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Summary Possible worlds semantics is a general approach to theories of meaning, on which meanings (or, more precisely, semantic values) are assigned to sentences in terms of the truth-values they take across all possible worlds. The intuition is that the meaning of a sentence specifies how the world would have to be for that sentence to be true (or false). This is typically made precise by identifying the semantic value of a sentence with its possible-worlds intension, a function from possible worlds to truth-values. When those values are just true and false (and are mutually exclusive), possible worlds intensions are equivalent to sets of possible worlds (the worlds at which the sentence is question is true). The approach can be generalised by treating semantic values for sub-sentential items (such as nouns and verbs) as functions from possible worlds to other entities (such as particulars, properties and relations). ‘Possible worlds semantics’ is also used in a narrower sense, to refer to formal Kripke semantics for modal (and other) logics. 
Key works Carnap 1947 and Wittgenstein 1922 are important precursors to possible worlds semantics. Kripke developed the formal semantics for modal logic in Kripke 1959, 1963 and for intuitionistic logic in Kripke 1963. Key works applying possible worlds semantics to natural language include Cresswell 1973Lewis 1970, Montague 1973Kratzer 1977Lewis 1986 and Lewis 1973Hintikka 1962, 1967 develops formal possible worlds semantics and applies it to epistemic concepts.
Introductions Heim & Kratzer 1998 is a very comprehensive (although difficult) introduction to possible worlds semantics and its application to natural language. Lewis 1970 is a much shorter overview. Girle 2003 and Girle 2000 are introductory textbooks on formal possible worlds semantics in modal logic. Hughes & Cresswell 1996 is a classic textbook in modal logic. Sider 2010 includes a good presentation of quantified first-order logic.
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  1. C. Anthony Anderson (2009). The Lesson of Kaplan's Paradox About Possible World Semantics. In Joseph Almog & Paolo Leonardi (eds.), The Philosophy of David Kaplan. Oxford University Press. 85.
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  2. Andrew Bacon (forthcoming). Representing Counterparts. Australasian Journal of Logic.
    This paper presents and motivates a counterpart theoretic semantics for quantifi ed modal logic based on a fleshed out account of Lewis's notion of a `possibility.' According to the account a possibility consists of a world and some haecceitistic information about how each possible individual gets represented de re. A semantics for quanti ed modal logic based on evaluating formulae at possibilities is developed. It is shown that this framework naturally accommodates an actuality operator, addressing recent objections to counterpart theory, (...)
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  3. Derek Ball (2011). Property Identities and Modal Arguments. Philosophers' Imprint 11 (13).
    Physicalists about the mind are committed to claims about property identities. Following Kripke's well-known discussion, modal arguments have emerged as major threats to such claims. This paper argues that modal arguments can be resisted by adopting a counterpart theoretic account of modal claims, and in particular modal claims involving properties. Thus physicalists have a powerful motive to adopt non-Kripkean accounts of the metaphysics of modality and the semantics of modal expressions.
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  4. Stephen Barker (2011). Can Counterfactuals Really Be About Possible Worlds? Noûs 45 (3):557-576.
    The standard view about counterfactuals is that a counterfactual (A > C) is true if and only if the A-worlds most similar to the actual world @ are C-worlds. I argue that the worlds conception of counterfactuals is wrong. I assume that counterfactuals have non-trivial truth-values under physical determinism. I show that the possible-worlds approach cannot explain many embeddings of the form (P > (Q > R)), which intuitively are perfectly assertable, and which must be true if the contingent falsity (...)
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  5. Jiri Benovsky (2005). Branching Versus Divergent Possible Worlds. Kriterion 19:12-20.
    David Lewis' modal counterpart theory falls prey to the famous Saul Kripke's objection, and this is mostly due to his 'static' ontology (divergence) of possible worlds. This paper examines a genuinely realist but different, branching ontology of possible worlds and a new definition of the counterpart relation, which attempts to provide us with a better account of de re modality, and to meet satisfactorily Kripke's claim, while being also ontologically more 'parsimonious'.
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  6. Johan Benthem (1984). Possible Worlds Semantics: A Research Program That Cannot Fail? Studia Logica 43 (4):379 - 393.
    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 (reasonable) logic whatsoever can be modelled in this way. Thus, the enterprise would lose its essential tension. Fortunately, it may be shown that the so-called incompleteness-examples from modal logic resist possible worlds modelling, even in the above wider (...)
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  7. 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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  8. Tomasz Bigaj (2006). Non-Locality and Possible Worlds. A Counterfactual Perspective on Quantum Entanglement. Ontos Verlag.
    This book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the possible-world (...)
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  9. John C. Bigelow (1978). Believing in Semantics. Linguistics and Philosophy 2 (1):101--144.
    This paper concerns the semantics of belief-sentences. I pass over ontologically lavish theories which appeal to impossible worlds, or other points of reference which contain more than possible worlds. I then refute ontologically stingy, quotational theories. My own theory employs the techniques of possible worlds semantics to elaborate a Fregean analysis of belief-sentences. In a belief-sentence, the embedded clause does not have its usual reference, but refers rather to its own semantic structure. I show how this theory can accommodate quantification (...)
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  10. John C. Bigelow (1976). Possible Worlds Foundations for Probability. Journal of Philosophical Logic 5 (3):299--320.
  11. 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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  12. Ben Blumson (2010). Pictures, Perspective and Possibility. Philosophical Studies 149 (2):135 - 151.
    This paper argues for a possible worlds theory of the content of pictures, with three complications: depictive content is centred, two-dimensional and structured. The paper argues that this theory supports a strong analogy between depictive and other kinds of representation and the platitude that depiction is mediated by resemblance.
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  13. Raymond Bradley (1979). Possible Worlds: An Introduction to Logic and its Philosophy. B. Blackwell.
    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.).
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  14. Elke Brendel (1993). Partial Worlds and Paradox. Erkenntnis 39 (2):191 - 208.
    Since universal language systems are confronted with serious paradoxical consequences, a semantic approach is developed in whichpartial worlds form the ontological basis. This approach shares withsituation semantics the basic idea that statements always refer to certain partial worlds, and it agrees with the extensional and model-theoretic character ofpossible worlds semantics. Within the framework of the partial worlds conception a satisfactory solution to theLiar paradox can be formulated. In particular, one advantage of this approach over those theories that are based on (...)
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  15. Phillip Bricker (2006). David Lewis: On the Plurality of Worlds. In John Shand (ed.), Central Works of Philosophy, Vol. 5: The Twentieth Century: Quine and After. Acumen Publishing.
    David Lewis's book 'On the Plurality of Worlds' mounts an extended defense of the thesis of modal realism, that the world we inhabit the entire cosmos of which we are a part is but one of a vast plurality of worlds, or cosmoi, all causally and spatiotemporally isolated from one another. The purpose of this article is to provide an accessible summary of the main positions and arguments in Lewis's book.
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  16. Aaron Bronfman & Janice Dowell, J. L., Contextualism About Deontic Conditionals.
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  17. Aaron Bronfman & J. L. Dowell, Janice (forthcoming). The Language of Reasons and 'Ought'. In Daniel Star (ed.), Oxford Handbook of Reasons.
  18. Lauri Carlson (1988). Quantified Hintikka-Style Epistemic Logic. Synthese 74 (2):223 - 262.
    This paper contains a formal treatment of the system of quantified epistemic logic sketched in Appendix II of Carlson (1983). Section 1 defines the syntax and recapitulates the model set rules and principles of the Appendix system. Section 2 defines a possible worlds semantics for this system, and shows that the Appendix system is complete with respect to this semantics. Section 3 extends the system by an explicit truth operatorT it is true that and considers quantification over nonexistent individuals. Section (...)
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  19. Rudolf Carnap (1947/1956). Meaning and Necessity. University of Chicago Press.
    "This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence.
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  20. Joseph Chiari (1973). The Necessity of Being. New York,Gordian Press.
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  21. Charles S. Chihara (1998). The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic. Oxford University Press.
    A powerful challenge to some highly influential theories, this book offers a thorough critical exposition of modal realism, the philosophical doctrine that many possible worlds exist of which our own universe is just one. Chihara challenges this claim and offers a new argument for modality without worlds.
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  22. Matthew Chrisman (2012). On the Meaning of 'Ought'. In Russ Shafer-Landau (ed.), Oxford Studies in Metaethics, vol. 7. Oxford University Press. 304.
    Discussions about the meaning of the word “ought” are pulled in two apparently competing directions. First, in ethical theory this word is used in the paradigmatic statement of ethical principles and conclusions about what some agent is obligated to do. This leads some ethical theorists to claim that the word “ought” describes a real relation, roughly, of being obligated to (realism) or expresses some non-cognitive attitude toward agents acting in certain ways (expressivism). Second, in theoretical linguistics this word is classified (...)
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  23. B. Jack Copeland (2006). Meredith, Prior, and the History of Possible Worlds Semantics. Synthese 150 (3):373 - 397.
    This paper charts some early history of the possible worlds semantics for modal logic, starting with the pioneering work of Prior and Meredith. The contributions of Geach, Hintikka, Kanger, Kripke, Montague, and Smiley are also discussed.
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  24. B. Jack Copeland (2002). The Genesis of Possible Worlds Semantics. Journal of Philosophical Logic 31 (2):99-137.
    This article traces the development of possible worlds semantics through the work of: Wittgenstein, 1913-1921; Feys, 1924; McKinsey, 1945; Carnap, 1945-1947; McKinsey, Tarski and Jónsson, 1947-1952; von Wright, 1951; Becker, 1952; Prior, 1953-1954; Montague, 1955; Meredith and Prior, 1956; Geach, 1960; Smiley, 1955-1957; Kanger, 1957; Hintikka, 1957; Guillaume, 1958; Binkley, 1958; Bayart, 1958-1959; Drake, 1959-1961; Kripke, 1958-1965.
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  25. Fabrice Correia (2007). Modality, Quantification, and Many Vlach-Operators. Journal of Philosophical Logic 36 (4):473 - 488.
    Consider two standard quantified modal languages A and P whose vocabularies comprise the identity predicate and the existence predicate, each endowed with a standard S5 Kripke semantics where the models have a distinguished actual world, which differ only in that the quantifiers of A are actualist while those of P are possibilist. Is it possible to enrich these languages in the same manner, in a non-trivial way, so that the two resulting languages are equally expressive-i.e., so that for each sentence (...)
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  26. Fabrice Correia & Andrea Iacona (eds.) (2013). Around the Tree: Semantic and Metaphysical Issues Concerning Branching and the Open Future. Springer.
    Over the past few years, the tree model of time has been widely employed to deal with issues concerning the semantics of tensed discourse. The thought that has motivated its adoption is that the most plausible way to make sense of indeterminism is to conceive of future possibilities as branches that depart from a common trunk, constituted by the past and the present. However, the thought still needs to be further articulated and defended, and several important questions remain open, such (...)
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  27. Maxwell J. Cresswell (2006). From Modal Discourse to Possible Worlds. Studia Logica 82 (3):307 - 327.
    The possible-worlds semantics for modality says that a sentence is possibly true if it is true in some possible world. Given classical prepositional logic, one can easily prove that every consistent set of propositions can be embedded in a ‘maximal consistent set’, which in a sense represents a possible world. However the construction depends on the fact that standard modal logics are finitary, and it seems false that an infinite collection of sets of sentences each finite subset of which is (...)
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  28. Louis deRosset (2014). Possible Worlds for Modal Primitivists. Journal of Philosophical Logic 43 (1):109-131.
    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 (...)
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  29. John Divers (2006). Possible-Worlds Semantics Without Possible Worlds: The Agnostic Approach. Mind 115 (458):187-226.
    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 possible worlds (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 possible worlds, then assertion of such a theory, taken at face-value, does appear to bring commitment to the existence of a plurality (...)
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  30. John Divers (1995). Modal Fictionalism Cannot Deliver Possible Worlds Semantics. Analysis 55 (2):81--9.
  31. Cian Dorr, How to Be a Modal Realist.
    This paper investigates the form a modal realist analysis of possibility and necessity should take. It concludes that according to the best version of modal realism, the notion of a world plays no role in the analysis of modal claims. All contingent claims contain some de re element; the effect of modal operators on these elements is described by a counterpart theory which takes the same form whether the de re reference is to a world or to something else. This (...)
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  32. Janice Dowell, J. L. (2012). Contextualist Solutions to Three Puzzles About Practical Conditionals. In Russ Shafer-Landau (ed.), Oxford Studies in Metaethics, volume 7. Oxford.
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  33. Janice Dowell, J. L. (2011). A Flexible Contextualist Account of Epistemic Modals. Philosophers' Imprint 11 (14):1-25.
    On Kratzer’s canonical account, modal expressions (like “might” and “must”) are represented semantically as quantifiers over possibilities. Such expressions are themselves neutral; they make a single contribution to determining the propositions expressed across a wide range of uses. What modulates the modality of the proposition expressed—as bouletic, epistemic, deontic, etc.—is context.2 This ain’t the canon for nothing. Its power lies in its ability to figure in a simple and highly unified explanation of a fairly wide range of language use. Recently, (...)
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  34. Brian Ellis, Frank Jackson & Robert Pargetter (1977). An Objection to Possible-World Semantics for Counterfactual Logics. Journal of Philosophical Logic 6 (1):355 - 357.
  35. J. H. Fetzer & P. Humphreys (eds.) (1998). The New Theory of Reference: Kripke, Marcus, and its Origins. Kluwer.
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  36. Kit Fine (2003). The Problem of Possibilia. In Michael J. Loux & Dean W. Zimmerman (eds.), The Oxford Handbook of Metaphysics. Oxford University Press.
    Are there, in addition to the various actual objects that make up the world, various possible objects? Are there merely possible people, for example, or merely possible electrons, or even merely possible kinds? We certainly talk as if there were such things. Given a particular sperm and egg, I may wonder whether that particular child which would result from their union would have blue eyes. But if the sperm and egg are never in fact brought together, then there is no (...)
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  37. Kit Fine (2000). Semantics for the Logic of Essence. Journal of Philosophical Logic 29 (6):543-584.
    This paper provides a possible worlds semantics for the system of the author's previous paper 'The Logic of Essence'. The basic idea behind the semantics is that a statement should be taken to be true in virtue of the nature of certain objects just in case it is true in any possible world compatible with the nature of those objects. It is shown that a slight variant of the original system is sound and complete under the proposed semantics.
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  38. Kit Fine (1972). In so Many Possible Worlds. Notre Dame Journal of Formal Logic 13 (4):516-520.
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  39. Melvin Fitting, Possible World Semantics for First Order Lp.
    First we have individual variables, as usual in first-order logics. (We do not have individual constants, but this is a minor point.) The propositional logic LP has justification constants, but in FOLP these are generalized to allow individual variables as arguments. Thus we have as justification constants c, c(x), c(x, y), . . . . Similarly LP has justification variables, but in FOLP these can be parametrized with individual variables p, p(x), p(x, y), . . . . To keep terminology (...)
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  40. Graeme Forbes (1983). Thisness and Vagueness. Synthese 54 (2):235-259.
    This paper is about two puzzles, or two versions of a single puzzle, which deserve to be called paradoxes, and develops some apparatus in terms of which the apparently conflicting principles which generate the puzzles can be rendered consistent. However, the apparatus itself is somewhat controversial: the puzzles are modal ones, and the resolution to be advocated requires the adoption of a counterpart theoretic semantics of essentially the kind proposed by David Lewis, which in turn requires qualified rejection of certain (...)
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  41. Matthias Gerner (2009). Assessing the Modality Particles of the Yi Group in Fuzzy Possible-Worlds Semantics. Linguistics and Philosophy 32 (2):143-184.
    Of late, evidentiality has received great attention in formal semantics. In this paper I develop ‘evidentiality-informed’ truth conditions for modal operators such as must and may . With language data drawn from Luoping Nase (a Tibeto-Burman language spoken in the P.R. of China and belonging to the Yi Nationality), I illustrate that epistemic modals clash with clauses articulating first-hand information. I then demonstrate that existing models such as Kratzer’s graded possible-worlds semantics fail to provide accurate truth conditions for modals tagging (...)
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  42. Rod Girle (2003). Possible Worlds. Acumen.
  43. Dominic Gregory (2006). Functionalism About Possible Worlds. Australasian Journal of Philosophy 84 (1):95 – 115.
    Various writers have proposed that the notion of a possible world is a functional concept, yet very little has been done to develop that proposal. This paper explores a particular functionalist account of possible worlds, according to which pluralities of possible worlds are the bases for structures which provide occupants for the roles which analyse our ordinary modal concepts. It argues that the resulting position meets some of the stringent constraints which philosophers have placed upon accounts of possible worlds, while (...)
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  44. Dominic Gregory (2005). Keeping Semantics Pure. Noûs 39 (3):505–528.
    There are numerous contexts in which philosophers and others use model-theoretic methods in assessing the validity of ordinary arguments; consider, for example, the use of models built upon 'possible worlds' in examinations of modal arguments. But the relevant uses of model-theoretic techniques may seem to assume controversial semantic or metaphysical accounts of ordinary concepts. So, numerous philosophers have suggested that standard uses of model-theoretic methods in assessing the validity of modal arguments commit one to accepting that modal claims are to (...)
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  45. Dominic Gregory (2001). B is Innocent. Analysis 61 (3):225–229.
    The paper replies to an earlier paper by Yannis Stephanou, who presented an argument purportedly showing the falsity of certain instances of the characteristic axiom of the modal logic B. The paper argues that the B axiom was not to blame for the unsoundness of Stephanou's argument.
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  46. Dominic Gregory (2001). Completeness and Decidability Results for Some Propositional Modal Logics Containing “Actually” Operators. Journal of Philosophical Logic 30 (1):57-78.
    The addition of "actually" operators to modal languages allows us to capture important inferential behaviours which cannot be adequately captured in logics formulated in simpler languages. Previous work on modal logics containing "actually" operators has concentrated entirely upon extensions of KT5 and has employed a particular modeltheoretic treatment of them. This paper proves completeness and decidability results for a range of normal and nonnormal but quasi-normal propositional modal logics containing "actually" operators, the weakest of which are conservative extensions of K, (...)
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  47. Volker Halbach, Hannes Leitgeb & Philip Welch (2003). Possible-Worlds Semantics for Modal Notions Conceived as Predicates. Journal of Philosophical Logic 32 (2):179-223.
    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 (...)
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  48. Sven Ove Hansson, Semantics for More Plausible Deontic Logics.
    In order to avoid the paradoxes of standard deontic logic, we have to give up the semantic construction that identifies obligatory status with presence in all elements of a subset of the set of possible worlds. It is proposed that deontic logic should instead be based on a preference relation, according to the principle that whatever is better than something permitted is itself permitted. Close connections hold between the logical properties of a preference relation and those of the deontic logics (...)
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  49. Sven Ove Hansson (2006). Ideal Worlds — Wishful Thinking in Deontic Logic. Studia Logica 82 (3):329 - 336.
    The ideal world semantics of standard deontic logic identifies our obligations with how we would act in an ideal world. However, to act as if one lived in an ideal world is bad moral advice, associated with wishful thinking rather than well-considered moral deliberation. Ideal world semantics gives rise to implausible logical principles, and the metaphysical arguments that have been put forward in its favour turn out to be based on a too limited view of truth-functional representation. It is argued (...)
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  50. Nicolai Hartmann (2013). Possibility and Actuality. Walter de Gruyter.
    From a different perspective, “essential actuality” is related to logical actuality. It means plain existence in the ideal sphere of being. One is familiar with this, for example, in “mathematical existence.” This does not merge with validity, but implies ...
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