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Should possibility be analysed in terms of possible worlds?


To: Alistair L.
From: Geoffrey Klempner
Subject: Should possibility be analysed in terms of possible worlds?
Date: 25th February 2009 12:41

Dear Alistair,

Thank you for your email of 16 February, with your essay for the University of London Logic module, in response to the question, ''We use the notion of 'possibility' to assess claims about this world, not about some other possible world.' Discuss.'

In response to your request to suggest further topics in Logic, my advice would be to pick topics that grip you -- but also topics that you feel you can *do* given the time constraints -- without worrying too much about second-guessing what might or might not come up in an exam. You have done well so far. Unfortunately (or fortunately!) I don't have any access to the examiners' deliberations on this matter.

Look at the responses you have received to your essays. Do they raise questions which prompt further research? Look to fill in gaps in your knowledge which enhance what you have covered already, as well as extending the coverage further. If you are careful in this, you will find that you have plenty to fill the remaining time you have available for exam preparation.

This is a well-written essay, which would be a good answer to a general question like, 'Discuss some of the problems and issues around the use of possible worlds in the semantics for modal logic.'

As an answer to the question, 'We use the notion of possibility to assess claims about this world...', you do say things which are relevant -- for example, raising the question of transworld identity for individuals and contrasting Lewis's counterpart theory with Kripke's theory of rigid designators -- however, you don't say enough to 'cap the point'.

For example: is Kripke's view of possible worlds preferable (as Kripke indeed claims in 'Naming and Necessity') on the grounds that, e.g. when I consider what might have happened to me or what I might have done, my concern is with the actual GK, and not some counterpart of GK resembling me in this or that respect?

I find this a very difficult claim to assess, because it is difficult to see what hangs on the question. I don't find Kripke's explanation of the difference between 'essential' and 'accidental' attributes very convincing. But, even if we accept the account, why can't Lewis simply take the explanation of the difference between 'accidental' and 'essential' properties and use it as one of the bases for judging whether a given possible world is sufficiently 'similar' to the actual world in the respects that interest the person asking the question?

However, having said that, I don't think that the dispute between Kripke and Lewis is the main issue here. Lewis has been criticized for giving an account of possibility which, in effect, reduces possibility to actuality. Other possible worlds (you don't quite make this clear) are as 'real' as the actual world. What makes the world actual is merely a fact of local perspective (the same kind of fact that makes GK 'me', or from your point of view makes AL 'me'). Every other possible world is 'actual' to the inhabitants of that particular world.

What the question raises, is the issue whether 'how things are in other possible worlds' is what we really what we are concerned with when we make statements about possibilities. The question is not about the utility of possible worlds as simply a device of logic, but rather about the claim that reference to other possible worlds is an ineradicable aspect of human discourse concerning the actual world.

Consider, for example, the statement that this ladder is reliable. It is possible to climb up the ladder safely, or, better still, it is not possible that the ladder will break when you have climbed it. What you are describing is a property of the actual ladder. Actual things possess powers and potentialities (in something like an Aristotelian sense). This is a primitive fact about the world, or, equivalently, a primitive fact about the way our conceptual scheme classifies objects not only in terms of observable properties, but also in terms of dispositions which can be tested by performing experiments.

So far so good. However, the argument on the other side would be that we *do* dwell on 'how things might have been'. If I had stuck with my original National Lottery numbers I would now be sunbathing in my Greek villa. I am not describing a mere fantasy or mental image of sunbathing in Greece. My feelings of remorse have an object which is not just a mental entity but something 'real'.

I am not sure how to respond to this point. Perhaps the least that can be said is, as you state at one point in your essay, that the notion of possibility is sui generis, not reducible to any other notion. The assertion that possibility is sui generis counts against Lewis's view that all possible worlds are actual (to the inhabitants of the relevant worlds), but also (and with the same force) counts against the view that statements about possibility merely concern 'claims about this world'.

All the best,