 In his discussion of the syllogism Valla does not refer to an important principle employed by Aristotle and his commentators: dici de omni et nullo (to be said/predicated about all and about none). To quote Peter of Spain’s Summulae logicales: “To be said of every [dici de omni] is when there is nothing to to be taken under the subject [nichil est sumere sub subiecto] of which the predicate may not be said, like ‘every man runs’: here, running is said of every man, and under man there is nothing to to be taken of which running is not said. To be said of none [de nullo] is when there is nothing to be taken under the subject from which the predicate may not be eliminated, like ‘no man runs’: here, running is eliminated from any man at all [quolibet homine]” (ed. L. M. de Rijk 1972, 43; ed. Copenhaver et al., 2014, 170). This principle led Aristotle to conclude that only four moods of the first figure were immediately valid. That Valla does not make use of this fundamental condition is understandable from his oratorical point of view, since it would be an uninteresting or even irrelevant criterion of validity. It is therefore not surprising that he thinks that we might as well “reduce” the first figure to the second rather than vice versa. Likewise, from his oratorical point of view, he can only treat the third figure of the syllogism with contempt: it is a “completely foolish” form of reasoning; no one reasons as follows: every man is a substance; every man is an animal; therefore, some animal is a substance. In a similar vein, he rejects the use of letters in the study of syllogisms (Repastinatio, 1:297–300; 2:546–548; DD 2:264–71).