Peirce’s explorations in logic and the theory of signs opened several directions of generalization from logics of complete information (LOCI) to theories of partial information (TOPI). Naturally we hope these avenues of approach will eventually converge on a unified base camp from which to reach greater heights of understanding, but that is still a work in progress, at least for me.
Any passage from logic as a critical, formal, or normative theory of controlled semiotic conduct to the descriptive study of signs “in the wild” involves relaxing logical norms to statistical norms.
One of the headings under which Peirce expands the scope of logic to something more general — whether keeping or losing the name of “logic” is a secondary consideration — is found in his study of Generality and Vagueness as affecting signs not fully primed for logical use. There’s a bit about that at the following places.
- C.S. Peirce • Collected Papers (CP 5.448)
- FOM List • C.S. Peirce on “General” and “Vague” • (1) (2) (3)
As you can see, in this direction of generalization Peirce considers relaxing both the principle of contradiction and the principle of excluded middle.
- Logic Syllabus • Ampheck
- Logical Graphs • One • Two
- Propositions As Types Analogy
- Survey of Animated Logical Graphs
- Propositional Equation Reasoning Systems
- Survey of Abduction, Deduction, Induction, Analogy, Inquiry