Barbara. Celarent. obv. All M is P; -----------------------> No M is p (not-P); All S is M: -----------------------> All S is M: obv. ∴ All S is P. <------------------- ∴ No S is p (not-P). There is, then, only one fundamental syllogism. § 7. A new version of the mnemonic lines was suggested in _Mind_ No. 27, with the object of (1) freeing them from all meaningless letters, (2) showing by the name of each Mood the Figure to which it belongs, (3) giving names to indicate the ostensive reduction of Baroco and Bocardo. To obtain the first two objects, _l_ is used as the mark of Fig. I., _n_ of Fig II., _r_ of Fig. III., _t_ of Fig. IV. The verses (to be scanned discreetly) are as follows: Balala, Celalel, Dalii, Felioque prioris: {Faksnoko} Cesane, Camenes, Fesinon, { } secundæ: { Banoco,} Tertia, Darapri, Drisamis, Darisi, Ferapro, Doksamrosk} }, Ferisor habet: Quarta insuper addit. Bocaro } Bamatip, Cametes, Dimatis, Fesapto, Fesistot. De Morgan praised the old verses as "more full of meaning than any others that ever were made"; and in defence of the above alteration it may be said that they now deserve that praise still more. § 8. Indirect reduction is the process of proving a Mood to be valid by showing that the supposition of its invalidity involves a contradiction. Take Baroco, and (since the doubt as to its validity is concerned not with the truth of the premises, but with their relation to the conclusion) assume the premises to be true. Then, if the conclusion be false, its contradictory is true. The conclusion being in O., its contradictory will be in A. Substituting this A. for the minor premise of Baroco, we have the premises of a syllogism in Barbara, which will be found to give a conclusion in A., contradictory of the original minor premise; thus: Baroco. Barbara. All P is M; -----------------> All P is M; Some S is not M: <-----\ /-----> All S is P: \ / contradictory \/ /\ contradictory / \ ∴ Some S is not P ------/ \------ ∴ All S is M. But the original minor premise, _Some S is not M_, is true by hypothesis; and therefore the conclusion of Barbara, _All S is M_, is false. This falsity cannot, however, be due to the form of Barbara, which we know to be valid; nor to the major premise, which, being taken from Baroco, is true by hypothesis: it must, therefore, lie in the minor premise of Barbara, _All S is P_; and since this is contradictory of the conclusion of Baroco _Some S is not P_, that conclusion was true.