Xref: utzoo comp.ai:6159 sci.philosophy.tech:2184 Path: utzoo!utgpu!jarvis.csri.toronto.edu!cs.utexas.edu!swrinde!zaphod.mps.ohio-state.edu!uakari.primate.wisc.edu!aplcen!uunet!mcsun!ukc!sys.uea!jrk From: jrk@sys.uea.ac.uk (Richard Kennaway) Newsgroups: comp.ai,sci.philosophy.tech Subject: Re: Another letter to the New York Review Keywords: Penrose, Moravec Message-ID: <1339@sys.uea.ac.uk> Date: 4 Mar 90 12:07:48 GMT References: <18883@bcsaic.UUCP> <1589@skye.ed.ac.uk> <11488@venera.UUCP> <1754@skye.ed.ac.uk> <90Feb15.231415est.6212@neat.cs.toronto.edu> <2al902Zg8bnn01@amdahl.uts.amdahl.com> <3750@uceng.UC.EDU> radford@ai.toronto.edu (Radford Neal) writes: >In article kp@amdahl.uts.amdahl.com (Ken Presting) writes: >>Of course, computers are entirely > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ >>adequate to implement deductive systems, by the Church-Turing thesis. > ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ >I think you're suffering from a lack of imagination here. Penrose is >of course denying that computers are adequate to implement any >deductive system, if by "deductive system" you mean the process by >which real mathematicians establish new truths. If you're to understand >his argument, you have to try to imagine how this might be true. >Let's say that one day Penrose announces that he is able to solve, say, >the word problem for semi-groups - a well-known non-computable problem. >People give him instances of this problem. After a period of time >that goes up only reasonably with the size of the instance he announces >the answer: YES or NO. In those cases where the true answer is >subsequently determined, he always turns out to be right. This holds >even for very difficult cases that require increasingly subtle >arguments to establish that the answer is NO, as well as cases where >extremely complex reductions are needed to demonstrate that the answer >is YES. >I think it would be quite reasonable to conclude in the above situation >that Penrose can somehow perform non-computable operations, and hence >that the laws of physics must also be non-computable. You could construct >a similar scenario in which the word problem is solved by some physical >computer (obviously not Turing equivalent), rather than by a human being. And if pigs had wings they could fly. So what? -- Richard Kennaway SYS, University of East Anglia, Norwich, U.K. Internet: jrk@sys.uea.ac.uk uucp: ...mcvax!ukc!uea-sys!jrk