To: Pearl K.
From: Geoffrey Klempner
Subject: Do possible worlds account for our notion of possibility?
Date: 2 May 2012 13:43
Thank you for your email of 2 May with your University of London essay in response to the question, 'In order to understand what a possible world is, we have to first understand the notion of possibility. So, we cannot use possible worlds to explain possibility.' Discuss.
If you're interested, and still have time, you can look at the last chapter (18) of my book 'Naive Metaphysics' (downloadable from http://www.philosophypathways.com/download.html) which has some reflections on the similarity of Lewises indexical account of possibility/ actuality with the 'I-ness of I' and 'nowness of now'. More of that in a minute.
The notion of possible worlds only gets to do real philosophical work when we are looking at the truth conditions for subjunctive and counterfactual conditionals. This is what interested David Lewis. You could say something briefly about this.
It's only when we start defining similarity relations between possible worlds that the notion of possible world is doing real philosophical work, as opposed to merely being an interesting notational variant for box and diamond, or a 'model' for modal logic if you are into such things (I believe it was Kripke in an early paper on the semantics of modal logic who was responsible for resuscitating Leibniz's notion of possible worlds).
What is relevant to this question?
You allude to the debate between David Lewis who holds that S's counterpart exists in other possible worlds but not S, and Saul Kripke (see 'Naming and Necessity' -- I think that was the name you were fishing for) who holds that it is S, not S's counterpart who S thinks of when she considers 'what might have happened, if'.
You might think that you can't hold Kripke's view and still embrace Lewises strongly realist account of possible worlds. I'm not so sure. Kripke, in effect, gives a method for determining the 'essential properties' of an object. This is what we appeal to when we distinguish between 'rigid' and 'non-rigid' designators. However, we can perfectly well define a notion of 'transworld identity' using Lewises theory using the following definition:
S in w is transworld-identical to S' in w' if and only if S and S' have the same essential properties.
My interest in S', and S'' and S''' and so on is based on my interest in anyone who shares S's essential properties. That's just what I mean by 'S' in counterfactual situations.
OK, you say, S and S' are still 'different'! But the reply is that G today is in a sense 'different' from G yesterday. In response to someone who denied the logical coherence of personal identity over time -- i.e. someone who insists that the person you and I refer to as 'G' is merely a series of similar person-stages -- we can define a notion of identity as a class of person-stages which are *sufficiently* similar according to criterion C, whatever C may be. C turns out to be none other than the necessary and sufficient conditions for personal identity as held by a philosopher who DOES accept the coherence of the notion of personal identity over time.
Similarly, there may be no 'transworld identity' in the strict sense, but we can always define one, using a suitable criterion.
In other words, I don't think the issue between Lewis and Kripke over transworld identity is a big deal. It's a war of words. It is also a side-issue so far as the topic of this essay is concerned.
Put bluntly, the objection is that on Lewises view, there is no such thing as possibility. All so-called 'possible worlds' actually exist. The only difference is one of perspective (just as, the only difference between 'I' as used by you and 'I' as used by me is one of perspective, or, the only difference between 'now' uttered today and 'now' uttered yesterday is one of perspective).
Two things here. First, Lewis still owes us an account of why we 'take an interest' in other possible worlds. No explanation is needed why I take an interest in other subjects (S, David Lewis) and other times (yesterday, the day I was born). But what are other Lewis-style possible worlds to me?
What if I'd failed my Kant exam? Then today, G might be on some photography assignment somewhere and Pathways would never have existed. Why is that interesting? Because in some possible worlds (the ones most similar to the actual world, where G's counterpart fails the Kant exam) that's what actually happens. Thank God! (or, What a shame!).
The onus is on someone who accuses Lewis of not explaining the notion of possibility to come up with a reason why that explanation is not fully sufficient.
The other point is more 'metaphysical'. Why are we on this world? what makes this world so special? From Lewises standpoint, that's just like asking, 'Why am I, I?', or even more mind-bogglingly, 'Why is the time now?' I just am. It just is. There's nothing more to say.