Dave writes in relevant part: > also, if the Turing machine, the programmer, and the 'user' form an > appropriate triad, might it be said that the Turing machine 'knows' what > the programmer programmed and the user observes? None of the three > elements "possess" that knowledge in isolation, but 'triadically' they > all do.
I really like this formulation, except that I would go all the way and say that it's the triad (rather than any one or two of "Turing machine", "programmer", "user") that "knows" [something]. At least, with "Turing machine" replaced by something like "partly formalized proof", it can happen (and has happened to me more than once, sometimes with me in the role of "programmer"="formulator of partly formalized proof", and sometimes with me in the role of "user"="understander of partly formalized proof"--where the latter has, again more than once, been either "myself-at-later-time-stage-of-formulator" or "myself-as-different-person-than-formulator") that the second of these two triads "knows" something other than what the first knew (specifically, that the proof actually proved more than what it was claimed to prove; of course, the other case, where it didn't prove what it claimed, also happens but then it may not be fair to say "know" for the earlier state of affairs, depending on whether or not you epistemology insists that only truths can be known). Of course a "partly formalized proof" is not a Turing machine, but some of the programs people have been creating lately for doing various mathematical tasks (theorem verification, theorem generation) really are TMs, and I see no reason why similar phenomena couldn't happen there as well. ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives back to 2003: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
