The categorical syllogism is the principal form of deductive interference. Its absolute manner of inferring when applied to certain premises is the kind most suited for imparting scientific and philosophical knowledge.
We may describe the Categorical Syllogism as a form of mental discourse wherein two concepts are compared to a third ‘middle concept’, and from the agreement of both with the middle concept, the mind infers agreement of both concepts among themselves; whereas, from the agreement of one with the middle concept and the disagreement of the other with the middle concept, the mind infers the disagreement of the two concepts among themselves. E.g.:
Intellectual beings are progressive.
But, brutes are not progressive;
Therefore brutes are not intellectual beings.
STEPS OF CATEGORICAL SYLLOGISM
The mind takes several steps when making a categorical syllogism.
1. Apprehension or knowledge of three concepts.
2. Comparison of two of them with one of them, as a middle concept.
3. Perception of the agreement of the two concepts with the middle concept, and of the disagreement of other with it; and the pronouncement of the aforesaid in the manner of two propositional premises.
4. Perception and pronouncement of the agreement of the two concepts among themselves in the first case; or of the disagreement of the two concepts among themselves in the latter case, by way of interference.
TERMS IN CATEGORICAL SYLLOGISM
The categorical syllogism has three terms:
1. Major Term
Major Term is the predicate of the conclusion. The major term must occur in the conclusion and in one of the premises, generally the first, which is therefore called the MAJOR PREMISE. We shall designate the major term by P, or, to display the structure of a syllogism more graphically, by a rectangle. ().
2. Minor Term
The minor term is the subject of the conclusion. The minor term must occur in the conclusion and in the premise in which the major term does not occur. This MINOR PREMISE is often introduced by the adversative conjunction ‘but’ (because in controversy it introduces a turn of thought contrary to the expectations of an opponent). We shall designate the minor term by S, or, to display the structure of a syllogism more graphically by an ellipse ( ).
3. Middle Term
The middle term occurs in each of the premises but not in the conclusion. In the major premise it occurs in conjunction with the major tern; and in the minor premise, in conjunction with the minor terms. It is the medium through which the major and minor terms are syllogism. As opposed to the middle term, the major and minor terms are called the EXTREMES.
But as you can see, it is best that you arrange the propositions in their formal sequence; (i) major premise, (ii) minor premise, and (iii) conclusions. This may help you avoid mistakes. The major term is marks by a rectangular form. The minor term is marked by an ellipse and the middle term by an M figure. Notice also that each term appears twice.
Major Premise:All men are rational being.
Minor Term: but Francis is a man, (middle term)
Conclusion:therefore Francis is a rational being.
(Minor) (Major term)
PRINCIPLES OF SYLLOGISM
Every categorical syllogism states the identity or non-identity of two terms (S and P), because of their identity or non-identity with a third term (M). This process, which are analogous to, and indeed the matrix of the mathematical substitution of equal for equal’s derivatives of the metaphysical principles of identity and contradiction:
1. The Principle of Reciprocal Identity. Two terms identical with a third term are identical with each other. (Notice that we say, “identical” rather than “equal”, since “equal” applies only to quantities with which mathematics deals.)
2. The Principle of...