Important key notes on the Moods of Syllogism

Notion of the figure of syllogism alone is not adequate to determine the form of syllogistic arguments. Because both valid and invalid syllogistic forms may belong to the same figure. For example

(1) All men are mortal.

All kings are men.

Therefore, all kings are mortal.

And (2) some men are rich.

Some beggars are men.

Therefore, some beggars are rich.

Clearly, these two arguments belong to the first figure. Out of these two, the former is valid and the latter is invalid. Hence, just knowing the figure of a syllogism is not enough to know its form. Unless we know the form of a syllogism, we cannot decide its validity or invalidity. Therefore, in addition to the notion of figure, we also need the notion of “mood” of syllogism. These two notions taken together determine the form of a syllogism. In what follows we explain the notion of mood of a syllogism.

As we already know, a syllogism is called categorical if all its premises as well as the conclusion are all categorical propositions. Further, a categorical syllogism is put in its standard form if its major premise is stated first, the minor premise is stated after the major premise and finally the conclusion is stated.

The word “mood” in syllogistic logic is used in three different senses. Firstly, the mood of a syllogism is determined by the quality and quantity of the constituent premises. Since the quality and quantity of any premise is reflected by its logical form, the mood of a given syllogism is obtained by writing the logical form of each of the constituent premises.

Accordingly; the mood of the argument (1) given above is “AA”. This is so because the major and minor premises of the argument (1) are A-propositions. Similarly the mood of argument (2) given above is ‘II’.

As we know that a syllogism contains two premises and each of the premises can admit any one of the four possible forms (viz. A, E, I or O), so the total number of possible configurations on moods would be 4² = 4 x 4 = 16. This may be exhibited in tabular form as shown below.

A A	E A	I A	0 A
A E	E E	IE	0 E
A I	E I	II	0 I
A 0	E 0	10	0 0

The mood in this sense is also well-know as mood in the wide sense.

Since there are four figures, the total number of moods would be 64. We shall soon see that out of these sixty four moods only nineteen moods are valid. These are as follows

Figure	Valid moods
First Figure	A A, E A, A I and E I
Second Figure	E A, A E, A I and A 0
Third Figure	A A, I A, A I, E A, 0 A, and EI
Fourth Figure	A A, A E, I A, E A and EI

We may note that out of these nineteen valid moods, the mood “E A” and “E Fare valid in all figures.

Definition of Mood (in the second sense)

The mood of a syllogism is determined by the quality and quantity of the constituent propositions. In other words, the mood of a syllogism is obtained by specifying the logical forms of each of the constituent propositions. Unlike the first sense, here we have to consider the logical form of conclusion in addition to the logical forms of the premises.

For example, in this sense the mood of the syllogism of argument (1) given above is “AAA”. Similarly, the mood of argument (2) is “III”. Here the first, second and third vowel respectively represents the logical form of major premise, minor premise and the conclusion. Since a syllogism consists of three propositions and each of these propositions admits any one of the four possible logical forms, the total number of possible moods would be 4³ = 4 x 4 x 4 = 64. This may be shown as given below.

AAA	E A A	I A A	0 A A
A A E	E A E	I AE	0 A E
A A I	E A I	I A I	0 A I
A A 0	E A 0	I A 0	0 A 0
A E A	E E A	IE A	0 E A
A E E	E E E	IE E	0 E E
A E I	E E I	IE I	0 E I
A E 0	E E 0	I E 0	0 E 0
A I A	E I A	II A	0 I A
A IE	E IE	HE	0 IE
All	E 11	III	0 II
A 10	E 10	110	0 10
A 0 A	E 0 A	I 0 A	0 0 A
A 0 E	E 0 E	I 0 E	OOE
A 0 I	E 0 I	10 I	0 0 I
A 0 0	E 0 0	10 0	0 0 0

Since there are four figures, the total number of moods in all would be 64 x 4 = 256. The mood in this sense is called mood in the wider sense. In this sense, there will be twenty four valid moods. These are as follows:

Figure	Valid moods
First figure	A A A, A A I, E AE, E AO, A II, EIO
Second figure	E A E, E A 0, A E E, AE 0, E I 0, A 0 0
Third figure	A A I, I A I, All, EA0,0 A0,EI0
Fourth figure	A A I, A EE, A E 0,1 A I, E AO, EIO

It may be noted that the moods “E A O” and “EIO” are valid in every figure.

Definition of mood (in the third sense)

The word “mood” is used in the sense of valid moods of syllogism. For example, the syllogistic argument (2) as given in this section has the configuration “II” (understanding mood in the wide sense) or III (understanding mood in the wider sense). Since neither of them is valid, they are not moods in the third sense. This sense of mood is mood in the narrow sense.

We note that the division of three senses of mood (viz wider, wide and narrow) is dependent on the admission of the total number of moods in all the four figures. Since the total number of moods in the second sense is the highest (i.e. 256) it is called mood in the wider sense. Similarly, the total number of moods in the first sense is sixty four. So it is called mood in the wide sense. Finally the mood in the third sense is called mood in the narrow sense as the total number of moods in all figures is the lowest.

Representation of form of syllogism

The form of categorical syllogism is determined by its figure and mood. For example, consider the following syllogistic argument.

All M is P.

Some S is M.

Therefore, some S is P.

Clearly this syllogism belongs to first figure and its mood is “A II”. Thus the form of the above syllogism is described by the expression “A II – 1″. Where the first and second vowels denote the major and minor premise and the third vowel denotes the conclusion. Further,” 1″ denotes first figure. Similarly in case of “A II – 2”, “2” denotes second figure and so on. In what follows we discuss testing of moods in the first sense.