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no X's are Y's,

some Z's are Y's ; ... some Z's are not X's.

А00 all X's are Y's, some Z's are not Y's; .. some Z's are not X's.

The nature of the moods of the second figure is clearly shewn in the following figures: Fig. 10.

Fig. 11. (Cesare.)


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It will also be observed that in the second figure the minor premise may be any of the four A, E, I, O.

The third figure only proves particulars (I or 0), and it always has an affirmative minor premise (A or I). It also contains the greatest number of moods, since in no case is the conclusion a weakened one.

The fourth figure is usually considered unnatural and comparatively useless, because the same arguments can be more clearly arranged in the form of the first figure, which in some respects it resembles. Thus it proves all the propositions except A, namely, E, I, O, and its first mood AAI, is in reality a weakened form of AAA in the first figure. Many logicians, including in recent times Sir W. Hamilton, have rejected the use of this figure altogether.

It is evident that the several figures of the syllogism possess different characters, and logicians have thought that each figure was best suited for certain special purposes. A German logician, Lambert, stated these purposes concisely as follows :-“The first figure is suited to. the discovery or proof of the properties of a thing; the second to the discovery or proof of the distinctions between things; the third to the discovery or proof of instances and exceptions; the fourth to the discovery, or exclusion, of the different species of genus."

It may be added that the moods Cesare and Camestres are often used in disproving a statement, because they give a universal negative conclusion, founded upon the exclusion of one class from another. Thus if any one were still to assert that light consists of material particles it might be met by the following syllogism: Material particles communicate impetus to

whatever they strike,
Light does not communicate impetus to

whatever it strikes ;
Therefore light is not material particles.”

The moods Baroko and Festino are less used, but allow of a particular conclusion being established.

When we wish however to establish objections or

exceptions to a general statement, which is indeed the natural way of meeting it, we employ the third figure. The statement that “all metals are solids” would at once be disproved by the exception mercury, as follows:

Mercury is not solid,

Mercury is a metal ;

Therefore some metal is not solid. Were any one to assert that what is incomprehensible cannot exist, we meet it at once with the argument that Infinity is incomprehensible, but that infinity certainly exists, because we cannot otherwise explain the nature of a curve line, or of a quantity varying continuously; therefore something that is incomprehensible exists.' In this case even one exception is sufficient entirely to negative the proposition, which really means that because a thing is incomprehensible it cannot exist. But if one incomprehensible thing does exist, others may also; and all authority is taken from the statement.

According to the Aristotelian system the third figure must also be employed whenever the middle term is a singular term, because in Aristotle's view of the subject a singular term could not stand as the predicate of a proposition.



OF THE SYLLOGISM. In order to facilitate the recollection of the nineteen valid and useful moods of the syllogism, logicians invented, at least six centuries ago, a most curious system of artificial words, combined into mnemonic verses, which may be

readily committed to memory. This device, however in. genious, is of a barbarous and wholly unscientific character; but a knowledge of its construction and use is still expected from the student of logic, and the verses are therefore given and explained below.

Barbara, Celarent, Darii, Ferioque, prioris;
Cesare, Camestres, Festino, Baroko, secundæ;
Tertia, Darapti, Disamis, Datisi, Felapton,
Bokardo, Ferison, habet ; Quarta insuper addit
Bramantip, Camenes, Dimaris, Fesapo, Fresison.

The words printed in ordinary type are real Latin words, signifying that four moods whose artificial names are Barbara, Celarent, Darii and Ferio, belong to the first figure; that four others belong to the second; six more to the third ; while the fourth figure moreover contains five moods. Each artificial name contains three vowels, which indicate the propositions forming a valid mood ; thus, C'ElarEnt signifies the mood of the first figure, which has E for a major premise, A for the minor, and E for the conclusion. The artificial words altogether contain exactly the series of combinations of vowels shown in p. 140, excepting those in brackets.

These mnemonic lines also contain indications of the mode in which each mood of the second, third and fourth figures can be proved by reduction to a corresponding mood of the first figure. Aristotle looked upon the first figure as a peculiarly evident and cogent form of argument, the Dictum de omni et nullo being directly applicable to it, and he therefore called it the Perfect Figure. The fourth figure was never recognised by him, and it is often called the Galenian figure, because the celebrated Galen is supposed to have discovered it. The second and third figures were known to Aristotle as the Imperfect Figures, which it was necessary to reduce to the first

figure by certain conversions and transpositions of the premises, for which directions are to be found in the artificial words. These directions are as follows:

s indicates that the proposition denoted by the preceding vowel is to be converted simply.

indicates that the proposition is to be converted per accidens, or by limitation.

m indicates that the premises of the syllogism art to be transposed, the major being made the minor of a new syllogism, and the old minor the new major. The m is derived from the Latin mutare, to change.

B, C, D, F, the initial consonants of the names, indicate the moods of the first figure, which are produced by reduction; thus Cesare, Camestres and Camenes are reducible to Celarent, Darapti, &c., to Darii, Fresison to Ferio and so on.

k denotes that the mood must be reduced or proved by a distinct process called Indirect reduction, or reductio ad impossibile, which will shortly be considered.

Let us now take some syllogism, say in Camestres, and follow the directions for reduction. Let the example be

All stars are self-luminous
All planets are not self-luminous....... (2)
Therefore no planets are stars....

(3) The first s in Camestres shows that we are to convert simply the minor premise. The m instructs us to change the order of the premises, and the final s to convert the conclusion simply. When all these changes are made we obtain No self-luminous bodies are planets.......Converse of (2) All stars are self-luminous Therefore no stars are planets...............Converse of (3)

This, it will be found, is a syllogism in Celarent, as might be known from the initial C in Camestres.

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