## Peirce’s 1870 “Logic Of Relatives” • Preliminaries

I need to return to my study of Peirce’s 1870 Logic Of Relatives, and I thought it might be more pleasant to do that on my blog than to hermit away on the wiki where I last left off.

Peirce’s text employs lower case letters for logical terms of general reference and upper case letters for logical terms of individual reference.  General terms fall into types, for example, absolute terms, dyadic relative terms, or higher adic relative terms, and Peirce employs different typefaces to distinguish these.  The following Tables indicate the typefaces that are used in the text below for Peirce’s examples of general terms.

$\begin{array}{ll} \multicolumn{2}{l}{\text{Table 1.~~Absolute Terms (Monadic Relatives)}} \\[4pt] \mathrm{a}. & \text{animal} \\ \mathrm{b}. & \text{black} \\ \mathrm{f}. & \text{Frenchman} \\ \mathrm{h}. & \text{horse} \\ \mathrm{m}. & \text{man} \\ \mathrm{p}. & \text{President of the United States Senate} \\ \mathrm{r}. & \text{rich person} \\ \mathrm{u}. & \text{violinist} \\ \mathrm{v}. & \text{Vice-President of the United States} \\ \mathrm{w}. & \text{woman} \end{array}$

$\begin{array}{ll} \multicolumn{2}{l}{\text{Table 2.~~Simple Relative Terms (Dyadic Relatives)}} \\[4pt] \mathit{a}. & \text{enemy} \\ \mathit{b}. & \text{benefactor} \\ \mathit{c}. & \text{conqueror} \\ \mathit{e}. & \text{emperor} \\ \mathit{h}. & \text{husband} \\ \mathit{l}. & \text{lover} \\ \mathit{m}. & \text{mother} \\ \mathit{n}. & \text{not} \\ \mathit{o}. & \text{owner} \\ \mathit{s}. & \text{servant} \\ \mathit{w}. & \text{wife} \end{array}$

$\begin{array}{ll} \multicolumn{2}{l}{\text{Table 3.~~Conjugative Terms (Higher Adic Relatives)}} \\[4pt] \mathfrak{b}. & \text{betrayer to ------ of ------} \\ \mathfrak{g}. & \text{giver to ------ of ------} \\ \mathfrak{t}. & \text{transferrer from ------ to ------} \\ \mathfrak{w}. & \text{winner over of ------ to ------ from ------} \end{array}$

Individual terms are taken to denote individual entities falling under a general term.  Peirce uses upper case Roman letters for individual terms, for example, the individual horses $\mathrm{H}, \mathrm{H}^{\prime}, \mathrm{H}^{\prime\prime}$ falling under the general term $\mathrm{h}$ for horse.

The path to understanding Peirce’s system and its wider implications for logic can be smoothed by paraphrasing his notations in a variety of contemporary mathematical formalisms, while preserving the semantics as much as possible.  Remaining faithful to Peirce’s orthography while adding parallel sets of stylistic conventions will, however, demand close attention to typography-in-context.  Current style sheets for mathematical texts specify italics for mathematical variables, with upper case letters for sets and lower case letters for individuals.  So we need to keep an eye out for the difference between the individual $\mathrm{X}$ of the genus $\mathrm{x}$ and the element $x$ of the set $X$ as we pass between the two styles of text.

### References

• Peirce, C.S. (1870), “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic”, Memoirs of the American Academy of Arts and Sciences 9, 317–378, 26 January 1870.  Reprinted, Collected Papers (CP 3.45–149), Chronological Edition (CE 2, 359–429).  Online (1) (2) (3).
• 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.  Cited as (CP volume.paragraph).
• Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1981–.  Cited as (CE volume, page).
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### 12 Responses to Peirce’s 1870 “Logic Of Relatives” • Preliminaries

1. George Berger says:

Thanks, Jon.

2. Asim Raza says:

Thanks, Jon. I am eagerly waiting for more.