Torkel Franzen on truth
in [Logic]
|
From: G. Frege on 20 Dec 2007 21:54 On Thu, 20 Dec 2007 17:19:22 -0800 (PST), MoeBlee <jazzmobe(a)hotmail.com> wrote: > > I just love your 0 = {x | Ay ~yex} ... > On the other hand, 0 = x <-> Ay ~yex is just fine. :-) [I'm sure that this is what he originally had in mind here. ;-)] F. -- E-mail: info<at>simple-line<dot>de
From: MoeBlee on 20 Dec 2007 22:51 On Dec 20, 6:44 pm, G. Frege <nomail(a)invalid> wrote: > On Thu, 20 Dec 2007 18:16:17 -0800 (PST), MoeBlee <jazzm...(a)hotmail.com> > wrote: > > G. Frege, I basically agree with you and Peter that Peter is well > > within his intellectual prerogative to give a stipulative definition > > of 'formal language' so that a formal language has both a formal > > syntax and formal semantics, which also is in general lines of > > agreement with the Church quote you gave. But, just to be clear, the > > above quote doesn't say that a language has both a syntax and > > semantics. Rather, the above quote says that a LOGIC has a language, a > > deduction system, and a semantics. > > Sure. I now that. I posted it to back up /george's/ position (just to be > fair). Ah, that makes sense. > george: "There simply now IS a restricted sense of "formal language" in > which certain sets of strings are formal languages." > > --- You see, he's right. Of course we know that there are senses in which a formal language is a set of strings, also a sense in which the language is taken not to be the set of strings but rather a tuple that "encodes" a certain signature and sets of kinds of symbols (cf., e.g. Monk's textbook, which, for its elegance and rigor, I think is one of the best definitions of 'first order language'), and other senses of language as purely syntactical. But there are other notions (even if more in the minority these days) in which a language is a syntax and a semantics. And even of a language as a syntax, semantics, and pragmatics. And perhaps other conceptions of 'language' and 'formal language'. So, as long as Peter is clear that he's just giving his definition for the purpose of conveying his exposition, I see nothing wrong in that, and more power to him. MoeBlee
From: MoeBlee on 20 Dec 2007 22:59 On Dec 20, 6:54 pm, G. Frege <nomail(a)invalid> wrote: > On Thu, 20 Dec 2007 17:19:22 -0800 (PST), MoeBlee <jazzm...(a)hotmail.com> > wrote: > > > > > I just love your 0 = {x | Ay ~yex} ... > > On the other hand, > > 0 = x <-> Ay ~yex > > is just fine. :-) > > [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. MoeBlee
From: G. Frege on 20 Dec 2007 23:05 On Thu, 20 Dec 2007 19:51:17 -0800 (PST), MoeBlee <jazzmobe(a)hotmail.com> wrote: > > Of course we know that there are senses in which a formal language is > a set of strings, also a sense in which the language is taken not to > be the set of strings but rather a tuple that "encodes" a certain > signature and sets of kinds of symbols (cf., e.g. Monk's textbook, > which, for its elegance and rigor, I think is one of the best > definitions of 'first order language'), and other senses of language > as purely syntactical. > > But there are other notions (even if more in the minority these days) > in which a language is a syntax and a semantics. And even of a > language as a syntax, semantics, and pragmatics. And perhaps other > conceptions of 'language' and 'formal language'. > > So, as long as Peter is clear that he's just giving his definition for > the purpose of conveying his exposition, I see nothing wrong in that, > and more power to him. > I guess this (your account) is a reasonable approach. george, on the other hand, originally claimed: "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." And _that_ (i.e. george's last claim) is certainly not reasonable (imho). F. -- E-mail: info<at>simple-line<dot>de
From: Newberry on 20 Dec 2007 23:12
On Dec 17, 6:54 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > Newberry says... > > >Let me see if I can summarize your position. > >a) The human neural system does not surpass the Turing machine. > > Yes, I believe that. > > >b) We are NOT equivalent to any theory PA, ZFC, ZFC + an axiom of > >infity, T_3, T_4 for any n > > It depends on what you mean by being "equivalent". Humans don't > *have* a fixed theory. We can be talked into accepting statements > as true, but there is no good reason to think that we are perfectly > consistent about it. Perhaps a human could be talked into believing > the Continuum Hypothesis, but with a different argument, could be > talked into believing its negation. > > Humans are not very usefully characterized by a formal theory. > > >c) We are programmed as a heuristic learning algorithm > > I would say that we *have* heuristic learning algorithms. > I wouldn't say that we *are* those algorithms, or that we > were *programmed* (unless you want to call natural selection > a form of programming). > > >d) Mathematics is at least partially an empirical science > > Yes. > > >Is this a fair characterization of your position? > > Pretty good. I think that c) and d) are absurd. |