Abstracts of Comments W. V. Quine Noûs, Vol. 4, No. 1. (Feb., 1970), p. 12. Stable URL: http://links.jstor.org/sici?sici=0029-4624%28197002%294%3A1%3C12%3AAOC%3E2.0.CO%3B2-Q Noûs is currently published by Blackwell Publishing.
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3. Dummett, Michael, "Truth," Proceedings of the Aristoteliun Society, LIX (1958-9): 141-162. Reprinted in Philosophical Logic, ed. P. F. Strawson (Oxford University Press, 1967) : 49-68. 4. Jeffrey, Richard C., "On Indeterminate Conditionals," Philosophical Studies, XIV (April, 1963): 37-43. 5. Strawson, P. I?., Introduction to Logical Theory (London: Methuen, 1952). 6. Quine, W. V. O., Methods of Logic (New York: Holt, 1950). 7. von Wright, Georg Henrik, "On Conditionals," Logical Studies ( London: Routledge and Kegan Paul, 1957): 127-165.
ABSTRACTSOF COMMENTS A. by W. V. QUINE
Belnap connects three proposals: that the question of truth of a conditional assertion TA/Bl not arise for false A; that the universe be held open by universally quantifying only restrictedly (Geach, Peano) ; and that contraposition be abrogated to avoid Hempel's unblack nonraven paradox. This last, an unpublished proposal of P. K. Sen, appealed to me less than an alternative remedy, that of deeming complements of projectible predicates improjectible; but Belnap's link gives it new interest. TA/Bl is too poor for comfort when construed merely as a partial truth function. To enrich it Belnap makes it assert the same proposition as B when A is true (and none otherwise). So he must somehow cause meaning, or what proposition a sentence asserts, to depend on a factual truth A. He takes a proposition as any class of worlds, and a world as any class K of atomic sentences. (He says a world is a mapping w into {T, F}, but this is pointless; K =wK{T1.) The proposition asserted by a sentence S, then, would ordinarily contain each world K whose members, together with negations of other atomic sentences, logically imply S. Thus far, fact is no factor. However, fact can render r A / B l inassertive. Compounds containing r A / B l can then be so defined, in turn, as to assert different propositions according as r A / B l is assertive or not. Through this extraordinary channel, fact can determine whether S asserts one proposition or another. If this is the plan, the enrichment amounts in effect to adding a truth value.
