for x,y > 7 twins(x+y) <= twins(x) + twins(y)
in [Math]
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From: Jesse F. Hughes on 3 May 2010 22:47 Transfer Principle <lwalke3(a)lausd.net> writes: > All of this may be fine -- but so far, this doesn't > seem to relate to any "crank" claim at all. So let's > try to connect this to a "crank" claim. But which one > should we try? Fortunately, Hughes, in his infamous > .sig, provides us with a "crank" claim right here: > >> "I just define real numbers to be all those on the number line, as >> they were defined before Dedekind and Cauchy." >> -- Ross Finlayson's simple definition. > > In this post, RF eschews the standard real numbers as > defined via D-cuts or C-sequences. Instead, RF wants > to define the reals via geometry -- the points that lie > on a (number) line. RF is not alone in this thought -- > AP has also favored a geometric definition of the reals > as well. In particular, rather than have a "Ruler > Postulate" that automatically assigns a real number to > every point on the line, we want to describe the points > on the line _first_, then determine what type of numbers > best describe the points. Golly, I really don't understand *why* you want to proceed thus. You have a set theory in which not every set has a transitive closure. You also have a fairly random comment by RF regarding the reals. Maybe I'm missing something, but it seems to me that RF's claim is utterly unrelated to transitive closures. Your approach just seems to have veered off the tracks. You were originally interested in this axiom because it allowed one to prove ~Infinity (so you say -- I haven't looked at the details). But rather than really pursuing anything relating to the denial of infinity, you've grabbed a random signature quote and tried to tack it onto your theory. I just don't see why you think that this theory is related to Ross's opaque comment. -- Jesse F. Hughes "Women aren't that unpredictable." "Well, I can't guess what you're getting at, honey." -- Hitchcock's _Rear Window_
From: James Burns on 4 May 2010 13:19 Transfer Principle wrote: > On Apr 22, 12:43 pm, James Burns <burns...(a)osu.edu> wrote: > >>(Ask yourself who refers to the cranks most often >>as cranks, though maybe they don't mind as long as >>they are only called "cranks".) > > (For this question, I make the assumption that Burns > intends to say that _I_ am the one who uses the "crank" > label the most. If this assumption is false, then one > can ignore the following section and skip down to the > next quote from Burns.) You have correctly discerned my intent. It could be that I am incorrect; I certainly haven't made a study of the matter. The general impression I have of the sample of threads involving you on the topic of cranks is that /you/ write of the /group/ of cranks, and your "opponents" write of /individual/ cranks: Harris, BURT, whoever. Continuing the pattern, /you/ write of your "opponents" as a /group/, whether you finally decide to call us "anti-cranks", "standard theorists", "bullies", or something else. Everyone else, whether crank or not, has a tendency to address individuals, and to write of individuals. (James Harris may be an exception to this. He has a tendency to pontificate about the math community. You may surpass even him in this respect, though.) Therefore, because of your particular avidness for grouping people, you have more occasions to call people "cranks" than your "opponents". (This post of yours is an excellent example of the kind of grouping I refer to, by the way.) > When I first came up with the label "standard theorist," > it was with the intention of using a similar-sounding > label such as "nonstandard theorist" to describe the > standard theorists' opponents. Thus, instead of writing > "Many 'cranks' don't believe in uncountable sets," I'd > write "Many nonstandard theorists don't believe in > uncountable sets." > > But I decided to stick to "cranks," since that label is > much more well-known, so it's immediately identifiable > what I mean by "cranks" (rather than have to answer the > question "What do you mean by nonstandard theorists?" > over and over again). Since I don't believe that anyone > should be called "cranks," I at least put the label in > scare quotes, and sometimes even put "so-called" in > front of the word "crank." > > But I only use the word "crank" to echo their opponents' > use of the term. If it's true, as Burns hints at here, > that I actually use the word "crank" more than their > opponents (the "crank"-busters), then there is something > that I can do to emphasize that I only use the word in > response to their opponents' use of the word as follows: > > From today on, I shall not be the first poster in any > thread to use the word "crank." I shall only use the > word "crank" if an opponent has already used the word in > that thread. The same goes for any other five-letter > insult that commonly appears on sci.math. If the > opponents avoid the word "crank," then they should be > commended for not using the word -- I shouldn't try to > stir up trouble by using the word myself. May I make a suggestion? Instead of your proposal, perhaps you could pledge to write of neither "cranks" nor "crank-busters" /as a group/ (under whatever label) /except/ in response to to someone who has already referred to either /as a group/. This reduces the aspect of your writing that I actually find offensive, but leaves you free to defend individual posters from the dread "crank" label and free to attack individual posters for whatever you judge to be offensive. >>I think it is fair to say that your Grand Project >>has decayed to the point that you are only defending >>/your/ right to decide for /everyone else/ who is >>and is not a crank. > > What I'd rather do is defend my right to _convince_ > everyone else who is and isn't a "crank." But to do > this, I need to come up with a theory in which the > alleged "crank"'s claims are provable. That would > convince posters that there really is rigor behind > the post so that the poster isn't a "crank." > > But is such a theory possible? Earlier in this thread, > I attempted to write such a "crank"-defending theory, > but Hughes proved that it is inconsistent. Certainly, > inconsistent theories will convince no one that the > poster isn't a "crank." An ad hoc theory in which the > poster's claims are assumed as axioms won't stop the > "crank" accusations either. > > The reason that I haven't posted in this thread for > two weeks is that I was trying to fix the theory so > that it's no longer inconsistent. Since the proof in > ZF that every set has a transitive closure requires > the Axiom of Infinity, I considered a theory in which > we replace Infinity with the negation of that result: > > There is a set with no transitive closure. > > In other words: > > There exists a set a such that for every transitive > superset x of a, there exists another transitive > superset y of a such that x is not a subset of y. > > But even though this isn't obviously inconsistent, I > haven't been able to tie this to the claims of any > "crank" yet. > > What does this mean? Does it mean that there is _no_ > reasonable theory that can prove a "crank" claim? Does > this mean that my "project" really is "dead," as Burns > implies in the next line: > >>Why not bury the corpse of the project [...] > > My answer to this question is in the next line: > >>[...] and move on? > > The reason I don't "move on" is that I find nothing > appealing to "move on" to. If I admit that my project > is dead, then I'm saying that Burns and his allies are > right all along. Burns and his allies have a rigorous > theory, ZFC, on which to stand, while their opponents > post claims that contradict ZFC. If I accuse them of > opposing all theories other than ZFC, all they have to > do is ask for a rigorous theory in which their claims > are provable, and I won't be able to come up with a > rigorous theory quickly enough. So it's not that the > standard theorists oppose all theories other than ZFC, > but that there is _no_ rigorous theory that does what > their opponents want them to do, and so the use of the > word "crank" to describe them is justified. > > To me this is unacceptable. No matter what Burns says, > I won't "move on" to side with him and his allies, to > agree with him when he writes: > >>some posters just could not be reasoned with > > and that the posters who "can't be reasoned with" are > his opponents, and that the only reasonable posters > are Burns himself and those who agree with him. I have to say, I am surprised by this tack you've taken. My post to you was in response to you declaring a poster someone who can't be reasoned with, or so it looks to me: : Fine then. Since I'm not helping _any_ "cranks" by : defending _every_ "crank," I'll drop MR from the : list as being too "cranky" even for me to defend. <fbd5863b-02db-4be5-b534-3066dea0e012(a)z21g2000pre.googlegroups.com> I think it is time and past time for you to pull that beam out of your own eye. Then maybe we can talk about the mote in mine. By the way, your reference above to "Burns and his allies" is exactly the sort of lumping into a group that I find so offensive. Your assertion that I think that the only reasonable posters are those that I agree with is so far from the truth and so easily refuted by actually reading what I post, that I am unable to find it offensive, just silly. > Give me something more desirable to "move on" to, and > I'll consider "moving on" to it. Until then, I will keep > considering posts of the opponents of Burns and search > for rigorous theories in which their claims are provable > no matter how long it takes. In what way does showing a little discretion in how you lump people together prevent you from searching for these rigorous theories? Others have pointed out to you -- many times -- that your program (concisely outlined here) shows little prospect of changing how anyone gets referred to. Still, it is your time, you get to spend it however you want to. However, if you want results instead of just an enjoyable search for certain systems, I think you will do a great deal more if you just politely ask a poster who calls someone a crank not to do so, as it offends you. It will have no effect on any opinions about the irrationality of any particular poster, but you don't seem to care about that, just the use of the word "crank". Jim Burns
From: Aatu Koskensilta on 7 May 2010 08:13 James Burns <burns.87(a)osu.edu> writes: > However, if you want results instead of just an enjoyable > search for certain systems, I think you will do a great deal > more if you just politely ask a poster who calls someone > a crank not to do so, as it offends you. It will have no > effect on any opinions about the irrationality of any > particular poster, but you don't seem to care about that, > just the use of the word "crank". I doubt such polite admonitions would dissuade anyone from using the word "crank". -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: James Burns on 7 May 2010 12:36 Aatu Koskensilta wrote: > James Burns <burns.87(a)osu.edu> writes: > >>However, if you want results instead of just an enjoyable >>search for certain systems, I think you will do a great deal >>more if you just politely ask a poster who calls someone >>a crank not to do so, as it offends you. It will have no >>effect on any opinions about the irrationality of any >>particular poster, but you don't seem to care about that, >>just the use of the word "crank". > > I doubt such polite admonitions would dissuade anyone > from using the word "crank". Well, I never imagined that a polite request would dissuade everyone from using the word "crank", but I don't see why you think it would dissuade no one. A /polite/ request not to use "crank" seems to me to be roughly equivalent to a real-life request not to smoke, "because I don't care for the smell", or whatever. My experience has led me to believe that people generally try to get along with one another, unless the situation gets framed as a battle of some kind. A /demand/ that you not smoke, plus a detailed explanation of your failings for wanting to smoke, seems to me like it would be exceptionally ineffective. For much the same reason, I don't expect the way Transfer Principle is going about things to produce anything like what he says he wants. With a bar that low to get over (or so I believe), it wouldn't take much in the way of results to do better. Personally, I don't see it as a big deal, either way. I don't see "crank" as particularly offensive. I suspect that some cranks, at least, hold the term as a badge of honor -- the lone genius taking on the world! However, I can express the same thoughts using other words, if I want to. Jim Burns
From: Transfer Principle on 9 May 2010 03:00
On May 4, 10:19 am, James Burns <burns...(a)osu.edu> wrote: > Transfer Principle wrote: > > (For this question, I make the assumption that Burns > > intends to say that _I_ am the one who uses the "crank" > > label the most. If this assumption is false, then one > > can ignore the following section and skip down to the > > next quote from Burns.) > You have correctly discerned my intent. It could be that > I am incorrect; I certainly haven't made a study of the > matter. When I first started posting to sci.math, I didn't like how certain posters called others "cranks." I felt that use of that word divided posters into groups, the "cranks" and the "crank"-busters, and I wanted to help eliminate such divisions. But instead, all I proved is that I don't have the ability to refer to the divisions without being divisive myself. (Obviously, adding scare quotes, or the phrase "so-called," isn't the way to do it.) > > From today on, I shall not be the first poster in any > > thread to use the word "crank." I shall only use the > > word "crank" if an opponent has already used the word in > > that thread. The same goes for any other five-letter > > insult that commonly appears on sci.math. If the > > opponents avoid the word "crank," then they should be > > commended for not using the word -- I shouldn't try to > > stir up trouble by using the word myself. > May I make a suggestion? > Instead of your proposal, perhaps you could pledge to > write of neither "cranks" nor "crank-busters" /as a group/ > (under whatever label) /except/ in response to to someone > who has already referred to either /as a group/. It appears that something like this is best. Indeed, I was criticized earlier this week by my family, in a discussion unrelated to mathematics, for thinking that two incidents that were unrelated were actually related. This bad habit of mine manifests itself on sci.math when I group two people and claim they have something in common that they don't. And of course, in another recent thread there was a little talk about former President Clinton and his (in)famous remark about the definition of "is." This was the second time that I've seen a reference to Clinton, and so I tried to claim that the two remarks were related -- in essence, _grouping_ the two posters who brought it up. Burns, of course, criticized me for doing so. So did at least one other poster in that thread -- but now that I'm afraid of _grouping_ the posters who criticizeded me, I'll only refer to _Burns_ and his criticism of me. I'd like to pledge or promise that I'll stop grouping posters without reason, but habits as deeply ingrained as this one won't go away that easily. So instead, I'll say that I'll _resolve_ to do the following: -- I _resolve_ not be the first poster in any thread to use the word "crank." I shall only use the word "crank" if someone else has already used the word earlier in that thread. The same goes for any other five-letter insult that commonly appears on sci.math., as well as phrases such as "crank"-buster, "standard theorist," or similar grouping phrase. To see how this will work, let's consider the following hypothetical situation: let's say that tomorrow, someone posts a message similar to the following: 1. According to Cantor's diagonal argument, we can produce a new element that's not on the list. But then all we have to do is add this element to this list. Now, this list has become complete. Therefore, Cantor was wrong. And let's say someone responds to this message: 2. You haven't proved that Cantor is wrong. If you add the new element to the top of the list and diagonalize again, you have another element that's not on the list. Go read a book about set theory before you post such nonsense. At this point, I'd be inclined to post. I'd want to point out to the OP that there are some sets, such as NFU, which prove the existence of non-Cantorian sets, but the second poster assumes ZFC, in which all sets are Cantorian. The second poster is the type of poster who criticizes those who contradict ZFC (where Cantor was right), even though there are theories such as NFU (where Cantor is wrong). I'm aware, of course, that the OP wouldn't be the first poster to make this argument -- many posters have made similar attempts to discredit Cantor. And so if I were to start posting about NFU, someone might point out that there's no point in writing about NFU to yet another "crank" who challenges Cantor. And so, in anticipation of such a post, I might add some posters might call the OP a "crank" for challenging Cantor, but then I'd quickly call such posters "standard theorists" -- and suddenly, I'm grouping yet again. This also reveals another bad habit of mine -- I try to anticipate how another poster might respond too much. So, afraid that another poster might call the OP a "crank," I call the poster a "crank" myself, and this is the reason that I overuse the word "crank." So here's a more acceptable response for me to give in this hypothetical thread: 3. The OP disagrees with Cantor. The second poster gives an argument as to why Cantor's proof is valid in ZFC, but ZFC isn't the only set theory around. There's a theory called NFU, which proves the existence of sets that don't obey Cantor's theorem. Thus, the OP might find NFU less objectionable than standard ZFC. Now let's say that after this, the second poster writes again, and posts the following in response to me. 4. The OP is obviously a crackpot who doesn't understand set theory. There's no reason to mention NFU to him. In this example, the poster uses the derogatory term "crackpot," which means that according to my resolution, I'm allowed to use that word in my post. Notice that I still may not use the word "crank" -- I may only use the exact word "crackpot" that appears in the previous post, in order to emphasize that I'm using the word only because the previous poster used it, not because I'm trying to group the posters. So I might respond by writing the following: 5. Just because OP contradicts ZFC, it doesn't mean that the OP is a "crackpot." There are theories other than ZFC, and they prove results that contradict ZFC. The second poster should stop acting as if ZFC is the only set theory that matters. Now let's say a new poster enters the thread, and writes directly to the OP: 6. There are other ways to prove that there are more reals than natural numbers. Cantor actually wrote his "first uncountability proof"... and then goes on to describe this other proof. So now there are two posters arguing against the OP. Now I'm really tempted to _group_ the two posters who are attacking the OP. Even though their arguments are different, the underlying reason for arguing thus is the same -- namely that in the most common set theory ZFC, Cantor's theorem is a valid theorem. Now I really want to call both posters "standard theorists" who attack the OP merely for contradicting ZFC. Perhaps in order to avoid grouping posters, instead of referring to those two posters in the thread, I might focus on the OP himself: 7. The OP continues to be criticized just because he doesn't think that ZFC is the best theory there is... thus avoiding the phrase "standard theorists" or any other label to group the two posters. Let's leave this hypothetical example, and let me state how I _resolve_ to use some of these phrases: "crank," "troll," "crackpot" -- only use if used by a previous poster. "standard theorist" -- almost never use. Since I am the inventor of this phrase, it's doubtful that there will ever be a previous poster of this phrase in any thread, so there's no reason for me to use it. "Cantorian" -- almost never use. This phrase, invented by earlier sci.math posters, is the inspiration for my invented term "standard theorist." In hindsight, it might have been slightly better for me to have used "Cantorian" in lieu of "standard theorist," since at least I could claim that the term was invented by others, so that I didn't actually do the grouping. But nowadays, the posters who used the word "Cantorian" are long gone (except for Herc, who's now posting more about religion than Cantor). This is another phrase that I'll have no reason to use (but if the posters who used "Cantorian" starting post again, I might end up using "Cantorian," and not "standard theorist.") "bully" -- almost never use. This phrase was used by galathaea, but she rarely posts it anymore. So I can't use it unless she starts posting it again. "standard _theories_" (_not_ "theorists") -- use. I feel justified in referring to FOL, PA, and ZFC as the standard _theories_, since they are commonly used. "defender of ZFC" -- avoid. It sounds too divisive. "user of ZFC" -- use, but mainly in phrases such as, "Users of ZFC many prefer Infinity to its negation since the former is used to prove the exists of the reals, which are fundamental to classical analysis." "finitist," "ultrafinitist," "intuitionist," and similar words -- use with caution. Unlike the main five-letter insults, I don't consider a word such as "finitist" to be a word which I must avoid unless some other poster uses it first. The word serves well in phrases such as "Finitists tend to prefer ~Infinity to Infinity," or "Ultrafinitists believe in the existence of a largest natural number." Some posters have criticized me for describing certain posters such as WM as ultrafinitists. They point out that this isn't a completely accurate description of WM's philosophy (since WM doesn't have a largest natural). Perhaps, if a new poster make statements that suggest that he is sympathetic to ~Infinity, I might write, "The OP might be a finitist. If this is the case, then he doesn't deserve to be called a..." (insert five-letter word used by another poster in the thread, if any). > By the way, your reference above to "Burns and his allies" > is exactly the sort of lumping into a group that I find > so offensive. "ally," "opponent" -- be wary of their use. Maybe if it appears that two posters agree with each other, I might state that they agree, but in order to avoid excessive grouping, I'd have to be _extremely_ sure that the two posters agree -- they'd almost have to write identical statements -- before I may state this. "Opponent" is a trickier word. Perhaps a better way to say it would be, "Those who are currently arguing against the OP's claim in this thread..." A few other general resolutions: If a five-letter insult is used by another poster in the plural, I might change it to the singular instead. But if such a word is used only in the singular, I may _not_ use the plural form, since this leads to grouping. I must wait until another poster uses the plural form before I can use it. If the discussion in a thread sounds similar to another discussion in another thread, I must wait until someone else points this out before I mention this fact. Doing so would have prevented that Clinton/"is" mistake I made. > However, if you want results instead of just an enjoyable > search for certain systems, I think you will do a great deal > more if you just politely ask a poster who calls someone > a crank not to do so, as it offends you. It will have no > effect on any opinions about the irrationality of any > particular poster [...] What might actually have an effect on opinions about the irrationality of another poster is if I could post a _rational_ theory in which the poster's claims are in fact provable. The problem, of course, is that none of the theories that I've posted are sufficiently rational for anyone to accept. Once I become better at writing theories, then we can see what effect they will have on another poster's irrationality. This also brings up another key point. Previously, I've avoided posting alternate theories that satisfy the intuitions of a single poster (such as tommy1729, who often posts about mereology, three-valued logic, etc.) in favor of theories that satisfy the intuitions of several posters (all sets being countable, avoiding bijections between sets and their proper subsets, etc.). But claiming that a single theory satisfies the intuition of more than one poster might be considered grouping. To this end, it might actually be _preferable_ if I chose a single poster and only satisfy his intuitions. (But still tommy1729 would be a poor choice, since with all the demands he has considering mereology/three-valued logic, I'm likely to be unsuccessful at finding a theory that satisfies all of them.) I'd be better off starting off with those posters whose intuitions correspond to already-known theories (such as NFU, hyperreals, ZF-Infinity), then choose one poster whose intuitions don't correspond to a known theory but deviate from ZFC as little as possible, and attempt a theory that satisfies that one poster's intuitions. > just the use of the word "crank". Interestingly enough, the word "cranks" (plural) did appear in a recent thread. That thread, although originally about FLT, turned into set theory. But as it turned out, the "crank" claim stems from a mistaken statement based on a Mathforum error. Because of this, even though my resolution permits me to use the word "cranks" in that thread, I will not post in that thread at all, since I've no desire to defend a computer error. |