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