details re Z-R |- PA consistent
in [Math]
|
From: MoeBlee on 15 Jul 2010 12:54 On Jul 14, 7:55 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > On Jul 14, 3:51 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > On Jul 14, 5:39 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > > and that MoeBlee isn't himself dogmatic. > > My dogmas: > > (1) In unmarked intersections, pedestrians have the right of way. > > (2) The Axis powers were the bad guys in WWII. > > Godwin's law? > > > (3) In public laundromats, one should clean the lint trap after using > > a dryer. > > Other than that, I don't know on what points I'm supposed to have > > succumbed to dogma. > > The best way to find how out MoeBlee supposedly succumbed to > dogma is by quoting a poster who made such a claim. > > A Google search reveals a discussion from the 13th of August, 2008, > in a discussion about constructivism/intuitionism. > > MoeBlee: > > > [I'm] asking for a book that says: > > "Here are the primitive symbols of the language. Here are the > > formation rules for formulas of the language. Here are the exact > > axioms to be used in the book (or each axiom introduced at the first > > point it is used). And this book uses the intuitionistic predicate > > calculus only for proof of all theorems." > > And the poster Han de Bruijn responded as follows: > > Han de Bruijn: > In short, Moeblee is asking for a book that turns constructivism into > formalism. He doesn't want to know about constructivism. All he wants > is a perpetual confirmation of his own, narrow minded, picture of the > world, which is the _formalist_dogma_, nothing else. > (emphasis mine) Notice that de Bruijn is utterely confused about the matter. (And, if I recall, I mentioned how specifically in my posts in reply.) > How interesting is it in that the quote I found, not only is MoeBlee > called a dogmatist, but a formalist as well. And of course, in 2008 as > today, he denies both claims. > > So why did HdB refer to MoeBlee's "dogma"? My guess is that he, > like I, have noticed that MoeBlee is rather reluctant to consider > theories Where did I express such reluctance? > other than classical ZFC and its subtheories -- in > particular, > he has several requirements before he'd even consider another theory > as a foundational theory, including: > > 1) that the theory be written using formal symbolic language (hence > HdB's and my accusation that MoeBlee is a "formalist") > > 2) that the theory be applicable to axiomatize the sciences > > 3) that the theory be proposed concisely (since he complains about > having to "slog" through others' axioms all the time) (1) I don't require that the actaul exposition of a theory be in formal language, but rather it is enough that a formal context is stated and that we can see how the informal exposition be formalized. Also, that is not what "formalist" means. Also, this is as to formal theories. Of course, if one wishes to propose some notion of mathematics that we can't see how to formalize, then that is yet another discussion. I've never said that I require that all mathematical discussions be formal ones. (2) What I have said is: TO THE EXTENT that we seek a theory that proves the mathematical theorems used for the sciences, then we would compare foundational theories on this basis. If one has some notion of a foundational theory that does not include axiomatization of the theorems for the sciences, then one is free to propose it and explain the motivation. (3) I've never made concision a REQUREMENT. > But is it possible to propose such a theory in a single post? Any post > that contains axioms and enough information to convince MoeBlee > that the theory indeed axiomatizes for the sciences is likely to be so > long and disorganized that he'd complain about not having time to > "slog" > through the post. No, I am disinclined to slogging through ignorance, misinformation, confusion, and nonsense. Of course I recognize that an exposition my require more than a post. For that matter, I am willing to read books, articles, longer expositions than a mere post, while it is typical of cranks to say they don't have to bother reading books about such things as set theory (even when the cranks is spouting misinformation on the subject). > Of course, in 2008, MoeBlee doesn't ask for a _post_ about > intuitionism, > but rather a _book_ about intuitionism. And of course, in reality, no > single post can satisfy 1)-3) above -- it takes an entire _book_. > Since > presumably books about constructivism exist, and so MoeBlee can ask > HdB to provide him with one. Why would I need HdB to recommend books on constructivism when I already have whole bibliographies about constructivsm, several downloaded articles about constructivism, and books on constructivism? > But for those sci.math posters who are > inventing new theories from scratch, there is no book about their > theory, > nor are they able to publish such a book. Okay, and I never required such a thing. > The fact that MoeBlee requires posters to jump through so many hoops What "hoops"? YOU would call providing a formal language, axioms, definitions, and proofs as "hoops". I would call it "showing your formal theory". > before he would ever say, "yes, your theory is rigorous and sufficient > to > axiomatize the sciences" leads posters like HdB to call him "dogmatic" > and posters like me to agree with them. That's RIDICULOUS! I'm not dogmatic for saying that it has not been shown that a certain proposal is indeed a formal theory that axiomatizes the mathematics for the sciences. I am CORRECT and OPEN- MINDED NOT to declare "your proposal is a formal theory that axiomatizes mathematics for the sciences" when such a thing has NOT (at least not yet) been shown. > No, I don't expect MoeBlee to say "yes, your theory is rigorous and > sufficient to axiomatize the sciences" to _every_ poster who proposes > a > theory, but if only he'd say so to at least _one_ poster -- and it > need not > be HdB and constructivism -- then I'd be less inclined to agree with > HdB > that MoeBlee is "dogmatic." Why should I say it to even ONE poster unless there is a poster that SHOWED such a thing? (If I recall correctly, zuhair has provided some theories that are stronger than ZFC (?). So, if ZFC axiomatizes mathematics for the sciences, then some of zuhair's theories do too. Though, I don't recall what conclusions were found as to relative consistency of some of zuhair's theories.) > Instead, HdB and I conclude that the reason that MoeBlee requires us > to jump so many hoops before considering a foundational theory is that > he doesn't _want_ to consider the possibility that a theory other than > ZFC (and related theories) can be foundational And that is a terrible conclusion. A real non sequitur. (1) In fact I DO devote some of my time to trying to learn more about possible foundational theories other than ZFC (and related). *I* am one who has been mentioning such candidates in many posts. (2) And, again, what you call "hoops" are just basics of what a formal theory IS. Sure, if you want to propose something that is not a formal theory, then you're free to do so. But if one claims to have a formal theory that is a foundation for mathematics, and to the extent that we consider part of being a foundation proving the results of mathematics for the sciences, then it is not "hoops" to ask, "What are the language, rules, axioms, definitions, and proofs?" (3) And notice again that your inference regards my MOTIVES, which is information you just don't have, and even as my posting CONTRADICTS the motives you ascribe to me. > -- and that's why we > believe that MoeBlee is dogmatic. Great, what a terribly weak case - shot full of holes at every point - you've presented. MoeBlee
From: MoeBlee on 15 Jul 2010 12:59 On Jul 14, 8:31 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > "Herc's Axiom Of Pseudo Infinity (based on above equation AOF) > There is a set, I, that includes all the natural numbers that could > physically be computed > (before the end of the computer sustainable Universe)" That is NOT a formal axiom. So let's see what you say further: > Here are my attempts to write Herc's axioms more rigorously: > > Attempt #1 (Schema): > (phi(0) & (Ax (phi(x) -> phi(xu{x})))) -> phi(I) > > Attempt #2: > {} _is_ a (Frege) natural number. For convenience, please define again "is a Frege natural number" in the language of set theory (and if in some other formal language, then please specify it). Also, I take it that '{}' stands for the empty set. > "New Axiom: define finite-Natural Number as all less than 10^500 (the > largest meaningful > number in physics) and define infinite Natural Number as all those > equal to or larger than 10^500." Please define 'meaningful number in physics' in the language of set theory (and if in some other formal language, then please specify it). MoeBlee
From: MoeBlee on 15 Jul 2010 13:03 On Jul 15, 3:00 am, Transfer Principle <lwal...(a)lausd.net> wrote: > The only reason that I > called MoeBlee "dogmatic" is because _others_ have called him > "dogmatic" (i.e., it never would have even _occurred_ to me to use > the word "dogma" were it not for others) ???!!!??? > And so I'll wait for someone else to call MoeBlee "dogmatic" before > resuming the conversation. (If no one else ever does, then MoeBlee > will have been proved correct.) Proved correct in what sense? That I'm not dogmatic? Well, to whatever degree I am or am not dogmatic, that people might or might not comment on it is not itself reason to conclude that I am or am not. MoeBlee
From: James Burns on 15 Jul 2010 14:45 Transfer Principle wrote: > As for AP, he's recently provided the following axiom: > > "New Axiom: define finite-Natural Number as all less than > 10^500 (the largest meaningful number in physics) and > define infinite Natural Number as all those equal to or > larger than 10^500." It happens that the number of ways 8 poker decks of cards (with identical backs) can be shuffled together is one of these infinite Natural Numbers, (8*52)!/(8!)^52 =~ 1.25e671, as one of us Standard Theorists might oppressively put it. Do you or AP intend to distinguish that infinite Natural Number from any other infinite Natural Number? What if I were to destroy one card from the collection of 8 decks and shuffle again? A Standard Theorist might say that there are (8*52-1)!/(7!*(8!)^51) =~ 2.41e669 ways to shuffle the resulting deck. As far as you and AP are concerned, though, this is just another infinite Natural Number -- or so I understand you. Suppose I asked whether there were more, fewer, or the same number of shuffles in the first instance as in the second instance. Am I even allowed to ask this question? If I did, how would you recommend dealing with it, within the AP framework? Jim Burns
From: MoeBlee on 15 Jul 2010 15:13
On Jul 14, 8:31 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > "New Axiom: define finite-Natural Number as all less than 10^500 (the > largest meaningful > number in physics) and define infinite Natural Number as all those > equal to or larger than 10^500." That's a DEFINITION. It's not an axiom (except in the limited sense of a definitional axiom). Def: n is a fin-nat-numb <-> (n is a natural number & n < 10^500) Def: n is an inf-nat-numb <-> (n is a natural number & ~ n is a fin- nat-numb) Okay, so what? MoeBlee |