Chapter 3. The Logic of Relatives (cont.)
§4. Classification of Relatives (cont.)
227. These different classes have the following relations. Every negative of a concurrent and every alio-relative is both an opponent and the negative of a self-relative. Every concurrent and every negative of an alio-relative is both a self-relative and the negative of an opponent.
There is only one relative which is both a concurrent and the negative of an alio-relative; this is ‘identical with ──’.
There is only one relative which is at once an alio-relative and the negative of a concurrent; this is the negative of the last, namely, ‘other than ──’.
The following pairs of classes are mutually exclusive, and divide all relatives between them:
Alio-relatives and self-relatives,
Concurrents and opponents,
Negatives of alio-relatives and negatives of self-relatives,
Negatives of concurrents and negatives of opponents.
No relative can be at once either an alio-relative or the negative of a concurrent, and at the same time either a concurrent or the negative of an alio-relative.
228. We may append to the symbol of any relative a semicolon to convert it into an alio-relative of a higher order. Thus will denote a ‘lover of ── that is not ──’.
- Peirce, C.S. (1880), “On the Algebra of Logic”, American Journal of Mathematics 3, 15–57. Collected Papers (CP 3.154–251), Chronological Edition (CE 4, 163–209).
- Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1–6, Charles Hartshorne and Paul Weiss (eds.), vols. 7–8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931–1935, 1958. Volume 3 : Exact Logic, 1933.
- Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1981–. Volume 4 (1879–1884), 1986.