Lewis en Stalnaker over mogelijke werelden

Hieronder enkele fragmenten van een taak die ik geschreven heb voor het vak Meaning, Reference and Modality (over Lewis' modaal realisme schreef ik al eerder op deze blog: hier):

Question: Recapitulate two objections from Lewis against the ideas that a possibility is a theory, or another linguistic entity. What do his ideas imply for what we can know about possibilities? Lewis rejects the idea that possibilities are theories (or other linguistic entities). His first objection to this idea is that it is either circular or incorrect. For evident reasons, we want to restrict ourselves to consistent theories (otherwise, we would get the counterintuitive result that "p is possible'' is true for every sentence p). But what is consistency? Lewis describes two answers. (i) Saying that a theory is consistent might mean that (all sentences in) it can be (simultaneously) true. But now, we have used the modal notion "can", and since possible worlds are used to analyze notions such as this, this account is circular. (ii) Saying that a theory is consistent might mean that it does not entail any contradictions. Let T be a consistent theory (containing PA). By Gödel's incompleteness theorem, there exists a false sentence p of arithmetic such that neither T |-- p nor T |-- ~p. Since p is false, ~p is true; and since arithmetical truths are necessary, []~p is true. (The claim that arithmetical truths are necessary is accepted by almost all contemporary philosophers; it certainly is accepted by Lewis, who writes: "no falsehood of arithmetic is possibly true" (p. 183).) But since T is a consistent theory and it's not the case that T |-- ~p, the 'linguistic entities'-account incorrectly predicts that ~[]~p. Lewis' second objection is that if possible worlds are linguistic entities, then also the actual world is a linguistic entity, which he considers to be an absurd conclusion. Therefore, possible worlds aren't linguistic entities. (Note that this objection rests on the assumption that the actual world has the same ontological status as other possible worlds.) According to Lewis' own (realist) account of possible worlds, we can have very little knowledge about them: possible worlds are worlds, just like ours (the actual world), but causally completely isolated from it. This can be seen as a reductio of Lewis' position. He wants to use possible worlds to explain the meaning of a counterfactual like "If A had been the case, B would have been the case". Roughly, Lewis' theory says that this sentence is true if B is true in the closest possible world in which A is the case. But, according to his philosophical position about possible worlds, we cannot go' to the closest possible world in which A is the case, andcheck' whether B is the case there; i.e. we cannot know the truth value of the counterfactual. But intuitively, we do know the truth values of many counterfactuals. Question: Summarize Robert Stalnaker's two main points against Lewis' position. Do you think Stalnaker's way of thinking respects Lewis' two demands on what a metaphysical theory should accomplish? According to Lewis, the actual world and other possible worlds have the same ontological status. But he also says that a possible world is a way things could have been. For example, the actual world is the way things (actually) are. Stalnaker points out that these claims conflict: the way things (actually) are is a property of the actual world, not that world itself. Stalnaker's second objection concerns Lewis' ideas about the word actual'. According to Lewis, "actual" is an indexical word; people inhabiting a certain world w speak about w when they speak about "the actual world", people inhabiting w' speak about w' when they speak about "the actual world", etc. ... Stalnaker points out that this is a semantical thesis (which might even be correct), from which no ontological consequences about the (non-)existence of other possible worlds can be drawn. According to Lewis, there are two general demands that every metaphysical theory should meet: (i) it should be systematic and (ii) it should respect the pre-philosophical intuitions to which we are most firmly attached. According to Stalnaker'smoderate realism', possible worlds exist, but they are not of the same sort as the actual world: possible worlds are ways thing could have been. Thus, they are properties of the actual world; this means that they are abstract objects. In general, Stalnaker's moderate realism respects Lewis' desiderata for metaphysical theories. It is certainly systematic; it even eliminates a tension in Lewis' own philosophy (the tension between Lewis' claims (i) that possible worlds have the same ontological status as the actual world, and (ii) that possible worlds are ways things might have been, i.e. that they are properties of the (actual) world). Furthermore, it also respects our pre- philosophical intuitions: possible worlds are abstract objects which -- just like numbers -- can be quantified over; thus, Stalnaker can explain why we say things such as "there are 36 possible outcomes" when throwing two dice.