gburton@maytag.waterloo.edu (Grant Burton) (06/21/91)
In article <1991Jun19.033316.18773@athena.mit.edu> mlevin@jade.tufts.edu writes: > I was just reading Z. Pylyshin's "Computation and Cognition", and >at one point, he states something like: "the number of distinct human >thoughts is uncountable." Does anyone have any arguments for or >against the idea that the number of possible distinct human thoughts >(or mental states) is uncountably infinite? Note I do not mean >"astronomicallly large" - I mean infinite (and perhaps uncountably so) >in the strict mathematical sense. It seems plausible to me; does >anyone have a good argument either way? > >Mike Levin I do too many bizarre philosophy courses. It has warped my mind. Anyway I do have the right to voice my opinion, so here it is: Premise. My mind is a concequent of my brain. My brain is contained within a finite space. I am not an expert on the workings of the brain, but I am assuming that the underlying hardware (my gray stuff) uses finite elements of computation/cognition. For example neurons/atoms/electrons. There are a finite number of these, within a finite amount of space, much like the finite number of electronic components of a computer system. Conclusion. Then I am nothing more that a finite state machine (yes, just like modern day computers with a finite hardware capacity). Should we be able to show that the number of distinct thoughts/states are infinite, then I am more than a finite state machine. Implications. If the premise and conclusion are correct then we can argue that we can indeed have an infinte number of thoughts, but only those that can be enumerated via a regular language. If it can be shown that an infinite number of thoughts do not fit a regular language, then my mind must be above a finite state machine, since I can generate this non regular language. What does this mean? Either my premise is false, or we need a new model of computation since I am more than a finite state machine whose cognitive/computational power results from finite hardware (my brain). -Grant -- gburton@maytag.waterloo.edu /\ Department of Computer Science / \ University of Waterloo ________/ \ /\_______________________________ Waterloo, Ontario \/ The heartbeat of Ontario