To: Craig S.
From: Geoffrey Klempner
Subject: Explaining possibility by means of possible worlds
Date: 22nd December 2009 12:56

Dear Craig,

Thank you for your email of 12 December, with your essay for the University of London BA Logic module, in response to the question, 'Are we justified in using the notion of possible worlds to explain the notion of possibility?'

Thanks also for your excellent answer on causality, which will be posted on the new page of Questions and Answers, some time before the new year. I just wish I'd had the idea of inviting my UoL students onto the panel sooner!

The answer to, 'Why is there NCA rather than AN?', if there is one, would look rather like Anaximander's explanation for the world remaining suspended in the centre of the cosmos: that is to say, the answer is given in purely logical terms (e.g. considerations of 'symmetry') but the account as such is abductive, or inference to the best explanation, as we already have the fact (we assume) that we are seeking to explain. (In Anaximander's case, this required making a number of ad hoc assumptions about the sun and the moon, etc.)

In this context (the question 'why is there something rather than nothing') you could have mentioned realism about possible worlds, which appears to dispense entirely with the need to explain, 'why there is something'. Every possible world behaving according to every possible set of laws of nature exists, including the world of absolutely nothing, so there is nothing to explain.

I remember being thrilled by Lewis's 'Counterfactuals' when I was an undergraduate. In the last chapter of my 'Naive Metaphysics' I develop an analogy between the place of 'my world' in the objective order, and the place of the actual world in the universe of all possible worlds (a la Lewis).

In your essay, you have given a clear and concise argument for the view that only Lewis's account offers a 'rigorous' explanation of the notion of possibility. At one time, I would have agreed with you. However, I have begun to have doubts.

Let's start with the question 'what kind' of possibility we are interested in. You say that 'distinguishing these various kinds', i.e. logical, analytic, metaphysical, nomological and epistemic, 'is not central to the question'. However, let's start from the point of view of someone who is genuinely puzzled about how there can be such a thing as 'possibility'. How can anything BE, other than what IS?

Let's start with something easy: It's possible that my package from eBay was delivered today. There are two scenarios: the scenario where I arrive home to discover that the postman delivered the package, and the scenario where no package was delivered (Let's ignore other possibilities, like the world ending.) This is easy: to say that it is possible that the package arrived, is to say that it is consistent with what I know that the package arrived. In other words, epistemic possibility is just a variety of ignorance (or, IS ignorance).

What about logical possibility? This is harder for technical reasons, because there is room for real dispute over just what counts as 'logical'. However, it would not be too controversial to say that the terms, 'logically necessary', 'logically consistent', etc. apply to propositions of a given language. In propositional calculus, there is a simple test (truth tables) which reliably sorts sentences into those which are logically necessary, consistent or impossible.

I'll spare you the complete survey. The real problem comes (as I think you'll agree) with metaphysical possibility. Is there such a thing? I have the strong intuition that I might have decided not to come into work today, had the weather been worse, and that this is a fact. But what kind of fact? A fact calling for philosophical analysis. Lewis argues, quite convincingly, that the only way to deliver truth conditions for this counterfactual statement is in terms of possible worlds.

(I think here your essay would have been improved if you had been explicit on this point. There are alternatives to viewing counterfactuals as propositions or statements with truth conditions: Lewis needs to make the case that none of these alternatives -- e.g. the theory proposed by J.L. Mackie in his article 'Counterfactuals and Causal Laws' -- is adequate.)

But this is where I have a problem, and it is similar (or possibly the same) as the problem Kripke raises. Possible worlds actually exist. Indeed, towards the end of your essay you suggest possible physical theories which could accommodate the Lewis view. (Of course, there remains the problem that the number of actually existing physically alternate worlds must not fall short of the number of all possible worlds, otherwise the interpretation fails.)

Here's another theory which could be true. Forget quantum mechanics. Let's just say that, in time, which is infinite, every possible universe with every possible set of laws of nature has existed, or will exist, an infinite number of times. There are an infinite number of universes in the past and also in the future in which 'GK' stays at home on 22nd December because of a blizzard. But who cares about that?

In short, Lewis gives truth conditions for counterfactual statements, but at the cost of reducing possibility to actuality. His view is 'actualism' about possible worlds. There is no such thing as metaphysical possibility, in the intuitive sense. Perhaps he's right. But in that case, the cost is not just ontological extravagance about 'possible worlds' so-called, but also the elimination of our intuitive sui generis notion of metaphysical possibility, or possibility as such.

All the best for 2010,

Geoffrey