Tuesday, November 20, 2012

Possible worlds and the definition of necessity

To: Chris M.
From: Geoffrey Klempner
Subject: Possible Worlds and the definition of necessity
Date: 20th November 2008 12:23

Dear Chris,

Thank you for your email of 11 November, with your University of London BA Logic essay ,written under examination conditions, in response to the question, ''A statement is necessary if it is true in every possible world, and possible if it's true in some possible world.' Discuss.'

This is a competent answer. The part I liked best -- although I would have liked to have seen this developed further -- is your suggestion that 'evolution and natural selection provided us with a capacity to calculate possible courses of actions, to plan. So to develop and deal with scenario is something very elemental, maybe primitive of our nature.' But more of that in a minute.

What is the question asking for? Is it asking for any comment you can think of relating to the quoted statement? what is the angle?

There are two main approaches I can think of, which would help to highlight this as a philosophical question requiring a response.

First, we already have a notion of contingent and necessary truth defined by logic. A statement is necessary if it is logically valid: in predicate calculus, if it is true in all 'models', or assignments of names to objects, predicates to value ranges/ sets etc; or, in propositional calculus, true for all truth value assignments. Any true statement which is not logically valid is contingent. Why ask for more?

One response is that there are statements we regard as necessarily true which are not logically true: for example, 'No surface can be red and green all over.' This of course raises the huge question whether, in fact, there are such non-logical 'necessary truths'.

Second, the question says, 'A statement is necessary' or 'a statement... is possible'. You interpret this as the claim that there are truths of the form, 'It is possible that P' or 'It is necessary that P'. In other words, statements about necessity or possibility have truth conditions.

To accept that statements of modality have truth conditions is to accept the initial premise of David Lewises argument for modal realism. The argument, in effect, is by elimination: no other hypothesis will adequately account for the truth conditions of modal statements, or, in particular, the truth conditions of counterfactual statements.

One philosopher who rejects the view that counterfactuals have truth conditions is J.L. Mackie, whose article, 'Counterfactuals and Causal Laws' Lewis criticises in his book, 'Counterfactuals', pp. 65-70.

Mention of counterfactuals gives another, very good reason why we should 'ask for more'. If counterfactual statements can have truth conditions, then the definition of contingent truth as 'true but not logically valid' is not much help in explaining what these conditions are, or how we determine whether they have been satisfied (two different questions, of course).

A major criticism (which you don't mention) of David Lewises theory is that it doesn't, in fact, explain possibility at all. There are no possible but non-actual worlds in Lewises metaphysics because all so-called possible worlds are actual (the term used is 'actualism'). The truth conditions of counterfactuals may have been accounted for, but what remains behind is our raw intuition that there is such a thing as 'the possible'.

How is this intuition to be explained? Your speculation regarding evolution goes some of the way. No statement about what 'is' the case can substitute for a statement about what is not the case but might (metaphysically rather than epistemically) be the case were things different from the way they actually are. The actual world we inhabit is hemmed in on all sides by possibilities, the things that might have been or might have happened. For example, the cyclist who narrowly missed me as I carelessly ran across the road, the successful career as a photojournalist which I might have enjoyed had not turned my interest towards philosophy (an unlikely claim, as anyone who knew me would attest).

The cup on my desk is fragile. It could possibly break if dropped on the floor. The possible breakage exists as a fact, yet it is not reducible merely to atomic structure. 'The broken cup non-exists alongside the existing non-broken cup,' is a nonsensical way of putting it. The possibility is real even though non-actual.

This points to something. Accounting for truth conditions is not necessarily the only thing we require of a theory of modality. If the price of giving truth conditions is reducing talk of Fs to talk of Gs which are not F (as in modal actualism) then maybe we are better off embracing the reality of Fs but rejecting the demand for an account of truth conditions.

As you can see, there are a number of directions in which this question could be pursued: what is non-logical necessity, why do we need truth conditions for modal statements, what does it mean to claim that possibility is a 'sui generis' notion. And so on.

In Chapter 18 of my 'Naive Metaphysics' I speculate that the question about the relation of possible worlds to the actual world is analogous to the question the relation of subjects of experience to I (the person speaking), and also to the relation between different times to now (the time at which this statement is made). In other words, the real problem concerns the metaphysics of indexical expressions -- another possible line to pursue.

All the best,

Geoffrey