The Virgin Birth of Points
in [Physics]
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From: Shrew_D on 8 Dec 2007 00:33 On Fri, 7 Dec 2007 10:36:55 -0800 (PST), Randy Poe <poespam-trap(a)yahoo.com> wrote: >On Dec 7, 12:55 pm, stephenkwag...(a)gmail.com wrote: >> On Dec 6, 6:46 pm, Shrew_D <Shre...(a)paleo.net> wrote: >> >> >> >> > On Thu, 6 Dec 2007 09:21:35 -0800 (PST), stephenkwag...(a)gmail.com >> > wrote: >> >> > >On Dec 6, 11:52 am, Shrew_D <Shre...(a)paleo.net> wrote: >> > >> On Wed, 05 Dec 2007 22:33:18 -0500, Wolf Kirchmeir >> >> > >> <ElLoboVi...(a)RuddyMoss.com> wrote: >> > >> >> However I think my original point regarding Randy's use of "short- >> > >> >> hand" still stands because clearly the "shorthand" in a definition has >> > >> >> to be "shorthand" for something and I thinkLesteris correct on this >> > >> >> issue. >> >> > >> >Since I cannot figure out whatLestermeans by "predicates" etc, I can >> > >> >neither agree nor disagree. >> >> > >> You can't agree that "shorthand" means "shorthand for something"? >> >> > >What is your point? >> >> > >A definition is shorthand. >> >> > Shorthand for what? >> >> Did you really not understand the example? >> >> >> >> >> >> > >If I define 'regular graph' to be 'a graph in which all vertices have >> > >the same degree', >> > >then the phrase 'regular graph' is shorthand for the phrase 'a graph >> > >in which all vertices have the same degree'. >> >> > Then a definition is certainly more than merely shorthand because it >> > includes the phrase for which the shorthand stands. >> >> > > Anywhere the phrase >> > >'regular graph' appears, you can replace it with the phrase 'a graph >> > >in which all vertices have the same degree'. >> >> > Except adherents of the shorthand theory for the definition of >> > definition assure us definition is "just shorthand", which is plainly >> > absurd since it is the phrase to which the shorthand corresponds which >> > is the definition and not just the shorthand. >> >> > >In what sense do you not know "the something" the short hand is for? >> >> > In the same sense as proponents of the "just shorthand" definition of >> > definition neglect to include what the shorthand is shorthand for in >> > defining definition. >> >> At this point you seem to be trying to purposefully misunderstand. >> If so, then you will just love Lester. >> >> 'Adherents of the shorthand theory' know exactly what the purpose >> and nature of definitions are, and they know that when they define >> a regular graph as a graph in which every vertex has the same degree, >> then all they are saying is that 'regular graph' is shorthand for >> 'a graph in which every vertex has the same degree'. >> >> Do you really not understand that? > >Shrew is being pedantic, which is a slight improvement >over Lester's incoherence. And <grumble> pedancy is sort >of in the spirit of the math newsgroup, at any rate. "Pedancy"? Is that some sort of child molester?
From: Shrew_D on 8 Dec 2007 00:39 On Fri, 7 Dec 2007 10:35:13 -0800 (PST), Randy Poe <poespam-trap(a)yahoo.com> wrote: >On Dec 6, 7:39 pm, Wolf Kirchmeir <ElLoboVi...(a)RuddyMoss.com> wrote: >> Shrew_D wrote: >> > On Thu, 06 Dec 2007 13:46:17 -0500, Wolf Kirchmeir >> > <ElLoboVi...(a)RuddyMoss.com> wrote: >> >> >> Shrew_D wrote: >> >>> On Wed, 05 Dec 2007 22:33:18 -0500, Wolf Kirchmeir >> >>> <ElLoboVi...(a)RuddyMoss.com> wrote: >> >> >>>>> However I think my original point regarding Randy's use of "short- >> >>>>> hand" still stands because clearly the "shorthand" in a definition has >> >>>>> to be "shorthand" for something and I think Lester is correct on this >> >>>>> issue. >> >>>> Since I cannot figure out what Lester means by "predicates" etc, I can >> >>>> neither agree nor disagree. >> >>> You can't agree that "shorthand" means "shorthand for something"? >> >> >> Well, of course. The term defined is shorthand for the description. I >> >> thunk that was obvious. >> >> > Obviously it wasn't obvious to Randy when he claimed a definition was >> > just shorthand. >> >> Sure it was. That's why he said it. He just didn't say it very clearly, >> is all. I mean, I knew what he meant, but that's because he and share at >> least some notions about 'definition', etc. >> >> >> But that doesn't explain what Lester means by >> >> "predicates." >> >> > I didn't comment on what Lester means by predicates. I commented on >> > what Lester said when Randy neglects to say when he defines definition >> > as just shorthand. >> >> Yeah, but Lester used 'predicates' in his comment. I'm not surprised >> that Randy ignored that remark of Lester's - it shows that Lester has a >> confused notion of 'definition'. Randy knows this, and I know this, >> because we've both tried to get Lester to explain himself. He never does. >> >> >> For example, he seems to think "not" is a predicate, hence >> >> his famous "regression to self contradiction", which he then contradicts >> >> to create a tautology that he claims is "universally true." >> >> > Then perhaps you should take the matter up with Lester. >> >> Oh, I have. So have many, many others. Didn't help. >> >> >> See? >> >> >> I thought not. ;-) >> >> > My original comment was quite specific. It was only directed at >> > Randy's inability to say what the "just shorthand" in definitions was >> > shorthand for when taxed by Lester. >> >> Randy wasn't unable to say what you wanted to say, he just didn't. I >> think hen just decided to give up on Lester. Everybody who engages >> Lester in a serious conversation sooner or later gives up on him. > >I still "engage" Lester, if you can call it that, but I gave >up the idea of serious conversation with him a long >time ago. > >For the pedants who have apparently entered this thread, >let me try again: A definition is a statement of the form >"A is B" which establishes the word or phrase A as a substitution >for the set of words or phrases B (usually much longer). It >serves merely to establish that whereever A appears after >that definition, it can be use interchangeably with B. In other words a definition is more than shorthand. >So a definition CREATES a shorthand symbol. It does >not make any statement about the existence of A >(or, equivalently, B). I've never said anything about the "existence" of A or B since I don't know what the "existence" of A or B entails. Wolf was the one who wrote about "existence". All we can tell at present is that you didn't understand what a predicate was and you didn't understand what shorthand entails. Thus we're reluctant at present to credit what you think you understand about definitions.
From: Wolf Kirchmeir on 8 Dec 2007 09:12 Shrew_D wrote: > On Fri, 7 Dec 2007 10:35:13 -0800 (PST), Randy Poe > <poespam-trap(a)yahoo.com> wrote: > [...] >> For the pedants who have apparently entered this thread, >> let me try again: A definition is a statement of the form >> "A is B" which establishes the word or phrase A as a substitution >> for the set of words or phrases B (usually much longer). It >> serves merely to establish that whereever A appears after >> that definition, it can be use interchangeably with B. > > In other words a definition is more than shorthand. > >> So a definition CREATES a shorthand symbol. It does >> not make any statement about the existence of A >> (or, equivalently, B). > > I've never said anything about the "existence" of A or B since I don't > know what the "existence" of A or B entails. Wolf was the one who > wrote about "existence". All we can tell at present is that you didn't > understand what a predicate was and you didn't understand what > shorthand entails. Thus we're reluctant at present to credit what you > think you understand about definitions. No, it was you who implied that a definition says something about the existence of the referent of the terms. You did that when you asserted that a definition could be false. You expanded on that in your references and allusions to "square circle", which you asserted to be a self-contradictory predicate and thus made the definition of 'squircle' false. What you failed to notice is that you cannot assert the non-existence of squircles without first defining 'squircle' as the term referring to 'square circle.' But that means that the definition of the term is neither true nor false, it is merely a way of streamlining discussion. BTW, squircles can exist. Think about the square on the sphere. If you agree that square on the sphere is a figure with four equal sides, then you should be able to see that: a) the sides of the square are segments of great circles; and b) the largest possible square on the sphere is congruent with a great circle; and c) therefore the largest square on the sphere is equivalent to a circle; and d) the largest square on the sphere is a squircle; and e) the great circle is a squircle. QED. Corollary: Since there are an infinite number of great circles on a sphere, there are an infinite number of squircles, too. Whether it's mathematically interesting that squircles exist on spheres is another issue. I don't think it is, really. But the above argument might be useful in helping a student achieve an AHA about the differences between definitions and existence statements, for example. HTH
From: Lester Zick on 8 Dec 2007 18:10 On Sat, 8 Dec 2007 11:23:26 -0800 (PST), Marshall <marshall.spight(a)gmail.com> wrote: >On Dec 8, 10:40 am, Shrew_D <Shre...(a)paleo.net> wrote: >> On Sat, 8 Dec 2007 07:24:28 -0800 (PST), Randy Poe >> >> >Can you please explain to me the difference between >> >this position, with which you say you agree: >> >"... all they are saying is that X is shorthand >> >for Y..." >> >and my position with which you say you disagree: >> >"A definition establishes X as a shorthand for Y" >> >> You said nothing before about a definition being shorthand "for" >> anything. > >Saying something is "shorthand" is shorthand for saying something >is "shorthand for" something. Whereas saying something is "just shorthand" is not. > I'm hard pressed to believe >anyone could seriously think otherwise. What do you think >*shorthand* that is not *shorthand for* anything means? While saying anything is "just shorthand" means something? You might actually consider reading what was written for comprehension prior to commenting on it. >> Although I'm forced to wonder how X is supposed to be >> shorthand for Y. Why don't you just say Y? > >Brevity for one thing. That's why it's *short*hand. Whereas you're just kinda *short*think. ~v~~
From: Lester Zick on 8 Dec 2007 18:18
On Sat, 08 Dec 2007 12:13:09 -0700, Virgil <Virgil(a)com.com> wrote: >In article <quoll3lj199v7gajs1jvg55pqvr7jtujki(a)4ax.com>, > Shrew_D <Shrew_D(a)paleo.net> wrote: > > >> You said nothing before about a definition being shorthand "for" >> anything. Although I'm forced to wonder how X is supposed to be >> shorthand for Y. Why don't you just say Y? > >The point of shorthand is to shorten. >The point of an abbreviation is to make brief. Doesn't seem to work on you, Virgin. Any way to shorthand you? >If X is shorthand for or an abbreviation of >YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY, >or something even longer,then there is an obvious benefit to using X to >replace the longer expression, particularly if one or the other is >needed frequently. No lie? What if XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX is shorthand for Y? >For example, the Riemann definite integral symbol abbreviates in one >line what takes several paragraphs to express unabbreviated. > >Similarly dy/dx and f'(x) are shorthand for limit statements which are >considerably longer than their abbreviations. > >In ZF or ZFC, one normally defines the naturals as >{}, { {} }, { {}, { {} ] }, { {}, { {} }, { {}, { {} ] } }, ... >and abbreviates them as 0, 1, 2, 3, .... > >So lets see you "just say Y" and express 99 + 101 = 200 in unabbreviated >form. Well what's curious in all this is that no one seems particularly interested in recollecting what Randy originally claimed, that definitions were "just shorthand" and not "shorthand for". However that's faith based modern mathematics for you. Just point and click. ~v~~ |