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

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: CyberneticsOntolog ForumStructural ModelingSystems Science
cc: FB | Peirce Matters • Laws of Form (1) (2) • Peirce List (1) (2) (3) (4) (5) (6) (7)

This entry was posted in C.S. Peirce, Logic, Logic of Relatives, Logical Graphs, Mathematics, Relation Theory, Visualization and tagged , , , , , , . Bookmark the permalink.

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

  1. Pingback: Survey of Relation Theory • 3 | Inquiry Into Inquiry

  2. Pingback: Peirce’s 1870 “Logic Of Relatives” • Overview | Inquiry Into Inquiry

  3. Pingback: Peirce’s 1870 “Logic Of Relatives” • Comment 1 | Inquiry Into Inquiry

  4. Pingback: Survey of Relation Theory • 4 | Inquiry Into Inquiry

  5. Pingback: Survey of Relation Theory • 5 | Inquiry Into Inquiry

  6. Pingback: Peirce’s 1870 “Logic of Relatives” • Comment 12.1 | Inquiry Into Inquiry

  7. Pingback: Peirce’s 1870 “Logic of Relatives” • Comment 12.2 | Inquiry Into Inquiry

  8. Pingback: Peirce’s 1870 “Logic of Relatives” • Comment 12.4 | Inquiry Into Inquiry

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.