Part 42 (1/2)

CHAPTER XXV.

_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 a.s.sent 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.