Journal of Philosophical Logic 36 (1):61-95 (2007)

Authors
Jeffrey Barrett
University of California, Irvine
Abstract
There is significant interest in type-free systems that allow flexible self-application. Such systems are of interest in property theory, natural language semantics, the theory of truth, theoretical computer science, the theory of classes, and category theory. While there are a variety of proposed type-free systems, there is a particularly natural type-free system that we believe is prototypical: the logic of recursive algorithms. Algorithmic logic is the study of basic statements concerning algorithms and the algorithmic rules of inference between such statements. As shown in [1], the threat of paradoxes, such as the Curry paradox, requires care in implementing rules of inference in this context. As in any type-free logic, some traditional rules will fail. The first part of the paper develops a rich collection of inference rules that do not lead to paradox. The second part identifies traditional rules of logic that are paradoxical in algorithmic logic, and so should be viewed with suspicion in type-free logic generally.
Keywords Philosophy
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Reprint years 2007
DOI 10.1007/s10992-005-9024-5
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References found in this work BETA

Toward Useful Type-Free Theories. I.Solomon Feferman - 1984 - Journal of Symbolic Logic 49 (1):75-111.
The Consistency of The Naive Theory of Properties.Hartry Field - 2004 - Philosophical Quarterly 54 (214):78-104.
Property Theory and the Revision Theory of Definitions.Francesco Orilia - 2000 - Journal of Symbolic Logic 65 (1):212-246.

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Citations of this work BETA

Abstraction in Algorithmic Logic.Wayne Aitken & Jeffrey A. Barrett - 2008 - Journal of Philosophical Logic 37 (1):23-43.
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.
Abstraction in Fitch's Basic Logic.Eric Thomas Updike - 2012 - History and Philosophy of Logic 33 (3):215-243.

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