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.
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Bojadžiev, D. Arithmetical and specular self-reference. Acta Anal 19, 55–63 (2004). https://doi.org/10.1007/s12136-004-1012-9
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DOI: https://doi.org/10.1007/s12136-004-1012-9