All (or some) S are M. Barbara, Darii. All (or some) S are P.
All matter gravitates.
All (or some) air is matter. All (or some) air gravitates No M is P. Celarent All (or some) S is M. and No S is P; some S is not P. Feria.
No matter is destructible.
All (or some) air is matter.
No air is destructible; some air is not destructible.
The general scheme of the 2d figure is: P is 31. S is M S is P.
There are four syllogisms in all, which we may take in pairs thus: No P is M. Cesare All (or some) S are M. and No S is P; some S are not P. Festino.
"No destructible thing is matter," etc., as in the last form.
All P is M. Camestres • No S is M; some S is not 31. and No S is P; some S is not P. Baroko In this figure there is a certain distortion of the previous or regular figure. In the first of the two pairs, the major is, No P is 31, instead of the equivalent (1st figure), No M is P. In the first form of the second pair, the minor is, No S is M, instead of the equivalent, No 31 is S, which should be the major to be regular; the amended premises would then give, in conclusion, No P is S, equal to No S is P.
All matter is extended.
No mind is extended. Camestres.
No mind is matter.
The last form, with a particular conclusion, is exemplified thus: All matter is extended.
Some things are not extended.
Some things are not matter.
Phis is a form technically called Baroko, which is one of two that are especially difficult ,o reduce to the standard forms.
This figure proves only negatives.
The scheme of premises in the 3d figure is M. P.
M. S.
Six varieties of syllogism come under this figure; we may arrange them in three pairs, the first two pairs having the same major, and the third the same minor: All M is P. Darapti All (or some) 31 is S. and Some S is P. Datisi.
All planets move.
All (or some) planets are heavenly bodies.
Some heavenly bodies move.
No 31 is P. Felapton All (or some) 31 is S. and Some S is not P. Ferison.
• No solid body is perfectly transparent. All solid bodies gravitate.
Some gravitating things are not perfectly transparent.
Some 31 is P; some 31 is not P. .Disamis
All M is S.and Some S is P; some S is not P. Bokardo.
The first of the two is merely a standard syllogism (Darii), with transposed premises; the second (Bokardo) is more complicated, as in the example: Some men are not fit to rule.
But all men are liable to have dominion.
Some men, liable to have dominion, are not fit to rule.
In the 4th, figure, P is 31, 31 is S, there are five syllogisms. The mere forms are enough to quote: All.P are 31.
All M are S. Bramantip.
Some S are P. All P are M. No M is S. Camenes.
No S is P. Some P are 31.
All M are S. Dimaris.
Some S are P.
• No P is M. • All 31 are S. Fesapo.
Some S are not P.
No P is 31. • Some 31 are S. Fresison.
Some S are not P. ) The reasons why these syllogisms are true, and why no other of 256 possible com binations of propositions can give true conclusions, are certain laws, called the rules of the syllogism, which repose on first principles of the highest certainty.
Mr. ,Mill has laid down the following fundamental axioms of the syllogism, as stated in its standard forms in the first figure. (1.) "Attributes coinciding with the same attribute, coincide with one another." N, the middle term, coincides with P, the predi cate; S, the subject, coincides with M; therefore 'S and P coincide with one another. (2.) " Any attribute incompatible with a second attribute, is incompatible with whatever that second attribute coincides with." No M is P; M is incompatible with P; but S coincides with AI, and therefore it also is incompatible with P.
All the syllogisms of the last three tieures are reducible to the first, by conversion of prop; sitions and transposition of premises, according to the nature of the case. The symbolic name of each syllogism contains instruction for this process, as well as stating the composition of the syllogism. To aid the memory, these symbols are put together in five Latin hexameter verses of very ancient but unknown origin: " Barbara, Celarent, Darii, Ferioque prioris.