Self-referential theories

Journal of Symbolic Logic 85 (4):1687-1716 (2020)
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Abstract

We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing index for itself, and contains some other mild axioms, then that theory is untrue. We exhibit some families of true self-referential theories that barely avoid this forbidden pattern.

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10.1017/jsl.2020.54

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Samuel Allen Alexander
Ohio State University (PhD)

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References found in this work

Minds, Machines and Gödel.John R. Lucas - 1961 - Philosophy 36 (137):112-127.
Minds, Machines and Gödel.J. R. Lucas - 1961 - Etica E Politica 5 (1):1.
God, the Devil, and Gödel.Paul Benacerraf - 1967 - The Monist 51 (1):9-32.
God, the Devil, and Gödel.Paul Benacerraf - 2003 - Etica E Politica 5 (1):1-15.

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