The Definition of Points
in [Logic]
|
Prev: On Ultrafinitism
Next: Modal logic example
From: Lester Zick on 17 Apr 2007 18:19 On Tue, 17 Apr 2007 12:21:59 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> 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~~ > >Oh come on. Assumptions are considered true for the sake of the argument >at hand. That's what an assumption IS. So are "square triangles" or "blue squares" considered true for the sake of the argument at hand? Strange argument I must say. ~v~~
From: Lester Zick on 17 Apr 2007 18:20 On Tue, 17 Apr 2007 12:51:28 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Fri, 13 Apr 2007 13:42:06 -0400, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>> Lester Zick wrote: >>>> On Thu, 12 Apr 2007 14:23:04 -0400, Tony Orlow <tony(a)lightlink.com> >>>> wrote: >>>> >>>>> Lester Zick wrote: >>>>>> On Sat, 31 Mar 2007 16:18:16 -0400, Bob Kolker <nowhere(a)nowhere.com> >>>>>> wrote: >>>>>> >>>>>>> Lester Zick wrote: >>>>>>> >>>>>>>> Mathematikers still can't say what an infinity is, Bob, and when they >>>>>>>> try to they're just guessing anyway. So I suppose if we were to take >>>>>>>> your claim literally we would just have to conclude that what made >>>>>>>> physics possible was guessing and not mathematics at all. >>>>>>> Not true. Transfite cardinality is well defined. >>>>>> I didn't say it wasn't, Bob. You can do all the transfinite zen you >>>>>> like. I said "infinity". >>>>>> >>>>>>> In projective geometry points at infinity are well defined (use >>>>>>> homogeneous coordinates). >>>>>> That's nice, Bob. >>>>>> >>>>>>> You are batting 0 for n, as usual. >>>>>> Considerably higher than second guessers. >>>>>> >>>>>> ~v~~ >>>>> That's okay. 0 for 0 is 100%!!! :) >>>> Not exactly, Tony. 0/0 would have to be evaluated under L'Hospital's >>>> rule. >>>> >>>> ~v~~ >>> Well, you put something together that one can take a derivative of, and >>> let's see what happens with that. >> >> Or let's see you put something together that you can't take the >> deriviative of and let's see how you managed to do it. >> >> ~v~~ > >Okay. What's the derivative of 0? 46 ~v~~
From: Marcus on 17 Apr 2007 18:25 On Mar 19, 7:20 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > On Mon, 19 Mar 2007 13:07:30 EDT, "G.E. Ivey" > > > > <george.i...(a)gallaudet.edu> wrote: > >> On Tue, 13 Mar 2007 20:24:01 +0100, "SucMucPaProlij" > >> <mrjohnpauldike2...(a)hotmail.com> wrote: > > >> >"PD" <TheDraperFam...(a)gmail.com> wrote in message > >> >news:1173810896.000941.35900(a)q40g2000cwq.googlegroups > >> .com... > >> >> On Mar 13, 12:52 pm, Lester Zick > >> <dontbot...(a)nowhere.net> wrote: > >> >>> The Definition > >> of Points > > >> ~v~~ > > >> >>> In the swansong of modern math lines are composed > >> of points. But then > >> >>> we must ask how points are defined? However I > >> seem to recollect > >> >>> intersections of lines determine points. But if > >> so then we are left to > >> >>> consider the rather peculiar proposition that > >> lines are composed of > >> >>> the intersection of lines. Now I don't claim the > >> foregoing definitions > >> >>> are circular. Only that the ratio of definitional > >> logic to conclusions > >> >>> is a transcendental somewhere in the neighborhood > >> of 3.14159 . . . > > >> >>> ~v~~ > > >> >> Interestingly, the dictionary of the English > >> language is also > >> >> circular, where the definitions of each and every > >> single word in the > >> >> dictionary is composed of other words also defined > >> in the dictionary. > >> >> Thus, it is possible to find a circular route from > >> any word defined in > >> >> the dictionary, through words in the definition, > >> back to the original > >> >> word to be defined. > > >> >> That being said, perhaps it is in your best > >> interest to find a way to > >> >> write a dictionary that eradicates this > >> circularity. That way, when > >> >> you use the words "peculiar" and "definitional", > >> we will have a priori > >> >> definitions of those terms that are noncircular, > >> and from which the > >> >> unambiguous meaning of what you write can be > >> obtained. > > >> >> PD > > >> >hahahahahahaha good point (or "intersections of > >> lines") > > >> And it might be an even better point if it weren't > >> used to justify > >> mathematikers' claims that lines are made up of > >> points. > > >> ~v~~ > > > Could you give a reference in which a mathematician (not a > > high-school geometry book- I would accept a college geometry book) > > states that lines are made up of points? In every text I have seen > >"points" and "lines" are undefined terms. > > That's probably why you never ever see those terms used in relation to > any another because they're undefined except by predicates specified > in relation to predicates of other objects which don't define them. > > > I believe > > it was Hilbert who said that "If you replace points and lines by > > beer steins and tables, every statement should still be true." > > The difficulty is that the statements "lines are made up of points" > and "the intersection of lines" defines or determines points are a > definitive circular regression. I don't care whether Hilbert liked the > idea or not. If he proclaimed beer steins and tables are undefined but > tables define beer steins and tables are made up of beer steins the > problem is identical. It's the logic which defines tables and beer > steins in relation to one another and it's the logic that's definitive > and definitively circular. > > As for the contention that "lines are made up of points" I got that > from Bob Kolker and I kinda like think he made that up from some > notion that a line is the set of all points on a line. Pretty slippery > but there it is. If you disagree then I suggest you take it up with > him. I don't really care as long as the logic isn't circular and you > don't try to claim that objects which have specific relations with > other objects are not claimed to be undefined by Hilbert or whoever. > > (By the way I would appreciate it if you could keep your line length > around 60 or so.) > > ~v~~ Can you answer Ivey's challenge? If not, then it seems that your so- called "problem" may not be a problem after all. M
From: Lester Zick on 17 Apr 2007 18:38 On Tue, 17 Apr 2007 13:12:57 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Fri, 13 Apr 2007 16:11:22 -0400, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>>>>>>>>> Constant linear velocity in combination with transverse acceleration. >>>>>>>>>> >>>>>>>>>> ~v~~ >>>>>>>>> Constant transverse acceleration? >> >>>>>>>> What did I say, Tony? Constant linear velocity in combination with >>>>>>>> transverse acceleration? Or constant transverse acceleration? I mean >>>>>>>> my reply is right there above yours. >>>>>>>> >>>>>>>> ~v~~ >>>>>>> If the transverse acceleration varies, then you do not have a circle. >>>>>> Of course not. You do however have a curve. >>>>>> >>>>>> ~v~~ >>>>> I thought you considered the transverse acceleration to vary >>>>> infinitesimally, but that was a while back... >>>> Still do, Tony. How does that affect whether you have a curve or not? >>>> Transverse a produces finite transverse v which produces infinitesimal >>>> dr which "curves" the constant linear v infinitesimally. >>>> >>>> ~v~~ >>> Varying is the opposite of being constant. Checkiddout! >> >> I don't doubt "varying" is not "constant". So what? The result of >> "constant" velocity and "varying" transverse acceleration is still a >> curve. >> >> ~v~~ > >I asked about CONSTANT transverse acceleration. Oy! So what? Constant transverse acceleration produces a curve. So does non constant transverse acceleration. >More exactly, linearly proportional velocity and transverse acceleration >produce the circle. It can speed up and slow down, as long as it changes >direction at a rate in proportion with its change in velocity. Close >your eyes, and watch.... I don't understand what the problem is here, Tony. I don't understand the qualification "linearly proportional" is intended for. Anyway what is the purpose of your question? ~v~~
From: Lester Zick on 17 Apr 2007 18:41
On Tue, 17 Apr 2007 14:07:09 -0400, Tony Orlow <tony(a)lightlink.com> wrote: >> I don't know what anything is, Tony. I'm still trying to come to terms >> with "truth". You seem to think you've already come to terms with >> "truth" "strings" "grammar" "language" and um "meaning". You're quite >> fortunate in this respect. I should be so lucky. It might help if I >> could just assume the truth of whatever I was babbling about without >> having to demonstrate its truth in mechanically exhaustive terms like >> you and Moe(x) but then I guess I'm just more particular. >> >>> What's the difference between a duck? >> >> 46. >> >> ~v~~ > >Incorrect. One leg is both the same. Swell. So what? >So, start with uncertainty. Then, build truth from such statements. >Start with the line, and determine the point of intersection. Just >remember, when the lines are moving, so is the point. Swell. Where do you get the line? ~v~~ |