Jamie wrote: > If there any viable system in which you -can- > both derive, and find useful application for, > the equation 0=1 ? (Of course If = Is, no logic applied<G>) The question shifts to "viable". What is a 'viable' system? MAYBE that what we find so (--> in our HUMAN logic, formally represented in Bruno's post). We have allowances even in that: we can think about a logical system, where 0 = 1 indeed. Where quantities are cut out and every numerical means just numerical. We usually don't use such, but "possible" it is, not in the sense as I questioned Hal's "all possible systems". (In human logic, that is).
Usually, however, I would say that the 0 = 1 logical system is NOT within our "possible systems" (humanly identified). It requires a different logic from the one we ordinarily apply - which does not make it "impossible" though. I personally (in my theoretical cravings) don't like "equations" because they deal with fixed model-quantities cutting off connotations beyond the set boundaries of our topical reduction. Of course in such 'open' wholistic thinking I cannot reach practical cponclusions (Yet? a good question). 0=1ly yours John Mikes ----- Original Message ----- From: "James N Rose" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Tuesday, November 30, 2004 10:09 AM Subject: Re: An All/Nothing multiverse model > If there any viable system in which you -can- > both derive, and find useful application for, > the equation 0=1 ? > > James Rose > > > Bruno Marchal wrote: > > > > At 13:40 26/11/04 -0500, Hal Ruhl wrote: > > >What does "logically possible" mean? > > > > A proposition P is logically possible, relatively to > > 1) a consistent set of beliefs A > > 2) the choice of a deduction system D (and then consistent > > means "does not derive 0=1). > > > > if the negation of P is not deductible (in D) from A. > > > > Concerning many theories, to say that a proposition > > (or a set of propositions) A is logically possible > > is the same as saying that A is consistent (i.e you > > cannot derive 0 = 1 from it), or saying that A has a > > model (a reality, a mathematical structure) satisfying > > it. > > > > Bruno > > > > http://iridia.ulb.ac.be/~marchal/ >