CHAPTER XXV.. _the Disjunctive Syllogism Regarded As an Immediate Inference_.

The Disjunctive Syllogism regarded as an Immediate Inference.

§ 770. If no stress be laid on the transition from disjunctive hypothesis to fact, the disjunctive syllogism will run with the same facility as its predecessor into the moulds of immediate inference.

§ 771.

Denial of Antecedent. Subalternation.

Either A is B or C is D, Every case of A not being B is a case of C being D. .'. A not being B, C is D. .'. Some case of A not being B is a case of C being D.

§ 772.

Denial of Consequent. Conversion by Contraposition + Subalternation.

Either A is B or C is D. All cases of A not being B are cases of C being D. .'. C not being D, A is B .'. All cases of C not being D are cases of A being B. .'. Some case of C not being D is a case of A being B.

§ 773. Similarly the two invalid types of disjunctive syllogism will be found to coincide with fallacies of immediate inference.

§ 774.

Affirmation of Antecedent. Contraposition without Conversion.

Either A is B or C is D. All cases of A not being B are cases of C being D. .'. A being B, C is not D .'. All cases of A being B are cases of C not being D.

§ 775. The affirmation of the antecedent thus comes under the formula--

All not-A is B, .'. All A is not-B,

a form of inference which cannot hold except where A and B are known to be incompatible. Who, for instance, would assent to this?--

All non-boating men play cricket. .'. All boating men are non-cricketers.

§ 776.

Affirmation of Consequent. Simple Conversion of A.

Either A is B or C is D. All cases of A not being B are cases of C being D. .'.C being D, A is not B. .'. All cases of C being D are cases of A not being B.

§ 777. We may however argue in this way--

Conversion of A per accidens. Either A is B or C is D. All cases of A not being B are cases of C being D. .'. C being D, A is sometimes B. .'. Some cases of C being D are cases of A not being B.

The men who pass this examination must have either talent or industry. .'. Granting that they are industrious, they may be without talent.