## 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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