Tomas Petricek's Cultures of Programming - 5. Fundamental limits of proofs of programs

See https://tomasp.net/cultures/ and these earlier post of mine.

My comment:

40:06 That's really interesting. I'd never heard of Fetzer before. The "Machine as empirical description" seems not to have been much appreciated by the MIT AI people in the early eighties. See for example the introduction in Jon Doyle's 1980 PhD thesis A Model for Deliberation, Action and Introspection. The sense then in which proof is empirical knowledge is entirely predicated on the machine actually behaving in the way its formal description says it does. So for example if a track on the PCB is cut at a certain place then your empirical knowledge about the device is quite possibly not worth anything. So empirical knowledge doesn't really sound like the right way to describe a proof. It's interesting that a year before Brian Cantwell Smith wrote that commentary on proof he wrote Reflection and semantics in LISP which led to all that "reflective towers of interpreters" stuff. Doyle in his thesis (page 1 footnote 1) thought that describing a machine (by a lisp program emulating it) was identical with a machine (modulo some hardware for I/O), the description being in some sense an abbreviation of the actual thing, from which follows some philosophically amazing consequences which John Searle talks eloquently about.

See Nada Amin - Metacircular Interpretation ad infinitum and also John Searle's Chinese Room Argument and John Searle - Syntax is Observer-Relative.

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