David Lewis Counterfactuals and Possible Worlds

David Lewis American philosopher, lived between UCLA and Princeton Modal realism

Today’s discussion Lewis’ account of Possible Worlds Lewis’ account of Counterfactuals A quick note on temporality

Possible Worlds Summary: There are worlds other than ours. For each of these worlds, their inhabitants call it ‘the actual world’. We can’t prove that this is true, but we can know that if it is true, many of the problems of philosophy of language and logic are dissolved.

Possible Worlds Lewis’ Argument: 1. Things could have been different than they are. 2. We can say, in ordinary language, that: ‘there are ways things could have been besides the way they actually are.’ This is an existential quantification. 3. ‘ ways things could have been ’ must refer to real entities. 4. Therefore, ‘ ways things could have been ’ are real entities. Let us call them ‘Possible Worlds’. Possible worlds exist! This view is called realism about possible worlds, or modal realism.

Modal Language Modals are words that express modalities, or words that qualify statements: Take the statement ‘It is the case that p ’ ‘It is usually the case that p ’ ‘It is never the case that p ’ ‘It is necessarily the case that p ’ ‘It is possibly the case that p The words usually, never, necessarily, and possibly above are examples of modal words, that is, words that qualify the claim that ‘it is the case that p’.

In Logic Some modalities have been translated to formal logic. The most common ones are: Modalities having to do with necessity Modalities having to do with possibility Modalities having to do with impossibility

Lewis’ Modal Realism Modal Realism: what we have been considering ‘modal’, that is, within the modality of possibility is actually real. For Lewis, to say that something is possible in our world is to say that such thing is real in some world. For every modal claim of the sort ‘if I had gone to class today, I would have learned something’, there is a possible world where it is a factual claim to be taken at face value. So we should take modal claims at face value, because they are factual claims in other worlds.

Taking claims at face value Not an inviolable principle, but one that should be favored unless: (1) Taking them at face value leads to trouble (2) Taking them some other way does not lead to trouble. In other words: avoid trouble! When we take modal claims at face value, that is, when we embrace modal realism, (1) it does not lead to trouble, and (2) all other ways of taking it lead to trouble, therefore (3) we should take it at face value.

Alternatives If our modal words aren’t quantifiers over possible worlds, what else can they be? Alternative answers that have been offered: (a) They could be unanalyzed primitives. Lewis’ reply: No! This is not a theory, but abstinence from theorizing.

Alternatives (b) They could be indicators of consistency: ‘Possibly x ’ only means that ‘ x ’ is a consistent sentence. Lewis’ reply: No! To say that x is consistent to say that it could be true, so we are explaining possibility in terms of possibility, which is circular reasoning.

Alternatives (c) They could be quantifiers over ‘possible worlds’ that are not real but only linguistic entities, such as sets of sentences. Lewis’ reply: No! How do we know which set of sentences our sentence belongs to? If we answer, “sentences about possibility,” again we are being circular… Additionally, our world isn’t a set of sentences, why should other worlds be?

Conclusion The less troubling alternative to explain modal language is to say that there really are possible worlds out there, and that modal words are quantifiers over these real possible worlds. “When I profess realism about possible worlds, I mean to be taken literally. Possible worlds are what they are, and not some other thing.” (page 97) What are possible worlds?

What are Possible Worlds? We all know what the actual world is; there are more things of that sort. Possible worlds are just like the actual world, but different things happen in each of them. Our actual world is one among others. We call it actual because it is the one we inhabit. Inhabitants of other worlds call their world actual. ‘ Actual’ is an indexical term, that is, a term which refers to a different thing in each circumstance of utterance (like the words I, you, here, etc.). It refers in each world W to that world W itself. This is what Lewis calls the ‘indexical theory of actuality’.

Arguments against Possible Worlds (1) Only our world exists! What is possible cannot be real, it is unactualized. Only what is actual is real. Lewis’ reply: this argument assumes what it wants to prove. It does not prove that what is possible cannot be real, so it is not a good argument against possible worlds. Additionally, we use language to talk about things that are not actual; how is such talk meaningful if it refers to what does not exist?

Arguments against Possible Worlds (2) We should only postulate the existence of things when absolutely necessary. It is not necessary to assume that possible worlds exist, therefore they don’t. We should be parsimonious with what we say exists. Lewis’ reply: there are two kinds of parsimony, qualitative and quantitative. Qualitative parsimony is to keep down the number of kinds of entity. Quantitative parsimony is to keep down the number of entities. Qualitative parsimony is good, but we shouldn’t care about quantitative parsimony. Realism about possible worlds disrespects only quantitative parsimony. It does not assume the existence of new kinds of things, only of more things like the actual world.

What are possible worlds like? Lewis’ answer: I can’t know, but believing in them solves many difficulties. They might obey different laws of physics (physics is contingent). They must have the same logic and arithmetic as ours (this is a pre- philosophical opinion). They might be worlds with a different distribution of the same matter. We might be able to arrive at such distributions through mathematics ( ersatz or substitute possible worlds). Many views on what these worlds could be like fit the requirement of avoiding philosophical trouble, and there is no way to pick between these views. All we can try to do is respect our pre- philosophical opinions.

Pre-philosophical opinions “One comes to philosophy already endowed with a stock of opinions. It is not the business of philosophy either to undermine or to justify these preexisting opinions, to any great extent, but only to try to discover ways of expanding them into an orderly system. A metaphysician’s analysis of mind is an attempt at systematizing our opinions about mind. It succeeds to the extent that (1) it is systematic, and (2) it respects those of our pre-philosophical opinions to which we are firmly attached. Insofar as it does better than any alternative we have thought of, we give it credence. There is some give-and-take, but not too much: some of us sometimes change our minds on some points of common opinion, if they conflict irremediably with a doctrine that commands our belief by its systematic beauty and its agreement with more important common opinions.” (page 99) In other words, Lewis admits that he adopts modal realism because it is the way of seeing the world most adequate to his pre-philosophical opinions AND the way that avoids most trouble in logic and philosophy of language.

Counterfactuals Summary: Lewis looks at counterfactual statements, that is, statements of the form ‘if x were true, then y would be true’. He then proposes two operators that make these statements translatable into logic. He finally claims that the truth of these statements in each world depends on the truth values of their antecedent and consequent at various possible worlds. In other words, he offers the truth-conditions for counterfactual statements.

Counterfactuals Example : ‘If he behaved himself, he would be ignored’ and ‘If he behaved himself, he might be ignored’. Lewis suggests two symbols to help translate this sort of statement into logical notation: (1)  This symbol means: ‘If it were the case that… then it would be the case that…’ (2)  This symbol means: ‘If it were the case that… then it might be the case that…’

Translation Translating our examples, we would have: ‘If he behaved himself, he would be ignored’ = He behaves himself  he is ignored ‘If he behaved himself, he might be ignored’ = He behaves himself  he is ignored The operators are interdefinable.

Lewis’ project Lewis wants to translate this feeling of ‘if x were true, then y would be true’ into logic. When is a sentence of this kind true? That is, what are the truth conditions for this kind of sentence?

Lewis’ Solution Lewis will conclude something like this: it is true in our world that ‘If kangaroos had no tails, they would topple over’ if, either there are no worlds where kangaroos have no tails (i.e. it is impossible for them not to have tails), or there is some possible world very similar to ours in which kangaroos have no tails, and, in that world, they do topple over. So there we have it: the truth conditions for counterfactuals, that is, a formula that tells us when these statements are true. And these truth conditions, for Lewis, require realism about possible worlds. Realism about possible worlds, therefore, helps us understand counterfactual statements.

Lewis and Temporality Remember Lewis’ indexical theory of actuality: The word ‘actual’ is indexical, that is, it refers in each world to that world. For Lewis, the present is also indexical. All the moments in time that have ever been and that will ever be are referred to as the ‘present’ by their own inhabitants, and all these ‘presents’ coexist. Socrates is speaking of the ‘present’ right now in 430 b.C., and what he means is his present. His present exists now even though it is our past and we cannot see it.

Two conceptions of time The present is all there is and time is a mysterious flow that passes us by. This view is called presentism. All times coexist. We are stuck in the present because we are three-dimensional beings. If we had one additional dimension, we would be able to move in the directions ‘past’ and ‘future’ just the way we move ‘up’ and ‘down’ or ‘left’ and ‘right’. What we ordinarily call ‘time’ does not exist; the flow is an illusion. This view is called eternalism. Lewis’ views are compatible with the later conception of time (eternalism).