As Sir William Hamilton has pointed out, “Some A is not B” may also be converted in the following form: “No B is some A.” Some men are not negroes; therefore, No negroes are some men (e.g., Europeans).

Contraries: All A is B No A is B 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.