Torkel Franzen on truth
in [Logic]
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From: G. Frege on 20 Dec 2007 23:10 On Thu, 20 Dec 2007 19:59:04 -0800 (PST), MoeBlee <jazzmobe(a)hotmail.com> wrote: >> >> [I'm sure that this is what he originally had in mind here. ;-)] >> > But what makes it egregious is that he was, in his usually charming > way, storming in tell everybody else that they're wrong (they > weren't), and even breathing fire about getting the definition wrong > when it wasn't even a DEFINITION that was at stake. > Yes, yes, we know good old george. :-) On the other hand, his posting manners have improved considerably in recent years. (Did you notice that?) F. -- E-mail: info<at>simple-line<dot>de
From: herbzet on 21 Dec 2007 01:37 Peter_Smith wrote: > george wrote: > > Prof.Smith and I have been talking, for example, about the > > intended model vs. the formal language. He is the one who > > said that he didn't think formal languages should even be referred > > to as a language. That is considerably less defensible than anything > > *I* have ever said. > > What I said was that uninterpreted syntax is just that, uninterpreted. > So not (yet) a vehicle for communicating anything. And so, in the > ordinary sense of the term, not a language. Hardly an indefensible > view. > > If some logicians, and according to George, many/most computer > scientists do talk of uninterpreted syntax as a language (without > qualification) then fine as long as the jargon is made clear: but it > *is* in that usage specialist jargon, and not -- to my mind -- > entirely happy jargon as it is potentially misleading in various ways. > I hesitate to add "as evidenced here". I just want to mention that the FOL theories under discussion don't come as entirely uninterpreted syntax. The logical operators (sentence connectives, quantifiers) come pre-installed with meaning. The "interpretation", in one technical sense, is confined to equipping the predicates with reference, and supplying a domain of discourse for that purpose. If the language contains constants and/or function symbols, they too will have to be "interpreted" to have a fully interpreted language. If you consider the sign for equality a logical symbol, its meaning will be conferred by the axioms concerning it. -- hz
From: Peter_Smith on 21 Dec 2007 04:03 On 21 Dec, 00:02, george <gree...(a)cs.unc.edu> wrote: > What assigns meanings to the wffs of the system is DESIGNATING > SOME OF THEM AS AXIOMS. Really? Well that sounds like magic to me. If I tell you that "mae glo yn du" is true in Welsh [heck, hope I've remembered that right], you don't thereby get to know what it means. Telling you the same about some other Welsh sentences won't help either. Telling you that in my fave axiomatized system "Fa" is an axiom (or is an axiom and true), you don't thereby get to know what it means. Telling you the same about some other sentences of the system won't help either.
From: G. Frege on 21 Dec 2007 08:07 On Thu, 20 Dec 2007 16:02:16 -0800 (PST), george <greeneg(a)cs.unc.edu> wrote: > > What assigns meanings to the wffs of the system is DESIGNATING > SOME OF THEM AS AXIOMS. This is an act that does have semantic > content simply because axioms have to be true [...]. > Wait a second. Aren't those axioms /true/ only when /interpreted/ (i.e. in a model)? Hence isn't it the /interpretation/ that assigns truth to an axiom? F. -- E-mail: info<at>simple-line<dot>de
From: herbzet on 21 Dec 2007 15:30
"G. Frege" wrote: > > On Thu, 20 Dec 2007 16:02:16 -0800 (PST), george <greeneg(a)cs.unc.edu> > wrote: > > > > > What assigns meanings to the wffs of the system is DESIGNATING > > SOME OF THEM AS AXIOMS. This is an act that does have semantic > > content simply because axioms have to be true [...]. > > > Wait a second. Aren't those axioms /true/ only when /interpreted/ > (i.e. in a model)? Hence isn't it the /interpretation/ that assigns > truth to an axiom? Well, they're true in all their models, by definition. Last time George and I spoke on this point, he was of the opinion, if I understood him correctly, that interpreting the axioms in structures which falsify (one or more of) them doesn't count -- axioms are always taken as true regardless of how they are interpreted; interpretation is otiose. I'll admit it seems like a rather pointless exercise to interpret axioms in structures in which they are false, it just happens to be involved in the Tarskian conception of logical consequence: in those structures too the axioms imply their theorems /and nothing else/. -- hz |