Studies and Exercises in Formal Logic

by John Neville Keynes

	All P is M,	⟍ ⟋	All M is S,
	All M is S,	⟋ ⟍	All P is M,
therefore,	Some S is P.	therefore,	All P is S,
		therefore,	Some S is P.

[³⁴⁴] See the last preceding [note].

[³⁴⁵] Compare, however, Hamilton, Logic, I. p. 264, and Spalding, Logic, pp. 230, 1.

m indicates that in reduction the premisses have to be transposed (metathesis praemissarum); as just shewn in the case of Bramantip, and also in the case of Camestres.

c signifies that the mood is to be reduced indirectly (i.e., by 322 reductio per impossibile in the manner shewn in the preceding [section]); and the position of the letter indicates that in this process of indirect reduction the first step is to omit the premiss preceding it, i.e., the other premiss is to be combined with the contradictory of the conclusion (conversio syllogismi, or ductio per contradictoriam propositionem sive per impossibile), The letter c is by some writers replaced by k, Baroko and Bokardo being given as the mnemonics, instead of Baroco and Bocardo.

The following lines are sometimes added to the verses given above, in order to meet the case of the subaltern moods:—

Quinque Subalterni, totidem Generalibus orti,
Nomen habent nullum, nec, si bene colligis, usum.[346]

[³⁴⁶] The mnemonics have been written in various forms. Those given above are from Aldrich, and they are the ones that are in general use in England. Wallis in his Institutio Logicae (1687) gives for the fourth figure, Balani, Cadere, Digami, Fegano, Fedibo. P. van Musschenbroek in his Institutiones Logicae (1748) gives Barbari, Calentes, Dibatis, Fespamo, Fresisom. This variety of forms for the moods of figure 4 is no doubt due to the fact that the recognition of this figure at all was quite exceptional until comparatively recently. Compare sections [262], [263].

According to Ueberweg (Logic, § 118) the mnemonics run,—

Barbara, Celarent primae, Darii Ferioque.
Cesare, Camestres, Festino, Baroco secundae.
Tertia grande sonans recitat Darapti, Felapton,
Disamis, Datisi, Bocardo, Ferison. Quartae
Sunt Bamalip, Calemes, Dimatis, Fesapo, Fresison.