Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!mailrus!cs.utexas.edu!swrinde!emory!wuarchive!decwrl!shelby!neon!geddis
From: geddis@Neon.Stanford.EDU (Donald F. Geddis)
Newsgroups: comp.ai
Subject: Re: What is a Symbol System?
Keywords: computation, symbol manipulation, syntax, formality
Message-ID: <1989Nov20.203823.24602@Neon.Stanford.EDU>
Date: 20 Nov 89 20:38:23 GMT
References: <11640@phoenix.Princeton.EDU> <32690@ucbvax.BERKELEY.EDU>
Sender: USENET News System <news@Neon.Stanford.EDU>
Reply-To: Geddis@CS.Stanford.EDU (Donald F. Geddis)
Organization: Computer Science Department, Stanford University
Lines: 15

In article <32690@ucbvax.BERKELEY.EDU> fateman@renoir.Berkeley.EDU.UUCP (Richard Fateman) writes:
>If you believe the syntactic rules (a^b)^c <--> a^(b*c) and a*b <--> b*a  then
>-1 = (-1)^1 = (-1)^(2* (1/2)) = ((-1)^2)^1/2) = 1^(1/2) = 1.

1^(1/2) = (-1 or 1), not just 1.  Your last step was not one of the "syntactic
rules" that I "believe".

If you reverse the order, so you start with 1=1 and then go to 1=1^(1/2), that
is false, in the strict sense.  The left-hand side is equivalent to 1, while
the right-hand side is equivalent to (-1 or 1).

	-- Don Geddis
-- 
Geddis@CS.Stanford.Edu
"There is no dark side of the moon, really.  Matter of fact, it's all dark."