Arithmetical and specular self-reference

Acta Analytica 19 (33):55-63 (2004)
Abstract
Arithmetical self-reference through diagonalization is compared with self-recognition in a mirror, in a series of diagrams that show the structure and main stages of construction of self-referential sentences. A Gödel code is compared with a mirror, Gödel numbers with mirror images, numerical reference to arithmetical formulas with using a mirror to see things indirectly, self-reference with looking at one’s own image, and arithmetical provability of self-reference with recognition of the mirror image. The comparison turns arithmetical self-reference into an idealized model of self-recognition and the conception(s) of self based on that capacity.
Keywords Gödel code  mirroring  diagonalization  self-reference  self-recognition
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DOI 10.1007/s12136-004-1012-9
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Gödel's Proof.Ernest Nagel - 1958 - New York University Press.
Languages in Which Self Reference is Possible.Raymond M. Smullyan - 1957 - Journal of Symbolic Logic 22 (1):55-67.
Consciousness as Self-Function.Donald R. Perlis - 1997 - Journal of Consciousness Studies 4 (4-5):509-25.

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