Abstract

Beginning with the traditional rules for syllogistic validity, Bird leads the reader without further ado through Aristotle's method of reduction, Keynes' treatment of the antilogism, Lukasiewicz's axiomatization, Ivo Thomas's extension of the last to negative terms, and on to the treatment of empty terms via informal Boolean algebra and the introduction of singular terms. Lukasiewicz's axiom system is investigated in some detail, and independence and consistency are proved. The problem of existential import is discussed quite thoroughly, though it is doubtful that the last word is spoken here. Modalities come in for discussion, but their relation to syllogistic is hardly indicated. Not covered are quantificational analyses of syllogistic. The presentation is marred though not vitiated by various imprecisions in the metatheory. Symbolism is used from the start, and Venn diagrams are resorted to throughout.—J. B. B.