nLab Charles Sanders Peirce

Charles Sanders Peirce (1839-1914), a philosopher, logician and scientist, was one of the founders of modern symbolic logic. In particular, he developed a form of predicate logic. Peirce devised a graphical notation, known as existential graphs, to represent logical calculi. There were three systems of such graphs: the system alpha, to represent propositional logic, the system beta, to represent predicate logic, and the system gamma, to represent modal logic.

Geraldine Brady and Todd Trimble have given a category theoretic interpretation of the alpha and beta systems. The latter, a form of string diagrammatic notation, was developed (PontoShul) into a string diagram notation for indexed monoidal categories. A development also appears in MellZeil.

Peirce’s philosophy can be seen as Schellingism transformed in light of (in Peirce’s time) modern physics, as Peirce himself notes in an 1894 letter to William James:

My views were probably influenced by Schelling - by all stages of Schelling, but especially the Philosophie der Natur. I consider Schelling as enormous, and one thing I admire about him is his freedom from the trammels of system, and his holding himself uncommitted to any previous utterance. in that, he is like a scientific man. If you were to call my philosophy Schellingism transformed in the light of modern physics, I should not take it hard.

References

Stanford Encyclopedia of Philosophy entries:

Other references

• Geraldine Brady and Todd Trimble (2000a). A Categorical Interpretation of C. S. Peirce’s Propositional Logic Alpha. Journal of Pure and Applied Algebra 149 (2000): 213-239

• Kate Ponto and Mike Shulman, Duality and traces in indexed monoidal categories, (web)

• Fernando Zalamea (2012), Peirce’s Logic of Continuity: A Conceptual and Mathematical Approach

• Frederik Stjernfelt (2014), Natural Propositions: The Actuality of Peirce’s Doctrine of Dicisigns

• Rosa Maria Perez-Teran Mayorga (2008), From Realism to ‘Realicism’: The Metaphysics of Charles Sanders Peirce

• Andrew Reynolds (2002), Peirce’s Scientific Metaphysics: The Philosophy of Chance, Law, and Evolution

• Matthew Moore (ed) (2010), New Essays on Peirce’s Mathematical Philosophy

• C.S. Peirce & Matthew Moore (ed) (2010), Philosophy of Mathematics: Selected Writings

• Paul-André Melliès and Noam Zeilberger (2016) A bifibrational reconstruction of Lawvere’s presheaf hyperdoctrine, (arXiv:1601.06098, cs.LO)

category: people, philosophy

Revised on June 5, 2017 13:04:13 by Todd Trimble (67.81.95.215)