The Definition of Points
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From: Lester Zick on 17 Apr 2007 18:02 On Tue, 17 Apr 2007 13:24:30 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <4624ff57(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> Mike Kelly wrote: > >> > And what does AC have to do with cardinality? >> >> What do any of the axioms of ZFC have to do with cardinality? >> Extensionality. > >Which of those axioms, or combination of axioms, is extensionally >equivalent to cardinality? 1, 2, 3 . . . ~v~~
From: Lester Zick on 17 Apr 2007 18:04 On 17 Apr 2007 14:12:41 -0700, Mike Kelly <mikekellyuk(a)googlemail.com> wrote: >You've lost me again. A bad analogy is like a diagonal frog. And a good analogy is like a diagonal metaphor. Either way you stay lost. Which is pretty much where you began. ~v~~
From: Lester Zick on 17 Apr 2007 18:06 On Tue, 17 Apr 2007 21:19:22 +0000 (UTC), stephen(a)nomail.com wrote: >In sci.math Tony Orlow <tony(a)lightlink.com> wrote: >> Mike Kelly wrote: >>> >>> The point that it DOESN'T MATTER whther you take cardinality to mean >>> "size". It's ludicrous to respond to that point with "but I don't take >>> cardinality to mean 'size'"! >>> >>> -- >>> mike. >>> > >> You may laugh as you like, but numbers represent measure, and measure is >> built on "size" or "count". > >What "measure", "size" or "count" does the imaginary number i represent? 46 > Is i a number? A definite maybe. >The word "number" is used to describe things that do not represent any sort of "size". Example of a number that doesn't represent any sort of size? ~v~~
From: Lester Zick on 17 Apr 2007 18:11 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? >In other words, is there a third option, for this or any other statement? Hard to tell without seeing the statement. ~v~~
From: Lester Zick on 17 Apr 2007 18:18
On Tue, 17 Apr 2007 12:20:59 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Fri, 13 Apr 2007 14:33:20 -0400, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>> Lester Zick wrote: >>>> On Thu, 12 Apr 2007 14:35:36 -0400, Tony Orlow <tony(a)lightlink.com> >>>> wrote: >>>> >>>>> Lester Zick wrote: >>>>>> On Sat, 31 Mar 2007 20:58:31 -0500, Tony Orlow <tony(a)lightlink.com> >>>>>> wrote: >>>>>> >>>>>>> How many arguments do true() and false() take? Zero? (sigh) >>>>>>> Well, there they are. Zero-place operators for your dining pleasure. >>>>>> Or negative place operators, or imaginary place operators, or maybe >>>>>> even infinite and infinitesimal operators. I'd say the field's pretty >>>>>> wide open when all you're doing is guessing and making assumptions of >>>>>> truth. Pretty much whatever you'd want I expect.Don't let me stop you. >>>>>> >>>>>> ~v~~ >>>>> Okay, so if there are no parameters to the function, you would like to >>>>> say there's an imaginary, or real, or natural, or whatever kind of >>>>> parameter, that doesn't matter? Oy! It doesn't matter. true() and >>>>> false() take no parameters at all, and return a logical truth value. >>>>> They are logical functions, like not(x), or or(x,y) and and(x,y). Not >>>>> like not(). That requires a logical parameter to the function. >>>> Tony, you might just as well be making all this up as you go along >>>> according to what seems reasonable to you. My point was that you have >>>> no demonstration any of these characteristics in terms of one another >>>> which proves or disproves any of these properties in mechanical terms >>>> starting right at the beginning with the ideas of true and false. >>>> >>>> ~v~~ >>> Sorry, Lester, but that's an outright lie. I clearly laid it out for >>> you, starting with only true and false, demonstrating how not(x) is the >>> only 1-place operator besides x, true and false, and how the 2-place >>> operators follow. For someone who claims to want mechanical ground-up >>> derivations of truth, you certainly seem unappreciative. >> >> Only because you're not doing a ground up mechanical derivation of >> true or false. You're just telling me how you employ the terms true >> and false in particular contexts whereas what I'm interested in is how >> true and false are defined in mechanically reduced exhaustive terms. >> What you clearly laid out are the uses of true and false with respect >> to one another once established. But you haven't done anything to >> establish true and false themselves in mechanically exhaustive terms. >> >> ~v~~ > >Again, define "mechanics". Tony, time for you to do a little work for yourself. I've already gone through this. You describe for me the mechanics of using binary truth values and I explain to you I'm interested in truth not binary truth values and how to ascertain truth in mechanical terms initially and not how to work with truth values mechanically once ascertained. By the way what is the truth value of "square triangles" and how does that differ from the truth value of "blue squares" and how do you know the difference? ~v~~ |