spaces. Dissertation, Australian National University
    In a possible world framework, an agent can be said to know a proposition just in case the proposition is true at all worlds that are epistemically possible for the agent. Roughly, a world is epistemically possible for an agent just in case the world is not ruled out by anything the agent knows. If a proposition is true at some epistemically possible world for an agent, the proposition is epistemically possible for the agent. If a proposition is true at (...)
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  11. Einar Duenger Bohn (2009). Must There Be a Top Level? Philosophical Quarterly 59 (235):193-201.
    I first explore the notion of the world's being such that everything in it is a proper part. I then explore the notion of the world's being such that everything in it both is and has a proper part. Given two well recognized assumptions, I argue that both notions represent genuine metaphysical possibilities. Finally I consider, but dismiss, some possible objections.
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  12. Phillip Bricker (2004). McGinn on Non-Existent Objects and Reducing Modality. [REVIEW] Philosophical Studies 118 (3):439-451.
    In this discussion of Colin McGinn's book, 'Logical Properties', I comment first on the chapter "Existence", then on the chapter "Modality." With respect to existence, I argue that McGinn's view that existence is a property that some objects have and other objects lack requires the property of existence to be fundamentally unlike ordinary qualitative properties. Moreover, it opens up a challenging skeptical problem: how do I know that I exist? With respect to modality, I argue that McGinn's argument that quantificational (...)
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  13. Berit Brogaard & Joe Salerno (2013). Remarks on Counterpossibles. Synthese 190 (4):639-660.
    Since the publication of David Lewis’ Counterfactuals, the standard line on subjunctive conditionals with impossible antecedents (or counterpossibles) has been that they are vacuously true. That is, a conditional of the form ‘If p were the case, q would be the case’ is trivially true whenever the antecedent, p, is impossible. The primary justification is that Lewis’ semantics best approximates the English subjunctive conditional, and that a vacuous treatment of counterpossibles is a consequence of that very elegant theory. Another justification (...)
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  14. Jeffrey Goodman (2004). An Extended Lewis-Stalnaker Semantics and The New Problem of Counterpossibles. Philosophical Papers 33 (1):35-66.
    Closest-possible-world analyses of counterfactuals suffer from what has been called the ‘problem of counterpossibles’: some counterfactuals with metaphysically impossible antecedents seem plainly false, but the proposed analyses imply that they are all (vacuously) true. One alleged solution to this problem is the addition of impossible worlds. In this paper, I argue that the closest possible or impossible world analyses that have recently been suggested suffer from the ‘new problem of counterpossibles’: the proposed analyses imply that some plainly true counterpossibles (viz., (...)
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  15. Gilbert Harman, Impossible Worlds and Knowledge of Necessary Truths.
    I propose that safety and sensitivity conditionals may be used to explain the reliability of beliefs in necessary truths, by appeal to a non-standard semantics for counterfactuals with impossible antecedents and necessarily true consequents.
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  16. José Hierro Pescador (1985). Mundos imposibles. Theoria 1 (1):143-157.
    An impossible world is a world which necessarily does not exist. Besides the paradigm of necessity, wich is logical necesslty, we must consider physical necessity and ethical necessity, both of wich can beexpressed in terms of logical necessity, in the way suggested by Montague. Accordingly, an impossible world can be logically impossible, physically impossible or ethically impossible, but in every case the impossibility can be reduced to logical impossibility, and in consequence an impossible world is irrational and cannot be understood (...)
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  17. Jaakko Hintikka (1975). Impossible Possible Worlds Vindicated. Journal of Philosophical Logic 4 (4):475 - 484.
  18. Brendan Balcerak Jackson (2012). Worlds and Individuals, Possible and Otherwise. Australasian Journal of Philosophy 90 (1):205 - 206.
    Australasian Journal of Philosophy, Volume 90, Issue 1, Page 205-206, March 2012.
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  19. Mark Jago (forthcoming). Are Impossible Worlds Trivial? In Vit Puncochar & Petr Svarny (eds.), The Logica Yearbook 2012. College Publications.
    Theories of content are at the centre of philosophical semantics. The most successful general theory of content takes contents to be sets of possible worlds. But such contents are very coarse-grained, for they cannot distinguish between logically equivalent contents. They draw intensional but not hyperintensional distinctions. This is often remedied by including impossible as well as possible worlds in the theory of content. Yet it is often claimed that impossible worlds are metaphysically obscure; and it is sometimes claimed that their (...)
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  20. Mark Jago (2014). The Impossible: An Essay on Hyperintensionality. Oxford University Press.
    Mark Jago presents an original philosophical account of meaningful thought: in particular, how it is meaningful to think about things that are impossible. We think about impossible things all the time. We can think about alchemists trying to turn base metal to gold, and about unfortunate mathematicians trying to square the circle. We may ponder whether God exists; and philosophers frequently debate whether properties, numbers, sets, moral and aesthetic qualities, and qualia exist. In many philosophical or mathematical debates, when one (...)
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  21. Mark Jago (2013). Impossible Worlds. Noûs 47 (3).
    Impossible worlds are representations of impossible things and impossible happenings. They earn their keep in a semantic or metaphysical theory if they do the right theoretical work for us. As it happens, a worlds-based account provides the best philosophical story about semantic content, knowledge and belief states, cognitive significance and cognitive information, and informative deductive reasoning. A worlds-based story may also provide the best semantics for counterfactuals. But to function well, all these accounts need use of impossible and as well (...)
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  22. Mark Jago (2013). Against Yagisawa's Modal Realism. Analysis 73 (1):10-17.
    In his book Worlds and Individuals, Possible and Otherwise (2010), Takashi Yagisawa presents and argues for a novel and imaginative version of modal realism. It differs both from Lewis’s modal realism (Lewis 1986) and from actualists’ ersatz accounts (Adams 1974; Sider 2002). In this paper, I’ll present two arguments, each of which shows that Yagisawa’s metaphysics is incoherent. The first argument shows that the combination of Yagisawa’s metaphysics with impossibilia leads to triviality: every sentence whatsoever comes out true. This is (...)
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  23. Mark Jago (2012). Constructing Worlds. Synthese 189 (1):59-74.
    You and I can differ in what we say, or believe, even though the things we say, or believe, are logically equivalent. Discussing what is said, or believed, requires notions of content which are finer-grained than sets of (metaphysically or logically) possible worlds. In this paper, I develop the approach to fine-grained content in terms of a space of possible and impossible worlds. I give a method for constructing ersatz worlds based on theory of substantial facts. I show how this (...)
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  24. Mark Jago (2009). Logical Information and Epistemic Space. Synthese 167 (2):327 - 341.
    Gaining information can be modelled as a narrowing of epistemic space . Intuitively, becoming informed that such-and-such is the case rules out certain scenarios or would-be possibilities. Chalmers’s account of epistemic space treats it as a space of a priori possibility and so has trouble in dealing with the information which we intuitively feel can be gained from logical inference. I propose a more inclusive notion of epistemic space, based on Priest’s notion of open worlds yet which contains only those (...)
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  25. Jeffrey C. King (2007). What in the World Are the Ways Things Might Have Been? [REVIEW] Philosophical Studies 133 (3):443 - 453.
    Robert Stalnaker is an actualist who holds that merely possible worlds are uninstantiated properties that might have been instantiated. Stalnaker also holds that there are no metaphysically impossible worlds: uninstantiated properties that couldn't have been instantiated. These views motivate Stalnaker's "two dimensional" account of the necessary a posteriori on which there is no single proposition that is both necessary and a posteriori. For a (metaphysically) necessary proposition is true in all (metaphysically) possible worlds. If there were necessary a posteriori propositions, (...)
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  26. Peter J. King (1993). Lycan on Lewis and Meinong. Proceedings of the Aristotelian Society 93:193 - 201.
    In his 1988 review of On the Plurality of Worlds (Lycan [1988]), William Lycan argued that what he called Lewis's 'mad-dog modal realism' (also 'rape-and-loot modal realism' and 'nuclear-holocaust modal realism' - I suspect that some reference to the supposed extremity of Lewis's position is intended) rested upon an unanalysed modal notion. Lycan accepted that actualists all seemed to be stuck with such unanalysed notions (adding that his own was the notion of compatibility as applied to pairs of properties), but (...)
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  27. Ira Kiourti, Impossible Worlds. Oxford Bibliographies in Philosophy.
  28. Ira Georgia Kiourti (2010). Real Impossible Worlds : The Bounds of Possibility. Dissertation, University of St Andrews
    Lewisian Genuine Realism (GR) about possible worlds is often deemed unable to accommodate impossible worlds and reap the benefits that these bestow to rival theories. This thesis explores two alternative extensions of GR into the terrain of impossible worlds. It is divided in six chapters. Chapter I outlines Lewis’ theory, the motivations for impossible worlds, and the central problem that such worlds present for GR: How can GR even understand the notion of an impossible world, given Lewis’ reductive theoretical framework? (...)
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  29. Barak Krakauer (2013). What Are Impossible Worlds? Philosophical Studies 165 (3):989-1007.
    In this paper, I argue for a particular conception of impossible worlds. Possible worlds, as traditionally understood, can be used in the analysis of propositions, the content of belief, the truth of counterfactuals, and so on. Yet possible worlds are not capable of differentiating propositions that are necessarily equivalent, making sense of the beliefs of agents who are not ideally rational, or giving truth values to counterfactuals with necessarily false antecedents. The addition of impossible worlds addresses these issues. The kinds (...)
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  30. Brian Leftow (2006). Impossible Worlds. Religious Studies 42 (4):393-402.
    Richard Brian Davis offers several criticisms of a semantics I once proposed for subjunctive conditionals with impossible antecedents. I reply to these.
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  31. Edwin D. Mares (1997). Who's Afraid of Impossible Worlds? Notre Dame Journal of Formal Logic 38 (4):516-526.
    A theory of ersatz impossible worlds is developed to deal with the problem of counterpossible conditionals. Using only tools standardly in the toolbox of possible worlds theorists, it is shown that we can construct a model for counterpossibles. This model is a natural extension of Lewis's semantics for counterfactuals, but instead of using classical logic as its base, it uses the logic LP.
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  32. Charles G. Morgan (1973). Systems of Modal Logic for Impossible Worlds. Inquiry 16 (1-4):280 – 289.
    The intuitive notion behind the usual semantics of most systems of modal logic is that of ?possible worlds?. Loosely speaking, an expression is necessary if and only if it holds in all possible worlds; it is possible if and only if it holds in some possible world. Of course, contradictory expressions turn out to hold in no possible worlds, and logically true expressions turn out to hold in every possible world. A method is presented for transforming standard modal systems into (...)
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  33. Daniel Nolan (1997). Impossible Worlds: A Modest Approach. Notre Dame Journal of Formal Logic 38 (4):535-572.
    Reasoning about situations we take to be impossible is useful for a variety of theoretical purposes. Furthermore, using a device of impossible worlds when reasoning about the impossible is useful in the same sorts of ways that the device of possible worlds is useful when reasoning about the possible. This paper discusses some of the uses of impossible worlds and argues that commitment to them can and should be had without great metaphysical or logical cost. The paper then provides an (...)
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  34. T. Parent, Content Externalism and Quine's Criterion Are Incompatible.
    Externalism holds that the content of our utterances and thoughts are determined partly by the environment. Here, I offer an argument which suggests that externalism is incompatible with a natural view about ontological commitment--namely, the Quinean view that such commitments are fixed by the range of the variables in your theory. The idea in brief is that if Oscar mistakenly believes that water = XYZ, the externalist ontologically commits Oscar to two waterish kinds, whereas the Quinean commits him to one (...)
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  35. T. Parent, Conservative Meinongianism.
    This paper defends the Meinongian thesis that “there are objects of which it is true that there are no such objects,” re: fictitious and illusory objects. I first formulate the problem of negative existentials in a novel way, and discuss why this new version is more forceful against anti-Meinongians. Additional data is then raised to vex anti-Meinongians—e.g., the truth of ‘Pegasus is imaginary’, and a reading of ‘There actually are illusory objects’ where it comes out true. The Meinongian, in contrast, (...)
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  36. Tommaso Piazza & Francesco Piazza (2010). On Inconsistent Entities. A Reply to Colyvan. Philosophical Studies 150 (2):301 - 311.
    In a recent article M. Colyvan has argued that Quinean forms of scientific realism are faced with an unexpected upshot. Realism concerning a given class of entities, along with this route to realism, can be vindicated by running an indispensability argument to the effect that the entities postulated by our best scientific theories exist. Colyvan observes that among our best scientific theories some are inconsistent, and so concludes that, by resorting to the very same argument, we may incur a commitment (...)
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  37. Graham Priest (1984). Logic of Paradox Revisited. Journal of Philosophical Logic 13 (2):153 - 179.
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  38. Graham Priest (1979). The Logic of Paradox. Journal of Philosophical Logic 8 (1):219 - 241.
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  39. Greg Restall (1997). Ways Things Can't Be. Notre Dame Journal of Formal Logic 38 (4):583-596.
    Paraconsistent logics are often semantically motivated by considering "impossible worlds." Lewis, in "Logic for equivocators," has shown how we can understand paraconsistent logics by attributing equivocation of meanings to inconsistent believers. In this paper I show that we can understand paraconsistent logics without attributing such equivocation. Impossible worlds are simply sets of possible worlds, and inconsistent believers (inconsistently) believe that things are like each of the worlds in the set. I show that this account gives a sound and complete semantics (...)
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  40. Maciej Sendłak (2010). Spór o niezaktualizowane możliwości. Filozofia Nauki 1.
    In 1947 Quine wrote one of the most important and influential articles in the twentieth century philosophy - "On What There Is". One of the aims of this article was a critique of Meinong's Theory of Object. The critique was especially focused upon nonactual possibilities, which (according to Meinong) are some kinds of nonexistent objects. In my paper I want to present Neo-Meinongian refutations of Quine's critique. In order to do this I discuss: (i) the main thesis of "On What (...)
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  41. Giacomo Sillari (2008). Quantified Logic of Awareness and Impossible Possible Worlds. Review of Symbolic Logic 1 (4):514-529.
    Among the many possible approaches to dealing with logical omniscience, I consider here awareness and impossible worlds structures. The former approach, pioneered by Fagin and Halpern, distinguishes between implicit and explicit knowledge, and avoids logical omniscience with respect to explicit knowledge. The latter, developed by Rantala and by Hintikka, allows for the existence of logically impossible worlds to which the agents are taken to have access; since such worlds need not behave consistently, the agents’ knowledge is fallible relative to logical (...)
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  42. David A. Vander Laan (1997). The Ontology of Impossible Worlds. Notre Dame Journal of Formal Logic 38 (4):597-620.
    The best arguments for possible worlds as states of affairs furnish us with equally good arguments for impossible worlds of the same sort. I argue for a theory of impossible worlds on which the impossible worlds correspond to maximal inconsistent classes of propositions. Three objections are rejected. In the final part of the paper, I present a menu of impossible worlds and explore some of their interesting formal properties.
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  43. David A. Vander Laan (1997). The Ontology of Impossible Worlds. Notre Dame Journal of Formal Logic 38 (4):597-620.
    The best arguments for possible worlds as states of affairs furnish us with equally good arguments for impossible worlds of the same sort. I argue for a theory of impossible worlds on which the impossible worlds correspond to maximal inconsistent classes of propositions. Three objections are rejected. In the final part of the paper, I present a menu of impossible worlds and explore some of their interesting formal properties.
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  44. Achille C. Varzi (1997). Inconsistency Without Contradiction. Notre Dame Journal of Formal Logic 38 (4):621-639.
    David Lewis has argued that impossible worlds are nonsense: if there were such worlds, one would have to distinguish between the truths about their contradictory goings-on and contradictory falsehoods about them; and this--Lewis argues--is preposterous. In this paper I examine a way of resisting this argument by giving up the assumption that ‘in so-and-so world’ is a restricting modifier which passes through the truth-functional connectives The outcome is a sort of subvaluational semantics which makes a contradiction ‘A & ~A’ false (...)
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  45. Z. Weber (2011). A Paraconsistent Model of Vagueness. Mind 119 (476):1025-1045.
    Vague predicates, on a paraconsistent account, admit overdetermined borderline cases. I take up a new line on the paraconsistent approach, to show that there is a close structural relationship between the breakdown of soritical progressions, and contradiction. Accordingly, a formal picture drawn from an appropriate logic shows that any cut-off point of a vague predicate is unidentifiable, in a precise sense. A paraconsistent approach predicts and explains many of the most counterintuitive aspects of vagueness, in terms of a more fundamental (...)
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  46. Takashi Yagisawa (2010). Worlds and Individuals, Possible and Otherwise. Oxford University Press.
    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.
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  47. Takashi Yagisawa (1988). Beyond Possible Worlds. Philosophical Studies 53 (2):175 - 204.
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  48. Edward N. Zalta (1997). A Classically-Based Theory of Impossible Worlds. Notre Dame Journal of Formal Logic 38 (4):640-660.
    The appeal to possible worlds in the semantics of modal logic and the philosophical defense of possible worlds as an essential element of ontology have led philosophers and logicians to introduce other kinds of `worlds' in order to study various philosophical and logical phenomena. The literature contains discussions of `non-normal worlds', `non-classical worlds', `non-standard worlds', and `impossible worlds'. These atypical worlds have been used in the following ways: (1) to interpret unusual modal logics, (2) to distinguish logically equivalent propositions, (3) (...)
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