# Categorical syllogism

A**categorical syllogism**is a valid argument of the following form:

- .
- .
- Therefore, .

A categorical syllogism contains two premises followed by a conclusion, both of which are generically known as propositions. There can be only three terms predicated through out the entirety of the syllogism. Each proposition must be in the following form: A subject linked to a predicate by a copula. A premise might go as follows: All S is P, where S is the subject, 'is' is the copula, and P is the predicate.

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2 Mood and Figure 3 Validity |

## Quality, Quantity and Distribution

*A proposition*is a universial affirmative: All S is P*E proposition*is a universial negative: No S is P*I proposition*is a particular affirmative: Some S is P*O proposition*is a particular negative: Some S is not P

## Mood and Figure

the mood would be AAA, seeing that all propositions are universial affirmative. Next to be discussed is the figure of a categorical syllogism. However, in order to comprehend the figure, one must be able to identify the three different types of terms: major term, minor term, and the middle term. The term occurring as the predicate of the conclusion is the major term. In the aforementioned syllogism B is the major term. The minor term is the term that occurs as the subject of the conclusion; C is the minor term. Finally, by process of elimination, it can be deduced that the middle term is the term does not occur in the conclusion, but instead once in each premise. Accordingly, A is the middle term. The figure of a categorical syllogism can be known by identifying the four possible arrangements of the middle term. The figures are represented numberically 1-4

- 1 the middle term occupies the subject of the first premise and the predicate of the second premise
- 2 the middle term occupies the predicate of both the first premise and second premise
- 3 the middle term occupies the subject of both the first premise and second premise
- 4 the middle term occupies the predicate of the first premise and the subject of the second premise

## Validity

You can obtain the remaining valid forms via the other methods. One method is to construct a Venn diagram. Since there three terms, a Venn diagram will require three over-laping circles which represent each class. First, construct a circle for the major term. Adjacent to the circle for the major term will be an over-laping circle for the minor term. Beneath those two will be the cirlce for the minor term. It should over-lap at three places: the major term, the minor term and the place at which the major term and minor term over-lap. If the syllogism is valid it would necessitate the truth of the conclusion by diagraming the premises. Never diagram the conclusion, for the conclusion must be infered from the premises. Always diagram the universal propositions first. This is accomplished by shading the areas in which one class does not have membership in the other class. In other words, shaded is equated with non-membership. So in the premise All A is B shade in all areas in which A does not over-lap with B, including where A over-laps with C. Then repeat the same procedure for the second premise. From those two premises we can infere that all members in the class of C also have membership in the class of B. However, we can not infere if all members of the class of B have membership in the class of C.The last method is to memorize six rules using the information presented thus far. While Venn Diagrams are good tools for illustrative purposes, it may be preferable for some to test validity with the following rules:

- As noted before, categorical syllogisms must contain exactly three terms, no more, no less (fallacy of four terms). As a cautionary note, beware that synonyms and antomyms can create the illusion of invalidity, but can sometimes rectified by subsititing the interexchangable terms for one of choice.
- If either premise is negative, then the conclusion must be negative (affirmative conclusion from a negative premise).
- Both premises cannot be negative (fallacy of exclusive premises).
- Any term distributed in the conclusion must be distributed in either premise.
- The middle term must be distributed once and only once (fallacy of the undistributed middle).
- You cannot draw a particular conclusion with two universial premises (existential fallacy).

*See also:*syllogistic fallacy.

*Other forms of syllogism:* hypothetical syllogism, disjunctive syllogism.