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- Daniel Nolan, Is Stalnaker Inconsistent About Indicative Conditionals?Robert Stalnaker’s formal semantics for his indicative conditional (which his 1975 paper takes over from his 1968 paper and Stalnaker and Thomason 1968) validate modus ponens, as one might expect. But they do so at the cost of a tension between his philosophical remarks in his 1975 paper and his formal constraints. Stalnaker commits himself to the following: he defines a “context set” as “the possible worlds not ruled out by the presupposed background information” (Stalnaker 1975 p 142). He later states a “pragmatic principle” that “normally a speaker is concerned only with possible worlds within the context set, since this set is defined as the set of possible worlds among which the speaker wishes to distinguish. So it is at least a normal expectation that the selection function should turn first to these worlds before considering counterfactual worlds—those presupposed to be non-actual” (p 144). Then two paragraphs later, in apparent reference to this principle he says “I would expect that the pragmatic principle stated above should hold without exception for indicative conditionals”. Yet when the actual world is not one in which the presuppositions all hold, from his definition of the “context set” it is not among the worlds of the context set, and elsewhere in his 1975 as well as his 1968 he stipulates that the selection function given the actual world and an antecedent true at the actual world yields the actual world (p 144 of Stalnaker 1975, condition 3 on p 104 of Stalnaker 1968). These remarks on the face of it lead to inconsistency if it is possible to presuppose falsehoods: for then the presuppositions create a context set which does not include the actual world (but may perfectly well nevertheless contain some possible worlds in which the antecedent of a given conditional holds when that antecedent is also actually true). In evaluating a conditional with a true antecedent which also holds in some world in the context set, Stalnaker enjoins us to employ a selection function which selects the actual world, and to (“without exception”) employ a selection function which selects some world in the context set in preference to any world outside it..Reading list | Discuss | Edit | Categorize |My bibliography
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Analytic philosophers usually think about modality in terms of possible worlds. According to the possible worlds framework, a proposition is necessary if it is true according to all possible worlds; it is possible if it is true according to some possible world. There are as many possible worlds as there are ways the actual world might be. Only one world is actual.
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| | Other links: otago.ac.nz | Scholar | More options ... 0. Relativistic Content In standard semantics, propositional content, whether it be the content of utterances or mental states, has a truth-value relative only to a possible world. For example, the content of my utterance of ‘Jim is sitting now’ is true just in case Jim is sitting at the time of utterance in the actual world, and the content of my belief that Alice will give a talk tomorrow is true just in case Alice will give a talk on the day following the occurrence of my belief state in the actual world. Let us call propositional content which has a truth-value relative only to a possible world ‘non-relativistic content’. Non-relativistic content can be treated as either structured or unstructured. On the unstructured-content view, non-relativistic content is a set of possible worlds and bears the truth-value true just in case the actual world is a member of that set. For example, the content of my utterance of ‘Jim is working now’ at time t is the set of worlds in which Jim is working at t, and this content is true just in case the actual world is among those worlds. On the structured-content view, non-relativistic content is a set or conglomeration of properties and/or objects, where properties are features which objects possess regardless of who considers or observes them and regardless of when they are being considered or observed. Such properties are said to be (or represent) functions from possible worlds to extensions. Relative to a possible world they determine a set of objects instantiating the property. For example, relative to the actual world the property of being human determines the set of actual humans. Not all content is non-relativistic. Let us say that propositional content is relativistic just in case it possesses a truth-value only relative to a centered world. A centered world is a possible world in which an individual and a time are marked, where the marked individual..
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| | Other links: brogaardb.googlepages.com sites.google.com | Scholar | At my library | More options ... §0. A familiar if obscure idea: an indicative conditional presents its consequent as holding in the actual world on the supposition that its antecedent so holds, whereas a subjunctive conditional merely presents its consequent as holding in a world, typically counterfactual, in which its antecedent holds. Consider this pair.
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| | Other links: blackwell-synergy.com blackwell-synergy.com dx.doi.org | Scholar | At my library | More options ... Two major themes in the literature on indicative conditionals are (1) that the content of indicative conditionals typically depends on what is known;1 (2) that conditionals are intimately related to conditional probabilities.2 In possible world semantics for counterfactual conditionals, a standard assumption is that conditionals whose antecedents are metaphysically impossible are vacuously true.3 This aspect has recently been brought to the fore, and defended by Tim Williamson, who uses it in to characterize alethic necessity by exploiting such equivalences as: A⇔¬A A. One might wish to postulate an analogous connection for indicative conditionals, with indicatives whose antecedents are (in some relevant sense) epistemically impossible being vacuously true: and indeed, the modal account of indicative conditionals of Brian Weatherson has exactly this feature.4 This allows one to characterize an epistemic modal by the equivalence A⇔¬A→A. For simplicity, in what follows we write A as KA and think of it as expressing that subject S knows that A.5 The connection to probability has received much attention. Stalnaker (1970) suggested, as a way of articulating the ‘Ramsey Test’, the following very general schema for indicative conditionals relative to some probability function P: P(A→B) = P(B|A) 1For example, Nolan (2003); Weatherson (2001); Gillies (2007). 2For example Stalnaker (1970); McGee (1989); Adams (1975). 3Lewis (1973). See Nolan (1997) for criticism. 4‘epistemically possible’ here means incompatible with what is known (where ‘what is known’ is to be cashed out in some relevant sense). 5This idea was suggested to me in conversation by John Hawthorne. I do not know of it being explored in print. The plausibility of this characterization will depend on the exact sense of ‘epistemically possible’ in play—if it is compatibility with what a single subject knows, then can be read ‘the relevant subject knows that p’. If it is more delicately formulated, we might be able to read as the epistemic modal ‘must’..
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| | Scholar | More options ... In his (1981) paper, Stalnaker has revised his old theory of conditionals and has given the revision an interesting defense. Indeed, Stalnaker shows that this new theory meets the standard objections put to the old. However, I argue that the revision runs into difficulties in the context of quantum mechanics: If Stalnaker's theory of the conditional is assumed, then from plausible assumptions certain Bell-like conflicts with experiment can be derived. This result, I go on to argue, is a good reason to reject Stalnaker's theory, at least for the quantum mechanical context.
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| | Other links: jstor.org | Scholar | At my library | More options ... I discuss an argument given by Dorothy Edgington for the conclusion that indicative conditionals cannot express propositions. The argument is not effective against Robert Stalnaker's context-dependent propositional theory. I isolate and defend the feature of Stalnaker's theory that allows it to evade the argument.
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| | Other links: mind.oxfordjournals.org jstor.org dx.doi.org | Scholar | At my library | More options ... Let’s fix some terminology at the start. A world (or possible world – for me, the ‘possible’ is redundant) is, first, an individual, not a set or class; second, a particular, not a property or universal; third, concrete in this sense: it is fully determinate in all qualitative respects; and, fourth, a maximal interrelated whole: each world is internally unified, and isolated from every other world.1 There is at least one world, the world we are part of. It is an actual world, the actual world if there are no “island universes.”2 Worlds that are not actual (if any) are merely possible. A realist about possible worlds believes that there is a plenitudinous plurality of worlds: whenever something is possible – for example, that donkeys talk, or that pigs fly – there is a world in which it is true.
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| | Other links: blackwell-synergy.com dx.doi.org | Scholar | At my library | More options ... One very popular kind of semantics for subjunctive conditionals is aclosest-worlds account along the lines of theories given by David Lewisand Robert Stalnaker. If we could give the same sort of semantics forindicative conditionals, we would have a more unified account of themeaning of ``if ... then ...'' statements, one with manyadvantages for explaining the behaviour of conditional sentences. Such atreatment of indicative conditionals, however, has faced a battery ofobjections. This paper outlines a closest-worlds account of indicativeconditionals that does better than some of its cousins in explaining thebehaviour of such conditionals. The paper then discusses objectionsoffered by Dorothy Edgington and Frank Jackson to closest-worldsaccounts of indicative conditionals, and shows that these objections canbe met by the account outlined.
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| | Other links: springerlink.com jstor.org dx.doi.org | Scholar | At my library | More options ... 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, that would mean that there were propositions true in all possible worlds but which could only be known to be true by acquiring empirical evidence. Consider such a purported proposition P. The role of empirical evidence for establishing P's truth would have to be to rule out worlds in which P is false. If there were no such worlds to be ruled out, we would not require evidence for P. But by hypothesis, P is necessary and so true in all metaphysically possible worlds. And on Stalnaker's view, the metaphysically possible worlds are all the worlds there are. So there can be no proposition that is true in all possible worlds, but that we require evidence to know. In this way, the motivation for Stalnaker's two dimensional account of the necessary a posteriori rests on his denying that there are metaphysically impossible Worlds. I argue that given his view of what possible worlds are, Stalnaker has no principled reason for denying that there are metaphysically impossible worlds. If I am right, this undercuts Stalnaker's motivation for his two dimensional account of the necessary a posteriori.
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| | Other links: jstor.org | Scholar | At my library | More options ... Possible worlds semantics has been very useful in modeling not only the intensionality of necessity and possibility, future and past. It has also found its place in modeling the intentionality of propositional attitudes like belief and knowledge. There is something fruitful in analyzing a belief as a set of possible worlds. The belief is the set of possible worlds in which the belief is true. The belief is true if and only if the actual world is in the corresponding set of propositions. The possible worlds in the set corresponding to the belief represent how the agent per- ceives the world to be. If the belief is false, then the world isn’t how the agent sees the world to be, and so the actual world isn’t in the set of worlds corresponding to the belief (see Lewis [4] and Stalnaker [9]). The same can be said of whole belief states just as much as it can be said of individual beliefs. My belief state is the set of worlds consistent with what I believe. This view has been very fruitful, not least because the set-theoretic structure of sets of possible worlds corresponds nicely with the logical structure of entailment relations among propositions and the behavior of propositional connectives like conjunction, disjunction, and negation. However, the story does not deal well with inconsistent belief. Inconsistent beliefs are true in no possible worlds, so they are each modeled by the same set of worlds—the empty set. My beliefs are often inconsistent, and so are those of many..
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| | Other links: projecteuclid.org:80 dx.doi.org | Scholar | At my library | More options ... Discussion of Daniel Nolan, Is Stalnaker inconsistent about indicative conditionals?
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