The mode in which thoughts are united in a Syllogism, is the leading example of the third case. Let us consider the following very familiar instance. "Every tree is a vegetable: every oak is a tree: therefore, every oak is a vegetable." This is evidently a process of naming. The primary idea is that of the object called an oak; from the name oak, I proceed to the name tree, finding that the name oak, is included in the name tree; and from the name tree, I proceed to the name vegetable, finding that the name tree is included in the name vegetable, and by consequence the name oak. This is the series of thoughts, which is marked in order, by the three propositions or predications of the syllogism.[56] [Editor's footnote 56: For the present I shall only remark on this theory of the syllogism, that it must stand or fall with the theory of Predication of which it is the sequel. If, as I have maintained, the propositions which are the premises of the syllogism are not correctly described as mere processes of naming, neither is the formula by which a third proposition is elicited from these two a process of mere naming. What it is, will be considered hereafter.--_Ed._] {189} The Predications of Arithmetic are another instance of the same thing. "One and one are two." This again is a mere process of naming. What I call one and one, in numbering things, are objects, sensations, or clusters of sensations; suppose, the striking of the clock. The same sounds which I call one and one, I call also two; I have for these sensations, therefore, two names which are exactly equivalent: so when I say, one and one and one are three: or when I say, two and two are four: ten and ten are twenty: and the same when I put together any two numbers whatsoever. The series of thoughts in these instances is merely a series of names applicable to the same thing, and meaning the same thing.