Journal of Philosophical Logic 33 (6):631-637 (2004)

Jeffrey Barrett
University of California, Irvine
There are theoretical limitations to what can be implemented by a computer program. In this paper we are concerned with a limitation on the strength of computer implemented deduction. We use a version of the Curry paradox to arrive at this limitation
Keywords Curry paradox  implication  modus ponens  theory of algorithms
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DOI 10.1023/B:LOGI.0000046077.72722.61
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References found in this work BETA

The Inconsistency of Certain Formal Logics.Alonzo Church & Haskell B. Curry - 1942 - Journal of Symbolic Logic 7 (4):170.
The Inconsistency of Certain Formal Logic.Haskell B. Curry - 1942 - Journal of Symbolic Logic 7 (3):115-117.
Paradoxes.John Myhill - 1984 - Synthese 60 (1):129 - 143.
A Method for Avoiding the Curry Paradox.Frederic B. Fitch - 1969 - In Nicholas Rescher (ed.), Essays in Honor of Carl G. Hempel. Reidel. pp. 255--265.

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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.
Variations on a Theme of Curry.Lloyd Humberstone - 2006 - Notre Dame Journal of Formal Logic 47 (1):101-131.
Abstraction in Algorithmic Logic.Wayne Aitken & Jeffrey A. Barrett - 2008 - Journal of Philosophical Logic 37 (1):23-43.
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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