§ 231. If we were to admit, under the term 'verbal proposition,' all statements which, though not actually contained in the definition of the subject, are implied by it, the whole body of necessary truth would have to be pronounced merely verbal, and the most penetrating conclusions of mathematicians set down as only another way of stating the simplest axioms from which they started. For the propositions of which necessary truth is composed are so linked together that, given one, the rest can always follow. But necessary truth, which is arrived at 'a priori,' that is, by the mind's own working, is quite as real as contingent truth, which is arrived at 'a posteriori,' or by the teachings of experience, in other words, through our own senses or those of others. § 232. The process by which real truth, which is other than deductive, is arrived at 'a priori' is known as Intuition. E.g. The mind sees that what has three sides cannot but have three angles. § 233. Only such propositions then must be considered verbal as state facts expressly mentioned in the definition. § 234. Strictly speaking, the division of propositions into verbal and real is extraneous to our subject: since it is not the province of logic to acquaint us with the content of definitions. § 235, The same distinction as between verbal and real proposition, is conveyed by the expressions 'Analytical' and 'Synthetical,' or 'Explicative' and 'Ampliative' judgements. § 236. A verbal proposition is called analytical, as breaking up the subject into its component notions. § 237. A real proposition is called synthetical, as attaching some new notion to the subject. § 238. Among the scholastic logicians verbal propositions were known as 'Essential,' because what was stated in the definition was considered to be of the essence of the subject, while real propositions were known as 'Accidental.' _Universal AND PARTICULAR Propositions_. § 239. A Universal proposition is one in which it is evident from the form that the predicate applies to the subject in its whole extent. § 240. When the predicate does not apply to the subject in its whole extent, or when it is not clear that it does so, the proposition is called Particular. § 241. To say that a predicate applies to a subject in its whole extent, is to say that it is asserted or denied of all the things of which the subject is a name. § 242. 'All men are mortal' is a universal proposition. § 243. 'Some men are black' is a particular proposition. So also is 'Men are fallible;' for here it is not clear from the form whether 'all' or only 'some' is meant. § 244. The latter kind of proposition is known as Indefinite, and must be distinguished from the particular proposition strictly so called, in which the predicate applies to part only of the subject. § 245. The division into universal and particular is founded on the Quantity of propositions.