ABSTRACT
Of course we might well have stopped with possible worlds as primitive, as most authors do.46 Two justifications (at least) can be given for this. The first is that we are doing logic (or philosophy of language) and therefore should not wish to prejudge the metaphysical issue by dogmatizing on the nature ofthe entities we assume. This is the attitude which, taken to extremes, results in the so-called 'truth-value' semantics47 in which truth-values are assigned directly to formulae without the trouble of having domains of values, and possible worlds are thought of as (certain kinds of) sets of formulae. This is thought to 'free' the logician from any possibly embarrassing 'ontological commitment' (as if there were a virtue in not having to believe in the existence of anything but languages). One reason for the title of this chapter is to make it clear to those who have a more sure idea than I about just what ought to be the logician's business that I am quite happy to regard myself in this chapter as doing not logic but meta-
This illustration is of course a materialistic one, though the general theory is not in that B may contain, if there are such things, nonmaterial basic particular situations. But no harm is lost in restricting ourselves for the moment to the case where B is the set of all spacetime points, since it seems plausible to suppose that there are at least as many possible worlds as there are sets of space-time points. I lay some stress on the possibility of such a materialistic analysis ofB since one important problem in the philosophy oflanguage is how to reconcile the idea that one can give a complete physical description of the world with the idea that not everything we say can be analysed in purely physical terms. What I have to say in this chapter and in Chapter Seven is intended to contribute to a solution to this problem. There is also some point to a materialistic illustration since those philosophers who are prepared to accept points of space, together with some set theory, will find that they can help themselves to all the entities required for a highly intensional theory of meaning without needing to lose the least sleep. 52
This is the intuitively inconvenient consequence of our earlier definition, since there are many cases in which we are not happy to
Consider two examples. In most propositional logics, if t:J. is a sentence and ~ E ..11 then a and <~, <~, a» are, under any assignment, the same proposition. I.e., a and <~,( ..... "a» are true in precisely the same set of worlds. This is because the meaning rule for ~ has the consequence that for any sentence t:J. and world w, V(a) is true in w (w E V(a)) iffV«~,a») is false in w (w ¢ V( <~,a) )). With this rule it is easy to see that for any a and any w, V( <~, <~,a») is true in w iffV(t:J.) is true in w, i.e., V(a) = V«~,<~,a»). So what we do if we want to avoid a replacement rule for tautologous equivalents,55 is require that it is only in the set C of classical worlds that the ordinary truth-table rule for ~ holds. I.e., ifw E C then w E V«~,a») iffw ¢ V(t:J.). Since we say nothing about what happens when w ¢ C it follows that although V(a) n C = V«",,<~,a») n C we need not have V(a) = V«~, <~,a»).
