1. THE FOUR FIGURES OF THE SYLLOGISM.

By a figure of a syllogism is meant some particular arrangement of the three terms in the two premises. The conclusion is eliminated from this discussion, because in it the arrangement of the terms is constant, the major term always being used as the predicate of the conclusion and the minor as the subject. Using the symbols M, G and S, we find that there are four possible arrangements and, therefore, but four figures. These may be represented as follows:

First figure	Second figure	Third figure	Fourth figure
M — G	G — M	M — G	G — M
S — M	S — M	M — S	M — S
S — G	S — G	S — G	S — G

No matter what the syllogism, if it is to be proved “logical,” it should be made to fit one of the four figure-types. To be sure, it may fit the figure without being logical, but it cannot be strictly logical without fitting the figure. The following valid syllogisms conform to the four figures as will be seen by the symbolized terms:

First figure: All M
men are G
mortal,

S
Socrates is a M
man,

∴ S
Socrates is G
mortal.

M — G

S — M

S — G

Second figure: All G
good citizens love their M
country,

No S
criminal loves his M
country,

∴ No S
criminal is a G
good citizen.

G — M

S — M

S — G

Third figure: All M
good citizens are G
law abiding,

All M
good citizens S
vote,

∴ Some who S
vote are G
law abiding.

M — G

M — S

S — G

Fourth figure: Some G
teachers are M
fair minded,

All who are M
fair minded are S
just,

∴ Some S
just persons are G
teachers.

G — M

M — S

S — G

Here, then, are the types that represent all the syllogisms which mediate inference may use. Logic recognizes no other. Since every successful student of logic must be familiar with the four figures, the following may be used as a suggestive aid to reproducing the figures at will:

First. It is easy for any one to remember this syllogism:

All men are mortal,

Socrates is a man,

∴ Socrates is mortal.

In fact, it comes down to us from the time of Aristotle, and is therefore a patriot of many generations to whom the faithful should touch their hats. Let us, then, be ready to reproduce this syllogism with automatic precision, since it will enable us to know at once the position of the terms in the first figure. Second. Converting the terms of the major premise of the first figure gives the second figure, as, e. g.:

First figure.		Second figure.
M — G	(Convert)	G — M
S — M		S — M
S — G		S — G

Third. Converting the terms of the minor premise of the first figure gives the third figure, as, e. g.:

First figure.		Third figure.
M — G		M — G
S — M	(Convert)	M — S
S — G		S — M

Fourth. Converting the terms of both the major and minor premises of the first figure gives the fourth, as, e. g.:

First figure.		Fourth figure.
M — G	(Convert)	G — M
S — M	(Convert)	M — S
S — G		S — G

To summarize: The second, third and fourth figures may be derived from the first. Converting the major premise of the first figure gives the second figure; converting the minor premise gives the third figure; and converting both premises gives the fourth figure.