Rosser Barkley. On the many-valued logics. American journal of physics, vol. 9 (1941), pp. 207–212.

ing confusions, and in undertaking this Ducasse is on sound ground. On the other hand the a t tempt to introduce the word probabili ty in a new sense, contrary to the established mathematical usage, and based on another and different refinement of the loose usage of ordinary discourse, seems to the reviewer unfortunate and likely only to lead to confusion. Ducasse may himself be guilty of such confusion in comparing his own ideas about probability with those of Keynes and Eaton without inquiring whether the word is being used in the same sense. Ducasse further introduces what he calls an expansion of the t radi t ional notion of prepositional quant i ty , considering such premisses as "75 per cent of Romans are handsome," and allowing a different propositional quant i ty for each possible percentage. This numerical quantification is distinguished from the numerical measure of inclination t o believe, and such inferences are considered as the following: "75 per cent inclination to believe 100 per cent of Romans handsome, and 100 per cent inclination to believe Socrates Roman, together validate 75 per cent inclination to believe Socrates handsome"; "75 per cent of Romans are handsome, Socrates is a Roman, therefore probably (in degree 75 per cent) Socrages is handsome."—In this development Ducasse is closely ant icipated by Lambert (82, vol. 2) who employs a similar numerical quantification of the subject (and, less convincingly, a sort of intensional numerical quantification of the predicate) and, in terms of probability ra ther than degree of inclination to believe, deals with similar inferences and others more complicated, and elaborates the theory of such quasi-syllogistic inference in considerable detail . ALONZO C H U R C H