Peirce’s 1870 “Logic of Relatives” • Selection 12

Posted on June 9, 2014 by Jon Awbrey

On to the next part of §3. Application of the Algebraic Signs to Logic.

Peirce’s 1870 “Logic of Relatives” • Selection 12

The Sign of Involution

I shall take involution in such a sense that x^y will denote everything which is an x for every individual of y.  Thus \mathit{l}^\mathrm{w} will be a lover of every woman.  Then (\mathit{s}^\mathit{l})^\mathrm{w} will denote whatever stands to every woman in the relation of servant of every lover of hers;  and \mathit{s}^{(\mathit{l}\mathrm{w})} will denote whatever is a servant of everything that is lover of a woman.  So that

(s^ℓ)^w = s^(ℓw)

(Peirce, CP 3.77)

References

  • Peirce, C.S. (1870), “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”, Memoirs of the American Academy of Arts and Sciences 9, 317–378, 26 January 1870.  Reprinted, Collected Papers 3.45–149, Chronological Edition 2, 359–429.  Online (1) (2) (3).
  • 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.
  • Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1981–.

Resources

cc: Cybernetics • Ontolog Forum • Structural Modeling • Systems Science
cc: FB | Peirce Matters • Laws of Form (1) (2) • Peirce List (1) (2) (3) (4) (5) (6) (7)

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