Peirce’s 1870 “Logic of Relatives” • Comment 10.1

What Peirce is attempting to do at CP 3.75 is absolutely amazing.  I did not run across anything on a par with it again until the mid 1980s when I began studying the application of mathematical category theory to computation and logic.  Gauging the success of Peirce’s attempt would take a return to his earlier paper “Upon the Logic of Mathematics” (1867) to pick up the ideas about arithmetic he sets out there.

Another branch of the investigation would require us to examine the syntactic mechanics of subjacent signs Peirce uses to establish linkages among relational domains.  The indices employed for this purpose amount to a category of diacritical and interpretive signs which includes, among other things, the comma functor we have just been discussing.

Combining the two branches of this investigation opens a wider context for the study of relational compositions, distilling the essence of what it takes to relate relations, possibly complex, to other relations, possibly simple.

Resources

• Peirce’s 1870 Logic of Relatives • Part 1 • Part 2 • Part 3 • References

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