Abstract
Raymond Smullyan was born in 1919, after the Great War and before the Great Depression. I have known him since I was a graduate student and he was my advisor.
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Notes
- 1.
I omit discussion of his lives as pianist and as magician.
- 2.
Elegant is the word most often used about Raymond’s work in reviews.
- 3.
Raymond also explored the topic more technically in his book Diagonalization and Self-Reference, (Smullyan 1994).
- 4.
We follow the standard mathematical practice of identifying properties with sets, and application of a property as membership in the set. Still, we continue to use the word property.
- 5.
Technically this function is not itself a set, but is characterized by a first-order formula in the language of set theory. We don’t need such details for what we are doing now. It suffices to note that everything thus far is legitimate in generally accepted formal set theories.
- 6.
Older usage calls computable functions recursive functions, and computably generated relations recursively enumerable relations. In recent years terminology has shifted.
References
Boolos, G. (1979). The Unprovability of Consistency. Cambridge University Press.
Solovay, R. M. (1976). Provability interpretation of modal logic. Israel Journal of Mathematics, 25, 287–304.
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Fitting, M. (2017). Introduction. In: Fitting, M., Rayman, B. (eds) Raymond Smullyan on Self Reference. Outstanding Contributions to Logic, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-68732-2_1
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