Am I a crank?
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From: Lester Zick on 8 Sep 2006 15:10 On Fri, 08 Sep 2006 09:17:30 +0200, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >Lester Zick wrote: > >> I believe peer reviewed articles are also more likely to reflect >> established orthodoxy whether good, bad, or indifferent. > >That's indeed one of the reasons I'm so shy of peer reviewed articles. Also true of moderated newsgroups. Worship of the revered status quo. ~v~~
From: Lester Zick on 8 Sep 2006 15:12 On Fri, 8 Sep 2006 01:00:39 GMT, "Dik T. Winter" <Dik.Winter(a)cwi.nl> wrote: >In article <4500552f(a)news2.lightlink.com> Tony Orlow <tony(a)lightlink.com> writes: > > Dik T. Winter wrote: >... > > > It is quite similar to the parallel postulate in Euclidean geometry. >... > > I really have a hard time imagining anything fruitful coming out of > > mathematics without some form of inductively defined sets or inductive > > proof. > >So have I. But I do not want to exclude the possibility. > > > Your point is well taken in general though, that the theory one > > creates depends entirely on the statements assumed true (axioms). The > > parallel postulate is a wonderful example, and LEM is another. Each rule > > included in the theory tends to restrict it in terms of the conclusions > > it can reach, which is necessary to some extent to ensure consistency. > >This is wrong. Adding axioms gives the possibility to prove stronger >(and more) theorems. And if you add too many, you may find that you >have the possibility to prove contradictionary theorems (and that >way show that there is no consistency). > >Consider the parallel axiom. With it you can prove that the angles of >a triangle when added fill half of a circle. Without it you can not >prove that. > > > As long as no two axioms contradict each other, directly or indirectly, > > the theory is consistent. > >Yes, but the problem is that it is in general impossible to prove (within >the theory) that it is consistent. Is it also impossible to prove that it is not inconsistent? If not the problem becomes empirical. ~v~~
From: Lester Zick on 8 Sep 2006 16:35 On Fri, 08 Sep 2006 12:33:40 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <03a3g2p6s0o7jc14jt3b2pcp5remsieb8n(a)4ax.com>, > Lester Zick <dontbother(a)nowhere.net> wrote: > >> On Thu, 07 Sep 2006 17:35:36 -0600, Virgil <virgil(a)comcast.net> wrote: >> >> >In article <ij61g2dls6044ds806e87t95r8h4tf1ogv(a)4ax.com>, >> > Lester Zick <dontbother(a)nowhere.net> wrote: >> > >> >> On Thu, 07 Sep 2006 13:26:12 -0600, Virgil <virgil(a)comcast.net> wrote: >> >> >> >> >In article <mah0g29jhf7u65h4um3k1jebid22us331o(a)4ax.com>, >> >> > Lester Zick <dontbother(a)nowhere.net> wrote: >> >> > >> >> >> On Wed, 06 Sep 2006 17:13:32 -0600, Virgil <virgil(a)comcast.net> wrote: >> >> > >> >> >> >Zick is the one whose trivia is founded in the trivium. Math is a part >> >> >> >of the quadrivium. >> >> >> >> >> >> And modern math is founded, whatever that means, in the trivium and >> >> >> not in the quadrivium. >> >> > >> >> >And how does someone so self-decaredly ignorant of mathematics know this? >> >> >> >> Because you self declaredly proclaim assumptions of truth in lieu of >> >> demonstrations. >> > >> >Zick frequently does this, but why does he deceive himself that >> >mathematicians emulate his idiocies? >> >> Because they don't and probably can't demonstrate their trivial >> assumptions of truth. >> >But, unlike Zick, they are careful to point out just what unproven >assumptions they are making. Hell that's easy enough: all of them. > Thus no one need be deceived by them, >though one cannot say the same about Zick's claims. ~v~~
From: Dik T. Winter on 8 Sep 2006 22:32 In article <d2g3g2d0s2l1u3spbjf6t3p1mg93mubc1v(a)4ax.com> Lester Zick <dontbother(a)nowhere.net> writes: > On Fri, 8 Sep 2006 01:00:39 GMT, "Dik T. Winter" <Dik.Winter(a)cwi.nl> > wrote: .... > > > As long as no two axioms contradict each other, directly or indirectly, > > > the theory is consistent. > > > > Yes, but the problem is that it is in general impossible to prove (within > > the theory) that it is consistent. > > Is it also impossible to prove that it is not inconsistent? If not the > problem becomes empirical. Indeed, it may be impossible to prove that it is either consistent or not consistent. However, empirical evidence is not sufficient in mathematics. And to get back at an example I already stated many times. Gauss conjectured that Li(x) was an overstimate for the number of primes in the range 1 .. x. I have no idea how you could disprove this with empirical evidence. Every empiric evidence you can come up with reveals that it is true. It is nevertheless false. -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Virgil on 8 Sep 2006 22:51
In article <03a3g2p6s0o7jc14jt3b2pcp5remsieb8n(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > On Thu, 07 Sep 2006 17:35:36 -0600, Virgil <virgil(a)comcast.net> wrote: > > >> >And how does someone so self-decaredly ignorant of mathematics know this? > >> > >> Because you self declaredly proclaim assumptions of truth in lieu of > >> demonstrations. > > > >Zick frequently does this, but why does he deceive himself that > >mathematicians emulate his idiocies? > > Because they don't and probably can't demonstrate their trivial > assumptions of truth. So Zick asserts that in this respect mathematicians are emulating Zick's idiocies? |