details re Z-R |- PA consistent
in [Math]
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From: Jesse F. Hughes on 12 Jul 2010 23:22 stevendaryl3016(a)yahoo.com (Daryl McCullough) writes: > Jesse F. Hughes says... > >>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. > > But there must be an alternative foundation for mathematics and logic > according to which Herc's beliefs are perfectly sensible. Sure. Why not? -- "Often times, when [...] looking for a sense of adventure, I'd doodle with math equations. Often too, when pressures of regular life were really bothering me, I'd go for the adventure of fiddling with math." -- James S. Harris, a man of many mathematical adventures!
From: Nam Nguyen on 12 Jul 2010 23:26 Daryl McCullough wrote: > Jesse F. Hughes says... > >> 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. > > But there must be an alternative foundation for mathematics and logic > according to which Herc's beliefs are perfectly sensible. Interesting observation I'd think. Which alternative foundation would that be, could you share with us? -- --------------------------------------------------- Time passes, there is no way we can hold it back. Why, then, do thoughts linger long after everything else is gone? Ryokan ---------------------------------------------------
From: Marshall on 13 Jul 2010 10:39 On Jul 12, 8:26 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote: > Daryl McCullough wrote: > > Jesse F. Hughes says... > > >> 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. > > > But there must be an alternative foundation for mathematics and logic > > according to which Herc's beliefs are perfectly sensible. > > Interesting observation I'd think. Which alternative foundation would > that be, could you share with us? I have to give credit to Nam for at least one thing: he has never claimed that satellites are tormenting him with sonar. Marshall
From: MoeBlee on 13 Jul 2010 11:41 On Jul 12, 8:04 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > On Jul 11, 12:28 pm, MoeBlee <jazzm...(a)hotmail.com> wrote: > > > On Jul 10, 10:36 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > > MoeBlee calls the other posters "dogmatic," and they call > > > MoeBlee "dogmatic" in return. Also, both sides regularly > > > insult each other all the time. Once again, that would make > > > those on both sides "cranks." > > Not by me. If Joe says Bob is dogmatic, that doesn't in itself make > > Joe a crank. > > But if Joe says Bob is dogmatic, and Bob says Joe is dogmatic, > why should I believe Joe that Bob is dogmatic? For I could > equally believe Bob's claim that Joe is dogmatic. > > If two posters make symmetrical yet opposing claims, then > absent any supporting information I see no reason to favor one > claim over the other. That's not at issue. What is at issue is your inference that both are cranks. > > > On the other hand, I do need to give credit where credit's due, and > > > praise those who do overcome their biases to become more > > > open-minded about alternate set theories. And so, in the most > > > recent Herc thread (where he discusses his newly found finitism), > > Herc has an alternative set theory? Pray tell its language, axioms, > > and definitions. > > In the current Herc thread, Herc states that he is replacing the > Axiom of Infinity (i.e., he is starting with a standard theory such as > ZF and replacing Infinity) with his "Axiom of No Infinity": > > "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." I assume by "element" he doesn't mean literally elements of the sequence (since the elements of a sequence are ordered pairs) but rather ENTRIES in the sequence (i.e., members of the range of the sequence). That's an axiom regarding an additional primitive operator 'size of' for sequences or it's supposed to be some kind of defintition of a defined operator 'size of' for sequences? And by 'element of the sequence' does he mean literally an element (which is an ordered pair) or rather some member of the range of the sequence? And what is the quantification? Is it, "If, for some Q, the Qth element [...]"? > He also has what he calls his "Axiom of Pseudo Infinity": > "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)" Please define "physically computed" in the language of Herc's theory. > Right now, I'm guessing (not _lying_, but _guessing_) that > MoeBlee is going to criticize these axioms because they aren't > symbolic enough. Symbols per se are not so much at issue. > Fine then -- this makes me the bridge between > the formalist MoeBlee and the informalist Herc. I don't subscribe to any particular formalist philosophy in full. Asking what formal theory is actually being proposed, and critiquing it as not actually being a formal theory, does not in itself make one a "formalist". MoeBlee
From: Jack Campin - bogus address on 13 Jul 2010 11:43
>> there must be an alternative foundation for mathematics and >> logic according to which Herc's beliefs are perfectly sensible. > Sure. Why not? Because if Herc was confronted with *any* theory that employed coherent strategies of reasoning and had a community of people working on it, he'd assume they created it all with the covert purpose of entrapping him into sticking his head in a microwave. ----------------------------------------------------------------------------- e m a i l : j a c k @ c a m p i n . m e . u k Jack Campin, 11 Third Street, Newtongrange, Midlothian EH22 4PU, Scotland mobile: 07800 739 557 <http://www.campin.me.uk> Twitter: JackCampin |