Now it is only a limited number of conclusions which are true—their truth depends on the particular combinations of the premisses and figures which they accompany. The total figure thus represented may be called the universe of thought in respect to these four constituents, and out of the universe of possibly existing combinations it is the province of logic to select those which correspond to the results of our reasoning faculties. We can go over each of the premisses in each of the moods, and find out what conclusion logically follows. But this is done in the works on logic; most simply and clearly I believe in “Jevon’s Logic.” As we are only concerned with a formal presentation of the results we will make use of the mnemonic lines printed below, in which the words enclosed in brackets refer to the figures, and are not significative:— Barbara celarent Darii ferio_que_ [prioris]. Caesare Camestris Festino Baroko [secundae]. [Tertia] darapti disamis datisi felapton. Bokardo ferisson _habet_ [Quarta insuper addit]. Bramantip camenes dimaris ferapton fresison. In these lines each significative word has three vowels, the first vowel refers to the major premiss, and gives the mood of that premiss, “a” signifying, for instance, that the major mood is in mood _a_. The second vowel refers to the minor premiss, and gives its mood. The third vowel refers to the conclusion, and gives its mood. Thus (prioris)—of the first figure—the first mnemonic word is “barbara,” and this gives major premiss, mood A; minor premiss, mood A; conclusion, mood A. Accordingly in the first of our four cubes we mark the lowest left-hand front cube. To take another instance in the third figure “Tertia,” the word “ferisson” gives us major premiss mood E—_e.g._, no M is P, minor premiss mood I; some M is S, conclusion, mood O; some S is not P. The region to be marked then in the third representative cube is the one in the second wall to the right for the major premiss, the third wall from the front for the minor premiss, and the top layer for the conclusion. It is easily seen that in the diagram this cube is marked, and so with all the valid conclusions. The regions marked in the total region show which combinations of the four variables, major premiss, minor premiss, figure, and conclusion exist. That is to say, we objectify all possible conclusions, and build up an ideal manifold, containing all possible combinations of them with the premisses, and then out of this we eliminate all that do not satisfy the laws of logic. The residue is the syllogism, considered as a canon of reasoning.