A System of Logic, Ratiocinative and Inductive

by John Stuart Mill

Subtraries:
Some A is B
Some A is not B

Contradictories:
All A is B
Some A is not B

Also contradictories:
No A is B
Some A is B

Respectively subalternate:
All A is B and No A is B
Some A is B and Some A is not B

Professor Bain denies the claim of Singular Propositions to be classed, for the purposes of ratiocination, with Universal; though they come within the designation which he himself proposes as an equivalent for Universal, that of Total. He would even, to use his own expression, banish them entirely from the syllogism. He takes as an example,

Socrates is wise,
Socrates is poor, therefore
Some poor men are wise,

or more properly (as he observes) “one poor man is wise.” “Now, if wise, poor, and a man, are attributes belonging to the meaning of the word Socrates, there is then no march of reasoning at all. We have given in Socrates, inter alia, the facts wise, poor, and a man, and we merely repeat the concurrence which is selected from the whole aggregate of properties making up the whole, Socrates. The case is one under the head ‘Greater and Less Connotation’ in Equivalent Propositional Forms, or Immediate Inference.

“But the example in this form does not do justice to the syllogism of singulars. We must suppose both propositions to be real, the predicates being in no way involved in the subject. Thus

Socrates was the master of Plato,
Socrates fought at Delium,
The master of Plato fought at Delium.

“It may fairly be doubted whether the transitions, in this instance, are any thing more than equivalent forms. For the proposition ‘Socrates was the master of Plato and fought at Delium,’ compounded out of the two premises, is obviously nothing more than a grammatical abbreviation. No one can say that there is here any change of meaning, or any thing beyond a verbal modification of the original form. The next step is, ‘The master of Plato fought at Delium,’ which is the previous statement cut down by the omission of Socrates. It contents itself with reproducing a part of the meaning, or saying less than had been previously said. The full equivalent of the affirmation is, ‘The master of Plato fought at Delium, and the master of Plato was Socrates:’ the new form omits the last piece of information, and gives only the first. Now, we never consider that we have made a real inference, a step in advance, when we repeat less than we are entitled to say, or drop from a complex statement some portion not desired at the moment. Such an operation keeps strictly within the domain of equivalence, or Immediate Inference. In no way, therefore, can a syllogism with two singular premises be viewed as a genuine syllogistic or deductive inference.” (Logic, i., 159.)