Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!linus!philabs!cmcl2!seismo!caip!princeton!allegra!alice!ark
From: ark@alice.UucP (Andrew Koenig)
Newsgroups: talk.philosophy.misc
Subject: Re: Emotion and Logic
Message-ID: <6068@alice.uUCp>
Date: Tue, 16-Sep-86 18:29:55 EDT
Article-I.D.: alice.6068
Posted: Tue Sep 16 18:29:55 1986
Date-Received: Fri, 19-Sep-86 07:23:54 EDT
References: <15679@ucbvax.BERKELEY.EDU>
Organization: Bell Labs, Murray Hill
Lines: 11

>   If we were lucky to live in a world with infinite objects in it,
>we would probably have another natural number incorporated to our
>arithmetic, i.e. the number used to count an infinite set of chairs (or
>splitzleboards), which we may call: INF. Our arithmetic will be like:
>19+INF=INF, INF*INF=INF, "INF is the greatest natural number" (note
>that we don't have such natural number in our current arithmetic!),
>and so on.

Maybe yes, maybe no.  The trouble is that once you introduce INF,
you give up some other useful properties of natural numbers,
such as cancellation (x+z=y+z implies x=y).