We describe Peirce’s 1903 system of modal gamma graphs, its transformation rules of inference, and the interpretation of the broken-cut modal operator. We show that Peirce proposed the normality rule in his gamma system. We then show how various normal modal logics arise from Peirce’s assumptions concerning the broken-cut notation. By developing an algebraic semantics we establish the completeness of fifteen modal logics of gamma graphs. We show that, besides logical necessity and possibility, Peirce proposed an epistemic interpretation of the (...) broken-cut modality, and that he was led to analyze constructions of knowledge in the style of epistemic logic. (shrink)

It is commonly supposed that the pragmatisms of Peirce and James are fundamentally opposed; this view is supported by the fact that in 1905 Peirce deliberately chose a new name for his original doctrine. Yet Peirce and James were not only life-long friends but to a surprising extent were life-long collaborators. It is true that their approaches to philosophy were very different, reflecting their distinct personalities, with James exhibiting a pluralistic and humanistic style as opposed to Peirce the analyst and (...) formalist. James was a popular philosopher and Peirce a philosopher for philosophers. But they followed each other’s work, corresponded about philosophical problems, and deeply influenced each other. Peirce never completely renounced James’s broader pragmatism and tried hard to find common ground, even to some extent reshaping his own views to accommodate James’s. (shrink)

The background target of the research going into the present article is to forge an intellectual alliance between, on the one hand, active inference and the free-energy principle (FEP), and on the other, Charles S. Peirce’s theory of semiotics and pragmatism. In the present paper, the focus is on the allegiance between the nomenclatures of active and abductive inferences as the proper place to begin reaching at that wider target. The paper outlines the key conceptual elements involved in a naturalistic (...) rendering of Peirce’s late semiotic and logical notion of abductive reasoning. The target is a cognitive-biological model of abduction which preserves the functional integrity of an organism and fulfils the existential imperative for living beings’ evidence of existence. Such a model is an adaptation of Peirce’s late logical schema of abduction proposed in his largely unpublished works during the early 20th century. The proposed model is argued to be a feasible sketch also of recent breakthroughs in computational (sensu Bayesian) cognitive science. (shrink)