To: Alistair L.
From: Geoffrey Klempner
Subject: Necessity, possibility and possible worlds
Date: 6th May 2009 10:11

Dear Alistair,

Thank you for your email of 29 April, with your timed examination essay in response to the University of London Logic question, 'A statement is necessary if it is true in every possible world, and possible if it's true in some possible world.' Discuss.

The topic of this question is the semantic interpretation of modal logic. The pioneer in is Saul Kripke (in an early paper, 'Semantical considerations on modal logic'), a name conspicuous by its absence in your essay. In considering the vexed question of trans-world identity, you do talk briefly about the question whether individuals have 'essences' which would enable us to identify the 'same individual' in another possible world. However, you could have said more here. The notion that things have essences which determine the criteria for their identity over time is an Aristotelian idea which fell somewhat into disrepute amongst analytical philosophers, before being famously resurrected in Kripke's seminal paper, 'Naming and Necessity'.

To your credit, you also mention Lewises point about identity over time, as a way of easing our intuitions over the theory of counterparts. However, this observation is available as much (if not more so) to the Aristotelian/ Kripkean. It is very plausible to argue (following David Wiggins' influential account of identity in his book 'Sameness and Substance') that our notion of 'identity under a covering sortal concept' (e.g. 'same man') can be extended across worlds. This effectively is what Kripke does, in identifying the essence of an individual with his/ her origin (a given event of conception).

To get back to the main question: why do we need a semantic interpretation of modal logic? A point you could have made here is that consistency and completeness proofs play an important part in the development of logical systems. For this purpose, a semantic interpretation is essential. We can just employ possible worlds as a technical device; we don't have to go too far into the question of what possible worlds really are. But the latter question is inevitable if we are approaching modal logic as philosophers. We want to know what it means to say that such-and-such is 'possible'. Is there a notion of metaphysical possibility distinct from epistemic possibility? What do we mean when we state that it might (metaphysically) have been the case that P?

What are possible worlds? You credit Lewis with avoiding the 'circularity' of defining possibility in terms of 'possible' worlds, on the grounds that for Lewis possible worlds are indeed 'real'. But if they are real, where are they? It is not enough to say that possible worlds are real but 'not actual': Lewises idea is that actuality is relative to a space and time; so other possible worlds are in spaces and times unconnected with our space and time. In other words, actuality is a matter of local perspective. That's a pretty mind-boggling idea.

Lewis puts forward his account of possible worlds as a solution to the problem specifically of providing truth conditions for counterfactual statements (rather than the general need for a semantics for modal logic), and claims that an argue in favour of his approach is the inadequacy of alternative accounts. Well, maybe there just isn't a coherent truth-conditional analysis of counterfactual statements, because they just don't *have* truth conditions.

If we baulk at Lewises 'real' possible worlds, and consider another idea that you mention, that possible worlds are in some sense constructions -- e.g. sets of propositions or sentences -- the question arises whether the construction will do the work it is intended to do. The problem with sets of sentences, defined as linguistic entities, is that it is impossible in principle to give an exhaustive description of the world. Reality is not just infinite but non-denumerably infinite (e.g. the points on a line cannot be counted).

Another point -- which counts both against Lewis and the constructivist approach -- is that in both cases the special sense of 'possible' as contrasted with 'actual' has been lost. When I state something that might have been the case, I don't intend to describe something that is the case (somewhere else, or in a construction which I have created). Possible world semantics set out in these terms arguably loses the very thing we were aiming for: an understanding of what it is for an individual, or a truth, to be possible but not actual.

The impression I gained from your essay as a whole was that it was a reasonably good response to the question, although there were points which could, perhaps should have been covered -- which would gain more marks. As it stands, I would give this a mark in the lower 60's.

All the best,

Geoffrey