The Logical Form of the Categorical Syllogism: Figures and Moods The FIGURE of a categorical syllogism consist of the arrangement of the terms in the premises. There are four (4) figure and each is defined by the position of the middle term in the syllogism. 1 st Figure M T t M ( sub-pre ) 2 nd Figure T M t M ( pre-pre ) 3 rd Figure M T M t (sub-sub) 4 th Figure T M M t (pre-sub)
The MOODS of the categorical syllogism consists of the disposition of the premises according to quality and quantity. There are sixteen (16) possible arrangements of the premises according to quality and quantity, but only the following are valid. Major Premise: A A A A E E I O Minor Premise: A E I O A I A A Note: Not all these moods are valid in every figure.
THE FIRST FIGURE . In the first figure, the middle term is the subject of the major premise and the predicate of the minor premise ( sub-pre ). Major Premise: A A E E Minor Premise: A I A I Conclusion: A I E O Rules for the 1 st figure: 1. The major premise must be universal (A or E). 2. The minor premise must be affirmative (A or I).
Exercise: Apply both the general rules and the special rules of the first figure to the following syllogism.
Every B is a C;
but no A is a B;
therefore no A is a C.
2. No Z is an X; but every Y is a Z; therefore no Y is an X.
3. Every cat is an animal; but no dog is a cat; therefore no dog is an animal. 4. Some people are difficult to get along with; but all Americans are people; therefore some Americans are difficult to get along with. 5. Some men are walking; but Peter is a man; therefore Peter is walking.
THE SECOND FIGURE . In the second figure, the middle term is the predicate of both the premises ( pre-pre ). Major Premise: A A E E Minor Premise: E O A I Conclusion: E O E O Rules for the 2 nd figure: 1. The major premise must be universal (A or E). 2. One premise must be negative.
Exercise: Apply both the general rules and the special rules of the second figure to the following syllogism.
Some metal floats on water;
but potassium floats on water;
therefore potassium is a metal.
2. Democratic governments protect freedom; but this government protects freedom; therefore this government is democratic.
3. Filipinos are generous; but Don Juan is not generous; therefore Don Juan is not a Filipino. 4. All mammals are viviparous; but some fish are viviparous; therefore some fish are mammals. 5. C is not B; but A is B; therefore A is not C.
THE THIRD FIGURE . In the third figure, the middle term is the subject of both the premises ( sub-sub ). Major Premise: A A E E I O Minor Premise: A I A I A A Conclusion: I I O O I O Rules for the 3 rd figure: 1. The minor premise must be affirmative (A or I). 2. The conclusion must be particular (I or O).
Exercise: Apply both the general rules and the special rules of the third figure to the following syllogism.
Potassium floats on water;
but potassium is a metal;
therefore some metal floats on water.
2. Some Inquisitors were cruel; but some Inquisitors were good men; therefore some good men were cruel.
3. Ebony does not float on water; but ebony is wood; therefore some wood does not float on water. 4. Socrates was a philosopher; but Socrates was a Greek; therefore some Greek was a philosopher. 5. Some men are silly; but every man is an animal; therefore some animal are silly.
THE FOURTH FIGURE . In the fourth figure, the middle term is the predicate of the major premise and the subject of the minor premise ( pre-sub ). Major Premise: A A E E I Minor Premise: A E A I A Conclusion: I E O O I Rules for the 4 th figure:
If the major premise is affirmative (A or I), the minor premise must be universal (Aor E).
2. If the minor premise is affirmative (A or I), the conclusion must be particular (I or O). 3. If a premise (and the conclusion) is negative (E or O), the major premise must be universal (A or E).
Exercise: Apply both the general rules and the special rules of the fourth figure to the following syllogism.
Every hound is a dog;
but every dog is an animal;
therefore some animal is a hound.
2. All men have free will; but some having free will are potential doers of evil; therefore some potential doers of evil are men.
3. No person under 18 years of age is a voter; but some voters are university students; therefore some university students are not under 18 years of age. 4. All voters are over 18 years of age ; but some who are 18 years of age are university students; therefore some university students are voters.
THE PERFECT FIGURE The first figure is considered as the perfect figure. 1. The principles underlying the categorical syllogism regulate syllogisms of the first figure most directly and most obviously. 2. Only the first figure can have a universal affirmative conclusion, which is the kind of conclusion with which science is principally concerned. 3. The first figure is the only figure in which the middle term gives, or at least can give, reason why what is signified by the major term belongs to what is signified by the minor term.
Example: A spiritual substance is immortal; but the human soul is a spiritual substance; therefore the human soul is immortal. In this syllogism, the middle term “spiritual substance” contains the reason why immortality belongs to human soul – it is that the human soul is a spiritual substance, and a spiritual substance, as such , must be immortal. For the enumerated reasons, therefore, the first figure is known to be the figure of scientific and philosophical demonstration.
Principles of the Categorical Syllogism: A PRINCIPLE is something that is at first and from which something else or becomes or is known. A PRINCIPLE of KNOWLEDGE is knowledge from which other knowledge flows or on which other knowledge somehow depends. A FIRST PRINCIPLE is not dependent on any other principle. A DERIVED PRINCIPLE is first in its own order but not absolutely. It is either a particularization of some broader principle, or a conclusion deduced from premises.
Principles on which the validity of the Categorical Syllogism depends: The PRINCIPLE of IDENTIFYING THIRD (for affirmative syllogisms) “Two things that are identical with the same third are identical with one another”. The PRINCIPLE of SEPARATING THIRD (for negative syllogisms) “Two theories, of which one is identical with the same third but the other is not, are not identical with one another”.
The PRINCIPLE of IDENTITY - “What is, is” or “Everything is what it is”. This principle is true of things as they are in themselves and independently of their being thought of. The PRINCIPLE of CONTRDICTION – “A thing cannot be and not be in the same respect” or “A thing cannot both have and not have the same attribute in the same respect”. This principle is purely logical principle because it is not applicable to things as they are in themselves but only to things insofar as they are known, or mentally reproduced.