The Definition of Points
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From: Tony Orlow on 13 Apr 2007 13:45 Lester Zick wrote: > On Thu, 12 Apr 2007 14:31:52 -0400, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Lester Zick wrote: >>> On Sat, 31 Mar 2007 20:51:49 -0500, Tony Orlow <tony(a)lightlink.com> >>> wrote: >>> >>>> A logical statement can be classified as true or false? True or false? >>> You show me the demonstration of your answer, Tony, because it's your >>> question and your claim not mine. >>> >>> ~v~~ >> I am asking you whether that statement is true or false. If you have a >> third answer, I'll be happy to entertain it. > > The point being, Tony, that you don't have a first answer much less a > second or third. You can't tell me or anyone else what it means to be > true in mechanically exhaustive terms. Mathematikers routinely demand > students deal in the most exacting exhaustive mechanical terms with > axioms, theorems, and doctrines of their own. Yet the moment they're > required to deal with their own axioms, doctrines, and assumptions of > truth in mechanically exhaustive terms they shy away with complaints > no one can expect to prove the truth of what they assume to be true. > > You draw up all kinds of binary "truth" tables as if they meant or had > to mean something in mechanically exhaustive terms and demand others > deal with them in binary terms you set forth. Yet you can't explain > what you mean by "truth" or "falsity" in mechanically exhaustive terms > to begin with. So how do you expect anyone to deal with truth tables? > > ~v~~ Just answer the question above. 01oo
From: MoeBlee on 13 Apr 2007 13:48 On Apr 13, 10:21 am, Tony Orlow <t...(a)lightlink.com> wrote: > MoeBlee wrote: > > On Apr 12, 12:27 pm, Tony Orlow <t...(a)lightlink.com> wrote: > >> MoeBlee wrote: > >>> On Mar 31, 5:39 am, Tony Orlow <t...(a)lightlink.com> wrote: > >>>> In order to support the notion of aleph_0, one has to discard the basic > >>>> notion of subtraction in the infinite case. That seems like an undue > >>>> sacrifice to me, for the sake of nonsense. Sorry. > >>> For the sake of a formal axiomatization of the theorems of ordinary > >>> mathematics in analysis, algebra, topology, etc. > >>> But please do let us know when you have such a formal axiomatization > >>> but one that does have cardinal subtraction working in the infinite > >>> case just as it works in the finite case. > >>> MoeBlee > >> Sorry, MoeBlee, but when I produce any final product in this area, > >> cardinality will be a footnote, and not central to the theory. As I work > >> on other things, so do I work on this. > > > I really don't care what you work on. My point is that your commentary > > in these threads has virtually no formal mathematical import, as it > > comes down to a bunch of whining that your personal notions are not > > embodied in set theory even though you can't point to a formal system > > (either published or of your own, and the gibberish you've posted in > > threads and on your own site is not even a corhernt attempt toward a > > formal system) that does embody your personal notions and you can't > > even HINT at what such a system might be. > > > MoeBlee > > What does any of your whining have to do with the definition of points? The topic (as even quoted in inclusion in this post) was broader than the mere "definition of points", whatever you mean by "definition of points". > This is tiresome. Quite so. It would be most refreshing if you replied with some actual (your terminological gibberish does not qualify) mathematics (whether standard fare or original recipe, both are welcome) for a change. MoeBlee
From: Tony Orlow on 13 Apr 2007 13:49 Lester Zick wrote: > On Thu, 12 Apr 2007 14:30:32 -0400, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Lester Zick wrote: >>> On Sat, 31 Mar 2007 21:14:27 -0500, Tony Orlow <tony(a)lightlink.com> >>> wrote: >>> >>>>>> You need to define what relation your grammar denotes, or there is no >>>>>> understanding when you write things like "not a not b". >>> What grammar did you have in mind exactly, Tony? >> Some commonly understood mapping between strings and meaning, basically. >> Care to define what your strings mean? :)1oo > > What strings? Care to define what your "mappings" "between" "strings" > and "meaning" mean, Tony? Then we can get to the basis of grammar. > >>>>> Of course not. I didn't intend for my grammar to denote anything in >>>>> particular much as Brian and mathematikers don't intend to do much >>>>> more than speak in tongues while they're awaiting the second coming. >>>>> >>>> Then, what, you're not actually saying anything? >>> Of course I am. > > ~v~~ You do know what "strings" are, don't you? And grammar? And language? And, um, meaning? What's the difference between a duck? 01oo
From: Tony Orlow on 13 Apr 2007 13:56 Lester Zick wrote: > On 12 Apr 2007 14:07:53 -0700, "MoeBlee" <jazzmobe(a)hotmail.com> wrote: > >> On Apr 12, 11:30 am, Tony Orlow <t...(a)lightlink.com> wrote: >>> Lester Zick wrote: >>>> What grammar did you have in mind exactly, Tony? >>> Some commonly understood mapping between strings and meaning, >>> basically. >> Grammar is syntax, not meaning, which is semantics. What you just >> described, an intrepative mapping from strings to meanings of the >> strings is semantics, not grammar. > > Gee that's swell, Moe(x). Thanks for the lesson in semantics if not > much of anything else. Next time we need a lesson in modern math don't > call us we'll call you. > > ~v~~ Well, of course, Moe's technically right, though I originally asked Lester to define his meaning in relation to his grammar. Technically, grammar just defines which statements are valid, to which specific meanings are like parameters plugged in for the interpretation. I asked the question originally using truth tables to avoid all that, so that we can directly equate Lester's grammar with the common grammar, on that level, and derive whether "not a not b" and "not a or not b" were the same thing. They seem to be. One more time, is this correct, for the four combinations of a and b being true or false? a b "not a not b" F F T F T T T F T T T F 01oo
From: MoeBlee on 13 Apr 2007 14:01
On Apr 13, 10:38 am, Tony Orlow <t...(a)lightlink.com> wrote: > MoeBlee wrote: > > Zermelo's motivation was to prove that for every set, there exists a > > well ordering on it. > I am not sure how the Axiom of Choice demonstrates that. You don't know how the axiom of choice is used to prove that for every set there exists a well ordering of the set? Virtually any set theory textbook will give a cycle of proofs showing equivalence of (not necessarily in order) the axiom of choice (in its various formulations), Zorn's lemma, the well ordering theorem, the numeration theorem, etc. Among those textbooks I recommend Stoll's 'Set Theory And Logic' as it accomplishes some of the proofs without using the axiom schema of replacement while other textbooks do use the axiom schema of replacement for certain of the proofs, though, I don't recommend Stoll's book for an overall systematic treatment since it jumps around topics too much and doesn't have the kind of "linear" format that Suppes does so well. Anyway, even if you don't know the details of the proofs, don't you at least have an intuition how a choice function would come in handy toward proving the well ordering theorem? MoeBlee |