Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 6

Chapter 3. The Logic of Relatives (cont.)

§2. Relatives (concl.)

222.   Instead of considering the system of a relative as consisting of non-relative individuals, we may conceive of it as consisting of relative individuals.  Thus, since

\begin{array}{*{11}{c}}  \mathrm{A} & = &  \mathrm{A:A} & + & \mathrm{A:B} & + & \mathrm{A:C} & + & \mathrm{A:D} & + & \text{etc.},  \end{array}

we have

\begin{array}{*{11}{c}}  \mathrm{A:B} & = &  \mathrm{(A:A):B} & + & \mathrm{(A:B):B} & + & \mathrm{(A:C):B} & + & \mathrm{(A:D):B} & + & \text{etc.}  \end{array}

But

\begin{array}{*{11}{c}}  \mathrm{B} & = &  \mathrm{B:A} & + & \mathrm{B:B} & + & \mathrm{B:C} & + & \mathrm{B:D} & + & \text{etc.};  \end{array}

so that

\begin{array}{*{11}{c}}  \mathrm{A:B} & = &  \mathrm{A:(B:A)} & + & \mathrm{A:(B:B)} & + & \mathrm{A:(B:C)} & + & \mathrm{A:(B:D)} & + & \text{etc.}  \end{array}

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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This entry was posted in 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 • Selection 6

  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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