chapter  4
8 Pages

Chance

But why must a single property meet these three conditions? One reason for (i) we have seen already: it lets 'ch(P)= I' express the necessity that a sufficient cause must give its effects [3. I]. More generally, it lets eh(P) 'measure a contingent and quantitative ... possibility' [2. I], namely a possibility that P is a fact. For, obviously, the lower limit of this possibility is that P is impossible. But just as nothing that is necessary can fail to exist 44

Chance

[3.1], so nothing can exist that is impossible. Thus for ch(P)=O, ch(P),s lowest value, to make P impossible, it must entail -Po Similarly, for ch(P)=1 to entail the upper limit of P's possibility, i.e. make P necessary, it must entail P. That is obvious, as it is why ch(P) must also satisfy (iii), so that frequencies of P*s can be measures of this possibility of P [3.4].