## Peirce’s 1880 “Algebra Of Logic” Chapter 3 • Selection 7

### Chapter 3. The Logic of Relatives (cont.)

#### §4. Classification of Relatives

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.

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.

Concurrents express a mere agreement among objects.  Such, for instance, is the relative ‘man that is ──’, and a similar relative may be formed from any term of singular reference.  We may denote such a relative by the symbol for the term of singular reference with a comma after it;  thus $(m,\!)$ will denote ‘man that is ──’ if $(m)$ denotes ‘man’.  In the same way a comma affixed to an $n$-fold relative will convert it into an $(n + 1)$-fold relative.  Thus, $(l)$ being ‘lover of ──’, $(l,\!)$ will be ‘lover that is ── of ──’.

The negative of a concurrent relative will be one each of whose simple components is of the form $\mathrm{\overline{A : A}},$ and the negative of an opponent relative will be one which has components of the form $\mathrm{\overline{A : B}}.$

We may also divide relatives into those which contain individual aggregants of the form $\mathrm{A : A}$ and those which contain only aggregants of the form $\mathrm{A : B}.$  The former may be called self-relatives, the latter alio-relatives.  We also have negatives of self-relatives and negatives of alio-relatives.

### 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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