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

Peirce’s 1870 Logic Of Relatives

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