Conjunction, potentiality, and disjunction

pp. 417-456

in: E. M. Barth, The logic of the articles in traditional philosophy, Berlin, Springer, 1974

Abstract

In his Topics, Cicero ascribes to the dialecticians — or logicians as we would say nowadays — a remarkable inference form. It is remarkable on account of the very special conceptual connection it reveals between conjunction and negation. Cicero, however, does not reject this inference form, which is found in the fourteenth chapter of the Topics. After having summed up a number of well-known inference forms like the modus ponens and the modus tollens he goes on to say: "Septimus [modus dialecticorum] autem: Non et hoc et illud; non autem hoc; illud igitur" (XIV. 57). In Hubbell's translation: "This and that are not both true; this is not, therefore that is' (1949/425).¹