Abstraction in Fitch's Basic Logic

History and Philosophy of Logic 33 (3):215-243 (2012)
Abstract
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.
Keywords Abstraction  Combinatory Logic
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DOI 10.1080/01445340.2011.648312
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Fixing Frege.John P. Burgess - 2005 - Princeton University Press.
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