Journal of Philosophical Logic 37 (1):23-43 (2008)

Authors
Jeffrey Barrett
University of California, Irvine
Abstract
We develop a functional abstraction principle for the type-free algorithmic logic introduced in our earlier work. Our approach is based on the standard combinators but is supplemented by the novel use of evaluation trees. Then we show that the abstraction principle leads to a Curry fixed point, a statement C that asserts C ⇒ A where A is any given statement. When A is false, such a C yields a paradoxical situation. As discussed in our earlier work, this situation leaves one no choice but to restrict the use of a certain class of implicational rules including modus ponens
Keywords abstraction  algorithmic logic  Curry paradox
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DOI 10.1007/s10992-007-9051-5
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References found in this work BETA

Computer Implication and the Curry Paradox.Wayne Aitken & Jeffrey A. Barrett - 2004 - Journal of Philosophical Logic 33 (6):631-637.
Foundations of Constructive Mathematics.Michael J. Beeson - 1987 - Studia Logica 46 (4):398-399.
Stability and Paradox in Algorithmic Logic.Wayne Aitken & Jeffrey A. Barrett - 2007 - Journal of Philosophical Logic 36 (1):61-95.
Introduction to Combinators and Λ-Calculus.J. Roger Hindley & Jonathan P. Seldin - 1988 - Journal of Symbolic Logic 53 (3):985-986.

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Citations of this work BETA

Stability and Paradox in Algorithmic Logic.Wayne Aitken & Jeffrey A. Barrett - 2007 - Journal of Philosophical Logic 36 (1):61-95.
Abstraction in Fitch's Basic Logic.Eric Thomas Updike - 2012 - History and Philosophy of Logic 33 (3):215-243.
A Note on the Physical Possibility of Transfinite Computation.Wayne Aitken & Jeffrey A. Barrett - 2010 - British Journal for the Philosophy of Science 61 (4):867-874.

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