The philosophy of Charles S. Peirce is chock-full of triples, but especially present are his three universal categories of experience. Threes aren’t really my specialty, but while reading a chapter of Richard Bernstein’s book on the “pragmatic turn”, I was reminded of Peirce’s relational ontology: Firstness, Secondness, and Thirdness. Wondering how these could be extended to a Fourthness, I immediately found a fair amount of work on the subject.
Of course, Peirce argued that such a Fourthness was redundant, unnecessary to the structure of his systematic philosophy. He used various reasons for his conclusions, including mathematical, logical, and semiological. There is also a wealth of subsequent work by later researchers on defending this claim, but what is interesting is that others have investigated extending his three into a four.
So, what might be Fourthness? Some of the aspects of fourfolds collected here have commonalities with some of the attributes of Firstness, Secondness, and Thirdness. For Firstness: feeling, quality, possibility; For Secondness: will, fact, existence; For Thirdness: knowledge, law, representation. I really don’t have anything to add at the present time and I have merely gathered these notions together for my future consideration.
Carl G. Vaught / Semiotics and the Problem of Analogy: a critique of Peirce’s theory of categories. Trans. of the Charles S. Peirce Society, Vol. 22, No. 3 (1986) 311-326
Carl R. Hausman / Fourthness: Carl Vaught on Peirce’s categories. Trans. of the Charles S. Peirce Society, Vol. 24, No. 2 (1988) 265-278
Donald W. Mertz / Peirce: logic, categories, and triads. Trans. of the Charles S. Peirce Society, Vol. 15, No. 2 (1979) 158-175
Richard J. Bernstein / The Pragmatic Turn. Polity (2010)
Ben Goertzel / The Hidden Pattern: a patternist philosophy of mind
[*9.108, *9.109, *9.112]