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HUME, THE CAUSAL PRINCIPLE, AN'D KEMP SMITH When we say of a proposition that it is possible, we sometimes mean no more than that it is logically possible, that is, consistent with itself. A proposition can be possible in stronger senses than this, but not in any weaker one. For a sense of "p is possible" that did not entail "p is self-consistent , "would have to be a sense of "p is possible" which was consistent with "p is self-inconsistent" And it is obvious that there can be no such sense as that. One of the stronger senses in which a proposition can be possible is this: consistent (with itself and in addition) with every observation-statement. (I mean by an observationstatement , a proposition which, if it were true, could in principle be discovered by experience to be true.) If a proposition ? is contingent, (that is, neither necessarily true ??t necessarily false), then its negation (its contradictory) not-p is contingent too; and since contingent, not necessarily false; and since not necessarily false, consistent with itself. So, given any contingent propositions, its falsity is among those propositions which are possible in the first and weak sense mentioned above. If a proposition ? is not only contingent but unverifiable ,(that is, not deducible from any observation- statement) , then not-p is consistent both with itself and with every observation -statement. So, given any unverifiable contingent proposition , its falsity is among those propositions which are possible in the second and stronger sense mentioned above. Some stock examples. "Whatever is a raven is black" is contingent, and its falsity therefore possible in the first sense; so too is its contradictory "There are such things as non-black ravens" contingent, and its falsity possible in the first sense. But the latter proposition is not unverifiable , since there are observation-statements from which it is deducible . ("There are such things as green ravens", for example; or "A green raven was in captivity at Taronga Park Zoo in January 31st 1975".) The former proposition, on the other hand, is not only contingent but unverifiable; since there are no observation -statements from which it is deducible. Hence, "whatever is a raven is black" is a proposition the falsity of which is possible both in the first and in the second sense noticed above . A third and still stronger sense in which a proposition can be possible is the following: ? is possible if and only if (p is consistent with itself ,every observation-statement is consistent with p, and in addition) ? is neither more nor less probable in relation to the conjunction of e and n, where e is any observation-statement and ? any necessary truth, than it is in relation to ? alone. The last condition may be expressed, symbolically, as "P(p/n.e) » P(p/n) for all necessarily true ? and all observation-statements e"; or in Carnap' s phrase as, "every observation- statement is initially irrelevant to p." Some examples will quickly make the idea of initial irrelevance, and its opposite, more familiar; and hence will make the third sense of "p is possible" more familiar. Let ? be any necessary truth and e any observation-statement. Now let ? be, for- example,some necessarily false proposition; then, since P(p/n) « o = P(p/n.e), e is initially irrelevant to p. Or let ? be necessarily true; then, since P(p/n) ¦ 1 = P(p/n.e), e is again initially irrelevant to p. Again, let ? be "Whatever is a raven is black": then some observation- statements e are initially relevant to p. For if e is "This raven is black," for example, P(p/n.e)>P(p/n) ; or at any rate, that is what we think if we are not inductive sceptic?. Again, if ? is "The Holy Ghost proceeds from the Father and the Son", it is at least very plausible to say that every observational e is initially irrelevant to p; since there appears to be no observational e such that P(p/n.e)>P(p/n) , or P(p/n.e)


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