Peirce’s Anticipation of Game Theoretic Logic and Semantics
Immanuel Kant bequeathed to us four triadic divisions of “functions of judgment” under the headings of Quantity, Quality, Modality, and Relation.1 If we restrict attention to the simplest possible propositional forms, Peirce’s revised and improved version of Kant’s tables is represented by Figure 1.
KeywordsInverted Triangle Propositional Form Clause Rule Dialogical Logic Mouton Publisher
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- 1.The use of Kant’s headings here is merely an expository device. But see MS 291, 5.450.Google Scholar
- 2.Strictly, disjunctions and conjunctions are only analogues of indefinite and general propositions.Google Scholar
- 3.For terminology, see my unpublished dissertation on C.S. Peirce’s Logic of Vagueness Urbana, IL, 1969.Google Scholar
- 4.Some of the places in which such terminology occurs are MS 9; MS 515; 2.453; 3.463, 478; NE IV, p. 173.Google Scholar
- 5.In 3.479 ff., everything seems to be in one place, But the awkwardness of the graphical devices used leads Peirce into some strange and never-repeated remarks about the reiteration of quantifiers. A better source probably exists.Google Scholar
- 6.See Risto Hilpinen, “On C.S. Peirce’s Theory of the Proposition: Peirce as a Precursor of Game-Theoretical Semantics,” forthcoming in The Relevance of C.S. Peirce edited by E. Freeman, J. Smith and J. Hintikka. The existence of Professor Hilpinen’s paper came to my notice during the preparation of this one.Google Scholar