for x,y > 7 twins(x+y) <= twins(x) + twins(y)
in [Math]
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From: Jim Burns on 16 May 2010 13:07 Transfer Principle wrote: > On May 14, 10:11 am, James Burns <burns...(a)osu.edu> wrote: >> Transfer Principle wrote: >>> On May 10, 10:09 am, James Burns <burns...(a)osu.edu> wrote: >>> What does Burns mean by "the standard way"? If by "the >>> standard way," he means the definition in classical >>> analysis by which it is exactly equal to 1, then Poster >>> Y's assertion is equivalent to "1>1" (substitution). To >>> me, "1>1" is a statement which even I won't defend or >>> attempt to find a theory for. >> It's not hard to find a theory where "1 > 0.999..." >> is true. Just re-interpret the greater-than symbol >> as the greater-than-or-equal-to symbol. > > Too ad hoc. "Too ad hoc"? But /not/ too different from what the poster (very likely) intended? Do you feel any pressure /at all/ to read what seems to you to be what any given poster intended? >>> To me, simply by posting "1 > 0.999...," it is clear he >>> _doesn't_ mean to use those symbols in the standard way >>> at all. It's clear that Poster Y means to use the >>> symbols in a nonstandard way -- a way in which 0.999... >>> differs by 1 by a nonzero infinitesimal. And so it's up >>> to me to _find_ a way to use it that's rigorous and not >>> ad hoc. >> The particular example I had in mind of a poster >> asserting that "1 > 0.999..." was BURT. I am not having >> much luck with groups.google, so I'll have to settle for >> the vague memory of an extended exchange with him, >> where he made it clear he was correcting standard >> usage, not creating a new system. I think that, in this >> case, it really is clear he _does_ mean to use those >> symbols in the standard way. (No, he does not /succeed/ >> in using them the standard way, but he is trying to >> do that.) > > But what does one mean by "correcting" standard usage, in > the first place? Well, that would be up to BURT what he meant, of course, assuming my memory has not played me false. The only example I can think of, where common usage needed correcting, is set theory, pre-Russel's paradox. I could understand BURT's tenacity, if he thought that he had something like that. (I think it is BURT's misfortune to come up with this Big Idea /before/ he learned how to let go of mistakes. I expect him to reject further learning, because pretty much everything he'll see will "conspire" to tell he's wrong. If BURT's "1 > 0.999..." were a statement about some system that only a tiny, tiny fraction of the people on this planet were even aware that it existed, then I have a harder time understanding why he cares so much -- or, why he still hasn't explained this to us. > Notice that another poster, AP, does > make it clear that he's creating a new system (since he > explicitly names the proposed system "AP-reals" and calls > the current system "Old Reals"), yet the title of his > threads refer to "Correcting Math." > >>> But what exactly is Poster Y saying? I doubt that he >>> would be saying "1>1" -- which is what he would be saying >>> if he means the standard definition of 0.999.... >> Consider a small boy waiting to visit Santa in a department >> store. Unbeknownst to the boy, his father is working as >> the store's Santa right now. Can we say, "The boy does >> not know that his father is Santa"? But, the boy's >> father /is/ Santa. Isn't this the same as "The boy >> does not know that his father is his father"? >> Well, no, it isn't the same. > > (This reminds me of an old paradox about knowing that Venus > is the evening star, versus knowing that Venus is the > morning star. A quick Google search returns discussions > about "scalar" vs. "vector" logic.) > > I assume that the small boy in the story corresponds to MR, > Santa to 0.999..., and his father to unity. > > Let's discuss the possibilities for MR thus far: > > (1) MR is discussing an alternate theory T such that T > proves "1 > 0.999..." > (2) MR knows that ZFC proves "1 = 0.999..." but doesn't > like this result, so he talks about how 0.999... ought > to be strictly less than unity without referring to any > theory T in which it is provable. > (3) MR doesn't know that ZFC proves "1 = 0.999..." He > believes that standard theory proves "1 > 0.999..." > > Only in case (3) would I consider calling MR "wrong" to > make any sense. In particular, case (3) entails that MR > believes that "1 > 0.999..." is provable, and that > those who claim that "1 = 0.999..." is provable in a > standard theory need to be "corrected." > > Now assume Burns is correct, and let's say that from > MR's subsequent posts, we can determine that case (3) > is most likely, thereby justifying calling MR "wrong" > and other five-letter words. Does this mean that anyone > who posts in response to MR (including myself) _must_ > call MR "wrong"? Does this mean that I deserve ridicule > if I respond to MR in any other way than to tell him > that he is wrong? Consider what a poster like MR sees: "wrong", "wrong", "wrong", "maybe he's right", "wrong", "wrong", ... If I am right, and MR imagines he is correcting standard usage, then he is wrong and he needs to get past his error, if he wants to do anything more than make crank posts. Holding out the possibility that he is right, when he is not right, is more than not helpful. I think you actively harm posters like MR when you do that. > If so, than I'd rather not post in a thread at all than > to join five other posters and tell MR he's wrong. In > fact, I'd rather call a poster wrong in a thread in > which I'm the _first_ poster to call him wrong than > _repeat_ that he's wrong. (And believe it or not, I've > actually called posters "wrong" before, only because I > happened to be the first poster in the thread to do so.) > > Perhaps what I ought to do is ignore posters like MR in > case (3) after all, and instead focus on posters for > whom case (1) or (2) are more likely. > > In particular, a poster is likely to be actually trying > to create a new theory if one explicitly gives the > proposed theory a _name_. In particular, AP calls his > theory "AP-reals," tommy1729 calls his theory "TST," WM > calls his theory "MathRealism," and so on. For these > posters, it's clear that they _know_ their claims are > refutable in the standard theory, so they wish to come > up with new theories (AP-reals, TST, MathRealism) in > which their claims are provable. > > Case (2) may be more difficult to discern, but perhaps > if a poster were to write something like "I don't like > ZFC because I don't like Cantor." Perhaps in this case, > instead of writing that the OP is working in some > alternate theory, I simply state an alternate theory > (say NFU in this case) without claiming that the OP is > secretly working in it -- indeed, I just post NFU > without mentioning the OP at all. In that way, I don't > make refutable claims about the OP, and the OP can > learn that there are alternatives to ZFC. > >>> I start from the assumption that Poster Y is rational, >>> that the poster wouldn't write something as blatantly >>> false as "1>1" and search for a definition that does >>> make sense, such as "1 > 1-iota" for some nonzero >>> (infinitesimal) iota. Burns, on the other hand, appears >>> to start from the opposite assumption, namely that >>> Poster Y is _irrational_, when he criticizes me for >>> searching for an infinitesimal theory. (But I could be >>> wrong about Burns's assumption here.) >> I beg to differ. You start from the assumption that >> Poster Y is /correct/. I start from the assumption that >> a poster /may be mistaken/. I think my assumption does >> much less violence to their point of view than yours >> does. > > Yet calling a poster's point of view "wrong" and calling > him another five-letter word, doesn't do much "violence" > to their point of view? If their point of view is wrong, calling it wrong does no violence at all to the point of view. If Poster X has a lot of emotional investment in being right, being told he's wrong could hurt his feelings. However, if he's going to learn anything, he's got to get over being wrong. Just accept it and move on. Coming up with alternative interpretations /which Poster X did not mean/ encourages him to do anything, including lie about what he meant, rather than admit that he was wrong. I think that you are actively harming Poster X when you do this. >>> Have any of my newly introduced systems changed anyone's >>> mind about Poster Y's "crank"-hood yet? Not yet -- but >>> that could be because I have yet to post any theory that >>> is sufficently rigorous and non-ad hoc. (The closest >>> that I have come is declaring that 0.999... is the >>> surreal 1-1/omega, but even this causes problems as >>> 1-1/omega doesn't work exactly as Poster Y wants it to.) >> And yet, none of the criticisms I have seen of your >> attempts to wipe away someone's crank-hood have mentioned >> insufficient rigor or excessive ad-hoc-ness. How do >> you explain this? > > Au contraire. We go right back, earlier in this thread. I > had written: > >>> Schema 1: If phi is a one-place predicate that does not >>> mention the symbol N, then all closures of: >>> (phi(0) & Ax (phi(x) -> phi(xu{x}))) -> phi(N) >>> are axioms. > > And Jesse Hughes's response was: > > "In particular, let phi(x) be any standard formalization of "x is > finite" and we see that N is finite. Right?" > > And of course, by letting phi(x) be "x is infinite," we > see that N is infinite. Therefore N is both finite and > infinite, therefore the theory is inconsistent. > > So Hughes did respond that my theory lacks rigor -- > since what can be less rigorous than a theory that is > proved _inconsistent_? And so I eventually attempted > another theory that avoided the inconsistency -- only > for Hughes to imply that it's "ad hoc" when I tried to > tie it to RF's theory. > > Therefore, my theories have been criticized as lacking > rigor and being too ad hoc all the time. Okay. I consider myself corrected on this point. Jesse's point that he objected to /inconsistency/, not /lack of rigor/ is an important distinction, but not relevant here, I think. You were saying that you needed better theories in order order to change minds about the "five-letter insults". I accept that you have had objections to the quality of your theories. I still don't think that better theories will give you what you want, without those theories even corresponding to what the "five-letter insults" post. Even in the unlikely event of a FLI being right and everyone else wrong, what gets someone labeled a FLI is the /way/ they reason (or don't). You would not have changed that. Jim Burns
From: Jim Burns on 16 May 2010 13:51 Transfer Principle wrote: > My claim is that if someone posted a line of _borderline_ > rigor, a more reputable poster is more likely to be given > the benefit of the doubt (i.e., have the post treated as > if it were of full mathematical rigor) than one who has > received a five-letter label. Posts are always incomplete and the gaps need to be filled in by their readers. If I think that a writer knows what they're talking about, I will fill in the gaps in a knowledgeable way (if I can). If someone is a crank, or a student, or just doesn't seem to know much about whatever they're writing about, then, yes, I will be more ready to interpret some gap in my understanding of their post as mistaken thoughts, rather than say, mistaken expressions of their thoughts (typos, etc). In a real-life extended exchange, though, instead of an excerpted "gap", mistaken interpretations, either favorable or unfavorable to the writer, become apparent soon enough. One asks things like "What did you mean by that?" If you have a problem with that, then we will just have to disagree. To me, that is just responding as best I can to what I /think/ someone means, instead of what I /want/ them to mean. To me, this is just common courtesy, and I am not changing it. Jim Burns
From: Jim Burns on 16 May 2010 14:36 master1729 wrote: > jim burns wrote : >> What have you got here? A third poster "pointed >> out" that what you believed was true? Is this >> supposed to be evidence of some kind? I see >> someone agreeing with you, nothing more. >> (I'm curious: who is this mysterious poster?) > > who is ? > who 'are' ! > > this has been pointed out a few times by people such > as newbies , nonregular posters , students and others ; > to call some names of ' others ' : > quasi, galathaea and of course myself. You say you point things out. You are not pointing things out. You (and these other posters) are expressing their opinions about what would happen in some hypothetical situation -- JSH shows up, presumably says something dumb, and "doesn't get the time of day". You are welcome to your opinion, even though what has happened in the past has been JSH receiving detailed reasons why he is wrong, explicit counter- examples, his vague descriptions turned into algorithms, and much more. In spite of all that, though, your opinion is that he would not get the time of day. Have you got any examples of JSH not getting the time of day? That might be worth something. What you really need, though, is JSH being told he is wrong when he is right -- and presumably because he is JSH. I won't ask you for explicit motives. That sets the bar too high, I think. Jim Burns
From: master1729 on 16 May 2010 11:22 burns : > master1729 wrote: > > jim burns wrote : > > >> What have you got here? A third poster "pointed > >> out" that what you believed was true? Is this > >> supposed to be evidence of some kind? I see > >> someone agreeing with you, nothing more. > >> (I'm curious: who is this mysterious poster?) > > > > who is ? > > who 'are' ! > > > > this has been pointed out a few times by people > such > > as newbies , nonregular posters , students and > others ; > > to call some names of ' others ' : > > quasi, galathaea and of course myself. > > You say you point things out. You are not pointing > things out. You (and these other posters) are > expressing > their opinions about what would happen in some > hypothetical situation -- JSH shows up, presumably > says something dumb, and "doesn't get the time of > day". > > You are welcome to your opinion, even though > what has happened in the past has been JSH receiving > detailed reasons why he is wrong, explicit counter- > examples, his vague descriptions turned into > algorithms, > and much more. In spite of all that, though, your > opinion is that he would not get the time of day. > > Have you got any examples of JSH not getting the > time of day? That might be worth something. > > What you really need, though, is JSH being told > he is wrong when he is right -- and presumably > because he is JSH. I won't ask you for explicit > motives. That sets the bar too high, I think. > > Jim Burns > no jsh. and you dont seem to know these posters either , despite pretending so. tommy1729
From: christian.bau on 16 May 2010 17:28
On May 15, 11:40 pm, master1729 <tommy1...(a)gmail.com> wrote: > whatever ! I see. The only thing that was mathematics, and your answer is "whatever". Look, if you don't get mathematics, and you don't, why don't you try to learn some instead of making a fool of yourself? |