details re Z-R |- PA consistent
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From: Transfer Principle on 14 Jul 2010 20:55 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) 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 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) 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. 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. 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. The fact that MoeBlee requires posters to jump through so many hoops 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. 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." 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's why we believe that MoeBlee is dogmatic.
From: Nam Nguyen on 14 Jul 2010 21:08 Transfer Principle wrote: > > So what should I do? I want to discuss alternatives to ZFC > without being associated with the Adam-Herc or Atom Totality > theories, but posters continue to bring these non-mathematical > ideas over and over. Did you state the axioms for your alternative theories? -- --------------------------------------------------- Time passes, there is no way we can hold it back. Why, then, do thoughts linger long after everything else is gone? Ryokan ---------------------------------------------------
From: Transfer Principle on 14 Jul 2010 21:31 On Jul 14, 6:08 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Transfer Principle wrote: > > So what should I do? I want to discuss alternatives to ZFC > > without being associated with the Adam-Herc or Atom Totality > > theories, but posters continue to bring these non-mathematical > > ideas over and over. > Did you state the axioms for your alternative theories? Nguyen asks for the axioms for Herc's and AP's alternative theories. Herc starts with ZF-Infinity and adds the following axioms: "Herc's Axiom Of No Infinity If the Qth element of a sequence is the natural number Q, then the size of the sequence equals some element of the sequence." "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)" 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. (This axiom has been challenged by Jeffries, though.) 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."
From: Jesse F. Hughes on 14 Jul 2010 22:36 Transfer Principle <lwalke3(a)lausd.net> writes: > On Jul 12, 7:29 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: >> Transfer Principle <lwal...(a)lausd.net> writes: >> > But I'm not sure whether I want to resort to NFU to make Herc's >> > theory work. There might also be a trick using NBG and Srinivasan >> > to declare some object similar to D -- such as the class of all sets >> > of cardinality greater than n -- to equal the empty set 0. >> Herc doesn't have a theory. Herc is, as we all know, a radically >> deluded individual. >> Of all the persons that you "defend", Herc is clearly the worst choice. >> I'm not sure why you think that he is a mathematician at all. He is >> honestly incapable of rational argument. I don't say this to be mean or >> to defend my own biases regarding the existence of infinite sets (about >> which I really have no coherent philosophical views) but rather because >> we can all see that Herc is a disturbed individual who believes that he >> is Adam, that an unfortunate lady is his Eve and that satellites are >> tormenting him with sonar. These assertions are not wholly irrelevant >> to understanding his "mathematical" claims. > > And here we go again. I'd like to be able to discuss Herc's > mathematics independently of his unorthodox religious beliefs > about Adam and Eve, but according to Jesse Hughes, his > mathematical and non-mathematical claims are related. No, I did not say they are related. I said that the basic cognitive competence he shows in his non-mathematical claims is also a pretty good explanation for his so-called mathematical claims. The man is delusional, but you want to try to find a mathematical theory that is actually consistent with some of his delusions and thereby "defend" him. I just don't see the point. > This also comes up in the AP threads, where I'd like to discuss AP's > mathematics without becoming an Atom Totalitarian. Similarly, AP's "scientific" reasoning is of similar quality to his "mathematical" reasoning. The fact is that you can see his physical theories are simply nonsense, but nonetheless you pretend that his mathematical claims show great insight, if only you can find the right theory for them. > So what should I do? I want to discuss alternatives to ZFC > without being associated with the Adam-Herc or Atom Totality > theories, but posters continue to bring these non-mathematical > ideas over and over. And you miss the point over and over, but this is no surprise. -- "We are happy that you agree that customers need to know that Open Source is legal and stable, and we heartily agree with that sentence of your letter. The others don't seem to make as much sense, but we find the dialogue refreshing." -- Linus Torvalds to Darl McBride
From: Nam Nguyen on 14 Jul 2010 23:51
Transfer Principle wrote: > On Jul 14, 6:08 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> Transfer Principle wrote: >>> So what should I do? I want to discuss alternatives to ZFC >>> without being associated with the Adam-Herc or Atom Totality >>> theories, but posters continue to bring these non-mathematical >>> ideas over and over. >> Did you state the axioms for your alternative theories? > > Nguyen asks for the axioms for Herc's and AP's alternative theories. No. Read my post carefully: I asked for "_your_ alternative theories" since you yourself had expressed "I want to discuss alternatives to ZFC" without mentioning the name Herc of AP. (Btw nothing personal but I'm not interested in the "mathematical theories" from either of them). > > Herc starts with ZF-Infinity and adds the following axioms: > > Here are my attempts to write Herc's axioms more rigorously: > > Attempt #1 (Schema): > (phi(0) & (Ax (phi(x) -> phi(xu{x})))) -> phi(I) "Rigorously"? So what is '0' in this set-language? and what are the axioms concerning it? > > Attempt #2: > {} _is_ a (Frege) natural number. > (This axiom has been challenged by Jeffries, though.) In term of rigorousness, this is even worse than your attempt #1 above! Again, why don't you state your own axioms? -- --------------------------------------------------- Time passes, there is no way we can hold it back. Why, then, do thoughts linger long after everything else is gone? Ryokan --------------------------------------------------- |