The Definition of Points
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From: MoeBlee on 18 Apr 2007 18:44 On Apr 18, 3:17 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: P.P.S. Tony, in view of the fact that the link I gave is more concerned with historical aspects, I want to emphasize that I strongly believe that the way to understand set theory is to study one or two systematic and modern textbook treatments. The idea is to know a particular treatment that is the culmination of the historical process but is not bound to any informality, vagueness or problems that might be found in late 19th and early 20th century developments that have since been supplanted by systems that can be made fully rigorous. Especially, Cantor's own treatments are not at issue since his pre- formal theory and even Zermelo's own initial pre-formal theories have been supplanted by Z and various set theories that can be read in a way that we can see them as being formalizable with perfect rigor. Also, note that when talking about well ordering, sometimes when it gets down to the real technical nitty gritty, you have to be careful to distinguish between a well ordering that is reflexive (I call that a 'weak well ordering') and a well ordering that is irreflexive (I call that a 'strict well ordering' or just a 'well ordering') since different authors use 'well ordering' in those two different ways, and if you're fail to note which sense the author means, then you can be led to some erroneous conclusions. MoeBlee
From: Lester Zick on 18 Apr 2007 18:52 On Wed, 18 Apr 2007 12:40:56 -0700, Bob Cain <arcane(a)arcanemethods.com> wrote: >Alan Smaill wrote: >> Phil Carmody <thefatphil_demunged(a)yahoo.co.uk> writes: >>> >>> Can I have a coffee without milk? >>> I'm sorry, we don't have any milk. >>> Ah, OK, how about a coffee without cream? >> >> like the silent "k" in "frying pan" >> > >Note to Lester. The above contains demonstrations of wit. Perhaps, >by example, you can learn something both about wit and about >demonstration. Whereas from you I can learn something about being witless. ~v~~
From: Lester Zick on 18 Apr 2007 19:42 On Wed, 18 Apr 2007 14:31:35 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Tue, 17 Apr 2007 12:20:01 -0400, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>>> What question? You seem to think there is a question apart from >>>> whether a statement is true or false. All your classifications rely on >>>> that presumption. But you can't tell me what it means to be true or >>>> false so I don't know how to answer the question in terms that will >>>> satisfy you. >>>> >>>> ~v~~ >>> A logical statement can be classified as true or false? True or false? >> >> A logical statement as opposed to what, Tony? > >As opposed to, say, an arithmetic formula. So arithmetic formulas are not logical? >>> In other words, is there a third option, for this or any other statement? >> >> Hard to tell without seeing the statement. >> >> ~v~~ > >No, it's up to you. Good. The logical statement "it is black" is true. > A logical statement is one that has some measure of >truth, from false to true. One can consider just false and true, or one >can consider a multilevel logic like a scale from 1 to 10, or even a >probabilistic logic with all real values from 0 through 1. Since you >only speak of truth versus falsity, I imagine you are considering the >first type, or Boolean binary logic. So "black is crow" is either true or false? Or is not a logical statement? 'Fraid you'll just have to help me out here, Tony. Just tell me what you want me to say. ~v~~
From: Lester Zick on 18 Apr 2007 19:47 On Wed, 18 Apr 2007 21:51:14 +0000 (UTC), stephen(a)nomail.com wrote: >That does not make any sense. There is no point in giving a nonsensical >answer, unless you are aiming to emulate Lester. Or intent on emulating yourself, Mike, Virgil, or any of the other gang of four horses asses of the apocalypse. ~v~~
From: Lester Zick on 18 Apr 2007 19:49
On Wed, 18 Apr 2007 14:55:43 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Tue, 17 Apr 2007 13:33:39 -0400, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>>>> Is there a set >>>>> of statements S such that forall seS s=true? >>>> No idea, Tony. There looks to be a typo above so I'm not sure exactly >>>> what you're asking. >> >>> I am asking, in English, whether there is a set of all true statements. >> >> No. There are predicates to which all true statements and all false >> statements are subject respectively but no otherwise exhaustively >> definable set of all true or false statements because the difference >> between predicates and predicate combinations in true or false >> statements is subject to indefinite subdivision. >> >> ~v~~ > >Uh, what? Uh, whatever. Next time pay attention the first time around. ~v~~ |