Commens
Digital Companion to C. S. Peirce
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1867 | Upon Logical Comprehension and Extension | W 2:79-80; CP 2.409-12

The informed breadth and depth suppose a state of information which lies somewhere between two imaginary extremes. These are, first, the state in which no fact would be known, but only the meaning of terms; and, second, the state in which the information would amount to an absolute intuition of all there is, so that the things we should know would be the very substances themselves, and the qualities we should know would be the very concrete forms themselves. This suggests two other sorts of breadth and depth corresponding to these two states of information, and which I shall term respectively the essential and the substantial breadth and depth.

[—]

By the essential depth of a term, then, I mean the really conceivable qualities predicated of it in its definition.

The defined term will not perhaps be applicable to any real objects whatever. Let, for example, the definition of the term T be this,

Any T is both P’ and P” and P”’,

then this sums up its whole meaning; and, as it may not be known that there is any such thing as P’, the meaning of T does not imply that it exists. On the other hand, we know that neither P’, P”, nor P”’ is coextensive with the whole sphere of being. For they are determinate qualities, and it is the very meaning of being that it is indeterminate, that is, is more extensive than any determinate term. In fact, P’, for example, is a real notion which we never could have except by means of its contrast to something else. Hence we must know that

Whatever is not-P‘is not-T,
Whatever is not-P”is not-T,
and Whatever is not-P”’is not-T.

Thus, if we define the essential breadth of a term as those real things of which, according to its very meaning, a term is predicable, not-T has an essential breadth. We may therefore divide all terms into two classes, the essentially affirmative, or positive, and the essentially negative; of which the former have essential depth, but no essential breadth, and the latter essential breadth, but no essential depth.