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Lewis Carroll's Barber shop paradox

Arthur W. Burks

Mind 59 (234):219-222 (1950)

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The propositional logic of ordinary discourse.William S. Cooper - 1968 - Inquiry: An Interdisciplinary Journal of Philosophy 11 (1-4):295 – 320.details The logical properties of the 'if-then' connective of ordinary English differ markedly from the logical properties of the material conditional of classical, two-valued logic. This becomes apparent upon examination of arguments in conversational English which involve (noncounterfactual) usages of if-then'. A nonclassical system of propositional logic is presented, whose conditional connective has logical properties approximating those of 'if-then'. This proposed system reduces, in a sense, to the classical logic. Moreover, because it is equivalent to a certain nonstandard three-valued logic, its (...) Download Export citation Bookmark 76 citations
Connexive implication.Storrs Mccall - 1966 - Journal of Symbolic Logic 31 (3):415-433.details Download Export citation Bookmark 68 citations
Rewriting the History of Connexive Logic.Wolfgang Lenzen - 2022 - Journal of Philosophical Logic 51 (3):525-553.details The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with (...) Download Export citation Bookmark 9 citations
Directional Bias.Matheus Silva - manuscriptdetails There is almost a consensus among conditional experts that indicative conditionals are not material. Their thought hinges on the idea that if indicative conditionals were material, A → B could be vacuously true when A is false, even if B would be false in a context where A is true. But since this consequence is implausible, the material account is usually regarded as false. It is argued that this point of view is motivated by the grammatical form of conditional sentences (...) Download Export citation Bookmark
Reflexivity: a source-book in self-reference.Steven James Bartlett (ed.) - 1992 - New York, N.Y., U.S.A.: Distributors for the U.S. and Canada, Elsevier Science Pub. Co..details From the Editor’s Introduction: "The Internal Limitations of Human Understanding." We carry, unavoidably, the limits of our understanding with us. We are perpetually confined within the horizons of our conceptual structure. When this structure grows or expands, the breadth of our comprehensions enlarges, but we are forever barred from the wished-for glimpse beyond its boundaries, no matter how hard we try, no matter how much credence we invest in the substance of our learning and mist of speculation. -/- The limitations (...) Download Export citation Bookmark 7 citations
On Conditionals.Theresa Helke - 2018 - Dissertation, National University of Singaporedetails This thesis is about indicative conditionals and apparent counterexamples to classically valid argument forms. Specifically, it applies the following four theories: - material (inspired by Grice (1961, 1975 and 1989)); - possible-worlds (inspired by Stalnaker (1981); Lewis (1976); and Kratzer (2012)), - suppositional (inspired by Adams (1975) and Edgington (1995 and 2014)); and - hybrid (inspired by Jackson (1987)) to try and solve the following two counterexamples: - Vann McGee’s to modus ponens (1985); and - Lewis Carroll’s to modus tollens (...) Download Export citation Bookmark

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