As I suggested in an earlier discussion, the difference that makes a difference in Peirce’s contribution to our understanding of inference and reference is “due to his concurrent development of the logic of relative terms and the mathematics of relations, especially triadic relations.” It is only with the addition of these tools to our toolbox that we begin to form models adequate to the complexity of the object phenomena, namely, the whole panoply of activities involved in observation, conceptualization, communication, and inquiry.
I’ll be bringing these tools to bear as needed in the current engagement with Peirce’s incipient information theory, but only as the application calls for them. For a more general grounding in the relational logic and mathematics Peirce was developing in parallel at this time, see my notes, still in progress, on his 1870 Logic of Relatives:
- This Blog • Survey of Pragmatic Semiotic Information
- My Notes • Information = Comprehension × Extension
- C.S. Peirce • Upon Logical Comprehension and Extension