Deductive Logic - St. George William Joseph Stock

But logicians anxious for simplification asked, whether a predicate in any given case must not either apply to the whole of the subject or not? And whether, therefore, the third head of indefinite propositions were not as superfluous as the so-called 'common gender' of nouns in grammar?

§ 256. It is quite true that, as a matter of fact, any given predicate must either apply to the whole of the subject or not, so that in the nature of things there is no middle course between universal and particular. But the important point is that we may not know whether the predicate applies to the whole of the subject or not. The primary division then should be into propositions whose quantity is known and propositions whose quantity is unknown. Those propositions whose quantity is known may be sub-divided into 'definitely universal' and 'definitely particular,' while all those whose quantity is unknown are classed together under the term 'indefinite.' Hence the proper division is as follows—

§ 257. Another very obvious defeat of terminology is that the word 'universal' is naturally opposed to 'singular,' whereas it is here so used as to include it; while, on the other hand, there is no obvious difference between universal and general, though in the division the latter is distinguished from the former as species from genus.

Affirmative and Negative Propositions.

§ 258. This division rests upon the Quality of propositions.

§ 259. It is the quality of the form to be affirmative or negative: the quality of the matter, as we saw before (§ 204), is to be true or false. But since formal logic takes no account of the matter of thought, when we speak of 'quality' we are understood to mean the quality of the form.

§ 260. By combining the division of propositions according to quantity with the division according to quality, we obtain four kinds of proposition, namely—

(1) Universal Affirmative (A).

(2) Universal Negative (E).