Chapter 3. The Logic of Relatives (cont.)
§2. Relatives (cont.)
220. Every relative, like every term of singular reference, is general; its definition describes a system in general terms; and, as general, it may be conceived either as a logical sum of individual relatives, or as a logical product of simple relatives. An individual relative refers to a system all the members of which are individual. The expressions
may denote individual relatives. Taking dual individual relatives, for instance, we may arrange them all in an infinite block, thus,
In the same way, triple individual relatives may be arranged in a cube, and so forth. The logical sum of all the relatives in this infinite block will be the relative universe, where
whatever dual relative may be. It is needless to distinguish the dual universe, the triple universe, etc., because, by adding a perfectly indefinite additional member to the system, a dual relative may be converted into a triple relative, etc. Thus, for lover of a woman, we may write lover of a woman coexisting with anything. In the same way, a term of single reference is equivalent to a relative with an indefinite correlate; thus, woman is equivalent to woman coexisting with anything. Thus, we shall have
- 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.