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Rule of Contradiction

Contradictory statements are statements that differ in both quality and quantity

Rule of Contraries

Two statements are contrary to one another if they are both universals but differ in quality

Rule of Subcontraries

Two statements are subcontrary if they are both particular statements that differ in quality

Rule of Subalterns

Two statements are subalternate if they have the same quality but differ in quantity

1st Rule of Opposition

Contradictories cannot at the same time be true nor at the same time be false

2nd Rule of Opposition

Contraries cannot at the same time both be true, but can at the same time both be false

3rd Rule of Oppostion

Subcontraries may at the same time both be true, but cannot at the same time both be false

4th Rule of Opposition

Subalterns may both be true or both be false

Rule of Double Negation

A term which is not negated is equivalent to a term that is negated twice

Essential Law of Argumentation

If the antecedent is true, the consequent must also be true

Principle of Reciprocal Identity

Two terms that are identical with a third term are identical to each other

Principle of Reciprocal Non-Identity

Two terms, one of which is identical with a third term and the other of which is nonidentical with that third term, are nonidentical to each other

Dictum de Omni

What is affirmative universally of a certain term is affirmed of every term that comes under that term

Dictum de Nullo

What is denied universally of a certain term is denied of every term that comes under that term

Rule I

There must be three and only three terms

Rule II

The middle term must not occur in the conclusion

Rule III

If a term is distributed in the conclusion, then it must be distributed in the premises

Rule IV

The middle term must be distributed at least once

Rule V

No conclusion can follow from two negative premises

Rule VI

If the two premises are affirmative, the conclusion must also be affirmative

Rule VII

If either premise is negative, the conclusion must be negative

Fallacy of Four Terms

There are four clearly distinguishable terms in a syllogism

Fallacy of Equivocation

One of three terms is used in argument in two different senses

Fallacy of Illicit Major

The major term is distributed in the conclusion but not in the major premise

Fallacy of Illicit Minor

The minor term is distributed in the conclusion but not in the minor premise

Fallacy of Undistributed Middle

The middle term is not distributed in either premise

Fallacy of Exclusive Premises

When rule V is violated

Fallacy of Drawing a Negative Conclusion from Affirmative Premises

when rule VI is violated

Fallacy of Drawing an Affirmative Conclusion from Negative Premises

when rule VII is violated