David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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History and Philosophy of Logic 33 (3):215-243 (2012)
Fitch's basic logic is an untyped illative combinatory logic with unrestricted principles of abstraction effecting a type collapse between properties (or concepts) and individual elements of an abstract syntax. Fitch does not work axiomatically and the abstraction operation is not a primitive feature of the inductive clauses defining the logic. Fitch's proof that basic logic has unlimited abstraction is not clear and his proof contains a number of errors that have so far gone undetected. This paper corrects these errors and presents a reasonably intuitive proof that Fitch's system K supports an implicit abstraction operation. Some general remarks on the philosophical significance of basic logic, especially with respect to neo-logicism, are offered, and the paper concludes that basic logic models a highly intensional form of logicism
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References found in this work BETA
Wayne Aitken & Jeffrey A. Barrett (2004). Computer Implication and the Curry Paradox. Journal of Philosophical Logic 33 (6):631-637.
Wayne Aitken & Jeffrey A. Barrett (2007). Stability and Paradox in Algorithmic Logic. Journal of Philosophical Logic 36 (1):61 - 95.
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