order-systems. Not Quantity, but Order, is the fundamental category of exact thought about facts.[1]
Now what is the logical derivation of the category of
serial Order? The answer to this question requires us to
return to the study of what is logically implied in coming
to discriminate between any two objects. To such a study
I must devote a little space, despite the painfully abstract
nature of the topic.[2]
IV
In certain cases, as we have seen, to compare attentively two objects, as to their differences and likenesses, is to observe a situation which implies that something is between the two, and that the two themselves are again between another pair of objects. The process of discrimination and of synthesis thus initiated proves, at least in some such cases, recurrent, or self-repeating, and leads us to form postulates about the objective structure of the system of facts to which the things in question belong. In order to estimate more carefully the meaning and the uni-
- ↑ I am principally indebted for the substance of this remark to Mr. Charles Peirce, and to the study of Dedekind and Cantor. See the article on the Logic of Relatives in the Monist, Vol. VII, p. 205, sqq., by Mr. Peirce.
- ↑ The best way of forming, from a psychological point of view, a general sense of the practical importance of the process of conceiving facts in series, is to read the brilliant passages on the topic in Professor James’s larger Psychology (Vol. I, p. 490; Vol. II, pp. 644-669). What Professor James there takes as a fundamental psychological feature of the process of comparison, I here try to analyze in certain of its logical aspects. The discussion in the Supplementary Essay in our First Series has already dealt in full with that primary form, the Number-Series. Here we deal mainly with a derived type of Order.
