Clement reaffirmed the infallibility of the pope, in matters of fact (1705), and, in 1713, issued the bull Unigenitus, condemning ioi Jansenistic propositions extracted from the Moral Reflections of Pasquier Quesnel.
Thus, 1 - x would represent the operation of selecting all things in the world except horned things, that is, all not horned things, and (1 - x) (1 - y) would give us all things neither horned nor sheep. By the use of such symbols propositions could be reduced to the form of equations, and the syllogistic conclusion from two premises was obtained by eliminating the middle term according to ordinary algebraic rules.
They are excellent principles of the highest value, but they are in no sense the necessary premisses which must be proved before any other propositions of cardinal numbers can be established.
When once the fixed conditions which any hypothetical group of entities are to satisfy have been precisely formulated, the deduction of the further propositions, which also will hold respecting them, can proceed in complete independence of the question as to whether or no any such group of entities can be found in the world of phenomena.
Innocent, like his predecessor, hated heresy, and in the bull Summis desiderantes (5th of December 1484) he instigated very severe measures against magicians and witches in Germany; he prohibited (1486) on pain of excommunication the reading of the propositions of Pico della Mirandola; he appointed (1487) T.