Oppositional Inference

Oppositional Inference Opposite or Opposed Proposition are propositions that cannot be simultaneously true or that cannot be simultaneously false, or that cannot be either simultaneously true or simultaneously false. This impossibility of being simultaneously true, or false, or either true or false is the essential note of logical opposition. Propositions are opposed if they have the same subject and predicate but differ from one another in quality or quantity, or both in quality and quantity.

Contradictory Opposition Two propositions are contradictories if one is the denial or negation of the other, that is, if they cannot be both true and they cannot be both false. It is the opposition of a pair of propositions so related to one another that they cannot be either simultaneously true or simultaneously false. The truth of one excludes the truth of the other, and falsity of one exclude the falsity of the other. Quantified attributive propositions having the same subject and predicate but differing in both quality and quantity (A & O, E & I) are contradictories

The Rules for Contradictories: 1.) If one of two contradictory propositions is true, the other is false. 2.) If one is false, the other is true

Contrary Opposition Two propositions are said to be contraries if they cannot be both true, that is, if the truth of either one entails that the other is false. The opposition of a pair of propositions so related to one another that they cannot be simultaneously true but they can be simultaneously false. The truth of one excludes the truth of the other, but the falsity of one does not exclude the falsity of the other. Universal attributive, or categorical propositions having the same subject and predicate but differing in quality (A & E) are contraries.

The Rules for Contraries:

1.) If one of two contraries is true, the other is false. 2.) If one is false, the other is doubtful.

Subcontrary Opposition Two propositions are said to be subcontraries if they cannot both be false, although they may both be true. Subcontrary opposition is the opposition of two propositions that cannot be simultaneously false but can be simultaneously true: if one is false, the other must be true; but both of them can be true. Particular propositions having the same subject and predicate but differing in quality (I & O) are subcontraries.

The Rules for Subcontraries: 1.) If one of two subcontraries is false, the other is true. 2.) If one is true, the other is doubtful.

Subalternate Two propositions that have the same subjects and the same predicate terms, and agree in quality but differ only in quantity are subalterns. Subalterns are not, strictly speaking, opposites at all because neither the truth nor the falsity of either of them excludes the truth or falsity of the other. Both of them can be true and both of them can be false. Propositions having the same subject, predicate and quality but differing in quantity (A & I, E & O) are subalternates.

The Rules for Subalternates: 1.) If the universal is true, the particular is true; but if the universal is false, the particular is doubtful. 2.) If the particular is true, the universal is doubtful; but if the particular is false, the universal is false.

PEREZ, KRISTEL T.