Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.1

I wanted to call attention to a very important statement from Selection 7 (CP 3.225–226).  Peirce enumerates the fundamental forms of individual dual relatives in the following terms:

225.   Individual relatives are of one or other of the two forms

\begin{array}{lll}  \mathrm{A : A} & \qquad & \mathrm{A : B},  \end{array}

and simple relatives are negatives of one or other of these two forms.

And then he makes the following observation:

226.   The forms of general relatives are of infinite variety, but the following may be particularly noticed.

Relatives may be divided into those all whose individual aggregants are of the form \mathrm{A : A} and those which contain individuals of the form \mathrm{A : B}.  The former may be called concurrents, the latter opponents.

This tells us that Peirce understands the distinction between general dual relatives and individual dual relatives, the individuals being “aggregated” or logically summed to form the generals, and that singling out special cases of general relatives in the way he does next is but a first rough cut toward a complete classification.  This needs to be born in mind as we proceed toward the enumeration of triadic relations and beyond, especially as it affects the classification of triadic sign relations.

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

This entry was posted in Dyadic Relations, Logic, Logic of Relatives, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Triadic Relations and tagged , , , , , , , , . Bookmark the permalink.

3 Responses to Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Comment 7.1

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

  2. Pingback: Survey of Relation Theory • 2 | Inquiry Into Inquiry

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

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