The Definition of Points
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From: Lester Zick on 13 Apr 2007 18:33 On Fri, 13 Apr 2007 13:45:46 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >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. 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~~
From: Lester Zick on 13 Apr 2007 18:37 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~~
From: Lester Zick on 13 Apr 2007 18:39 On Fri, 13 Apr 2007 16:52:21 +0000 (UTC), stephen(a)nomail.com wrote: >In sci.math Tony Orlow <tony(a)lightlink.com> wrote: >> Lester Zick wrote: >>> On Mon, 2 Apr 2007 16:12:46 +0000 (UTC), stephen(a)nomail.com wrote: >>> >>>>> It is not true that the set of consecutive naturals starting at 1 with >>>>> cardinality x has largest element x. A set of consecutive naturals >>>>> starting at 1 need not have a largest element at all. >>>> To be fair to Tony, he said "size", not "cardinality". If Tony wishes to define >>>> "size" such that set of consecutive naturals starting at 1 with size x has a >>>> largest element x, he can, but an immediate consequence of that definition >>>> is that N does not have a size. >>> >>> Is that true? >>> >>> ~v~~ > >> Yes, Lester, Stephen is exactly right. I am very happy to see this >> response. It follows from the assumptions. Axioms have merit, but >> deserve periodic review. > >> 01oo > >Everything follows from the assumptions and definitions. And since definitions are considered neither true nor false everything follows from raw assumptions which are considered neither true nor false. ~v~~
From: Lester Zick on 13 Apr 2007 18:42 On Fri, 13 Apr 2007 10:06:51 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Mike Kelly wrote: >> >> a) A consecutive set of naturals starting with 1 with size X can not >> have any maximum other than X. >> b) A consecutive set of naturals starting with 1 with size X has >> maximum X. > >Whoa! If a -consectutive-(!!!) set of naturals with 1 as its least >element has cardinality X (an integer), then its last element must be X. > >A simple induction argument will show this to be the case. > >Can you show a counter example? You mean a true counter example, Bob, or just a counter example whose truth is assumed true because you're too lazy or stupid to consider the truth of what you say but not too lazy or stupid to say it anyway. ~v~~
From: Lester Zick on 13 Apr 2007 18:43
On Fri, 13 Apr 2007 10:08:14 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >Bob Kolker wrote: > >> Mike Kelly wrote: >> >>> >>> a) A consecutive set of naturals starting with 1 with size X can not >>> have any maximum other than X. >>> b) A consecutive set of naturals starting with 1 with size X has >>> maximum X. >> >> >> Whoa! If a -consectutive-(!!!) set of naturals with 1 as its least >> element has cardinality X (an integer), then its last element must be X. >> >> A simple induction argument will show this to be the case. >> >> Can you show a counter example? > >I should have said, for I assumed it, that X is finte. Sorry about that. Or you regret your assumptions of truth in this particular instance but not in general? ~v~~ |