Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 8

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 (l;\!) will denote a ‘lover of ── that is not ──’.

References

  • 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.

Resources

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3 Responses to Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 8

  1. Pingback: Relations & Their Relatives : 10 | Inquiry Into Inquiry

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