"Sylvia Else" <sylvia@not.here.invalid> wrote... > On 19/06/2010 7:23 PM, |-|ercules wrote: >> "Sylvia Else" <sylvia@not.here.invalid> wrote >>> On 19/06/2010 4:14 PM, |-|ercules wrote: >>>> "Sylvia Else" <sylvia@not.here.invalid> wrote ... >>>>> On 19/06/2010 1:40 PM, |-|ercules wrote: >>>>>> "Sylvia Else" <sylvia@not.here.invalid> wrote ... >>>>>>> On 19/06/2010 12:45 PM, |-|ercules wrote: >>>>>>>> "Sylvia Else" <sylvia@not.here.invalid> wrote >>>>>>>>> On 19/06/2010 6:50 AM, WM wrote: >>>>>>>>>> On 18 Jun., 09:37, Sylvia Else<syl...@not.here.invalid> wrote: >>>>>>>>>>> On 18/06/2010 5:31 PM, |-|ercules wrote: >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>>> "Sylvia Else"<syl...@not.here.invalid> wrote ... >>>>>>>>>>>>> On 18/06/2010 4:52 PM, |-|ercules wrote: >>>>>>>>>>>>>> "Sylvia Else"<syl...@not.here.invalid> wrote ... >>>>>>>>>>>>>>> On 18/06/2010 3:03 PM, |-|ercules wrote: >>>>>>>>>>>>>>>> "Sylvia Else"<syl...@not.here.invalid> wrote >>>>>>>>>>>>>>>>> On 18/06/2010 10:40 AM, Transfer Principle wrote: >>>>>>>>>>>>>>>>>> On Jun 17, 6:56 am, Sylvia Else<syl...@not.here.invalid> >>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>> On 15/06/2010 2:13 PM, |-|ercules wrote: >>>>>>>>>>>>>>>>>>>> the list of computable reals contain every digit of ALL >>>>>>>>>>>>>>>>>>>> possible >>>>>>>>>>>>>>>>>>>> infinite sequences (3) >>>>>>>>>>>>>>>>>>> Obviously not - the diagonal argument shows that it >>>>>>>>>>>>>>>>>>> doesn't. >>>>>>>>>>> >>>>>>>>>>>>>>>>>> But Herc doesn't accept the diagonal argument. Just >>>>>>>>>>>>>>>>>> because >>>>>>>>>>>>>>>>>> Else accepts the diagonal argument, it doesn't mean that >>>>>>>>>>>>>>>>>> Herc is required to accept it. >>>>>>>>>>> >>>>>>>>>>>>>>>>>> Sure, Cantor's Theorem is a theorem of ZFC. But Herc said >>>>>>>>>>>>>>>>>> nothing about working in ZFC. To Herc, ZFC is a "religion" >>>>>>>>>>>>>>>>>> in which he doesn't believe. >>>>>>>>>>> >>>>>>>>>>>>>>>>> Well, if he's not working in ZFC, then he cannot make >>>>>>>>>>>>>>>>> statements >>>>>>>>>>>>>>>>> about >>>>>>>>>>>>>>>>> ZFC, and he should state the axioms of his system. >>>>>>>>>>> >>>>>>>>>>>>>>>> Can you prove from axioms that is what I should do? >>>>>>>>>>> >>>>>>>>>>>>>>>> If you want to lodge a complaint with The Eiffel Tower that >>>>>>>>>>>>>>>> the >>>>>>>>>>>>>>>> lift is >>>>>>>>>>>>>>>> broken >>>>>>>>>>>>>>>> do you build your own skyscraper next to the Eiffel Tower to >>>>>>>>>>>>>>>> demonstrate >>>>>>>>>>>>>>>> that fact? >>>>>>>>>>> >>>>>>>>>>>>>>> That's hardly a valid analogy. >>>>>>>>>>> >>>>>>>>>>>>>>> If you're attempting to show that ZFC is inconsistent, >>>>>>>>>>>>>>> then say >>>>>>>>>>>>>>> that >>>>>>>>>>>>>>> you are working within ZFC. >>>>>>>>>>> >>>>>>>>>>>>>>> If you're not working withint ZFC, then you're attempting to >>>>>>>>>>>>>>> show that >>>>>>>>>>>>>>> some other set of axioms is inconsistent, which they may be, >>>>>>>>>>>>>>> but >>>>>>>>>>>>>>> the >>>>>>>>>>>>>>> result is uninteresting, and says nothing about ZFC. >>>>>>>>>>> >>>>>>>>>>>>>>> Sylvia. >>>>>>>>>>> >>>>>>>>>>>>>> That would be like finding a fault with the plans of The >>>>>>>>>>>>>> Leaning >>>>>>>>>>>>>> Tower >>>>>>>>>>>>>> Of Piza. >>>>>>>>>>> >>>>>>>>>>>>>> I might look at ZFC at some point, but while you're presenting >>>>>>>>>>>>>> Cantor's >>>>>>>>>>>>>> proof >>>>>>>>>>>>>> in elementary logic I'll attack that logic. >>>>>>>>>>> >>>>>>>>>>>>>> Instead of 'constructing' a particular anti-diagonal, your >>>>>>>>>>>>>> proof >>>>>>>>>>>>>> should >>>>>>>>>>>>>> work equally >>>>>>>>>>>>>> well by giving the *form* of the anti-diagonal. >>>>>>>>>>> >>>>>>>>>>>>>> This is what a general diagonal argument looks like. >>>>>>>>>>> >>>>>>>>>>>>>> For any list of reals L. >>>>>>>>>>> >>>>>>>>>>>>>> CONSTRUCT a real such that >>>>>>>>>>>>>> An AD(n) =/= L(n,n) >>>>>>>>>>> >>>>>>>>>>>>>> Now to demonstrate this real is not on L, it is obvious that >>>>>>>>>>>>>> An AD(n) =/= L(n,n) >>>>>>>>>>> >>>>>>>>>>>>>> Therefore >>>>>>>>>>>>>> [ An AD(n) =/= L(n,n) -> An AD(n) =/= L(n,n) ] proves >>>>>>>>>>>>>> superinfinity! >>>>>>>>>>> >>>>>>>>>>>>>> And THAT is Cantor's proof! >>>>>>>>>>> >>>>>>>>>>>>>> Want to see his other proof? That no box contains the box >>>>>>>>>>>>>> numbers >>>>>>>>>>>>>> (of >>>>>>>>>>>>>> boxes) that >>>>>>>>>>>>>> don't contain their own box number? >>>>>>>>>>>>>> That ALSO proves superinfinity! >>>>>>>>>>> >>>>>>>>>>>>>> Great holy grail of mathematics you have there. >>>>>>>>>>> >>>>>>>>>>>>>> Herc >>>>>>>>>>> >>>>>>>>>>>>> What are you trying to prove? >>>>>>>>>>> >>>>>>>>>>>> There is only one type of infinity. >>>>>>>>>>> >>>>>>>>>>> Infinity is a mathematical construct. Before you can even >>>>>>>>>>> being to >>>>>>>>>>> discuss it, you have to have a set of axioms. >>>>>>>>>> >>>>>>>>>> What was the set that Cantor used? >>>>>>>>>> Nevertheless he "proved". >>>>>>>>> >>>>>>>>> He certainly was using some. For example, the diagonal argument >>>>>>>>> falls >>>>>>>>> apart if the axioms don't permit the construction of a number by >>>>>>>>> choosing digits different from those on the diagonal. >>>>>>>>> >>>>>>>>> It isn't even clear whether Herc is tying to invalidate Cantor's >>>>>>>>> proof >>>>>>>>> by finding a mistake in it, or to prove the inverse, which wouldn't >>>>>>>>> invalidate Cantor's proof, but would only show that the axioms on >>>>>>>>> which it is based are inconsistent. >>>>>>>>> >>>>>>>>> Herc cannot avoid the need to specify the set of axioms. >>>>>>>>> >>>>>>>>> Sylvia. >>>>>>>> >>>>>>>> How would one dispute axiomatic deductions if that were the case? >>>>>>> >>>>>>> What do you mean by "axiomatic deduction"? >>>>>>>> >>>>>>>> Are you saying all mathematical facts are either axioms or the >>>>>>>> result of >>>>>>>> (X & X->Y) -> Y >>>>>>>> ? >>>>>>> >>>>>>> Mathematics consists of axioms and statements (theorems) that can be >>>>>>> proved from those axioms. The axioms cannot themselves be proved, nor >>>>>>> disproved, though they may be shown to be inconsistent with one >>>>>>> another. >>>>>>> >>>>>>> Sometimes the axioms seem so self-evidently true that people aren't >>>>>>> even aware that they're there. But they are, if you look. >>>>>>> >>>>>>> Sylvia. >>>>>> >>>>>> blah blah blah... >>>>>> >>>>>> you skipped my question, but don't bother I wasn't arguing anything >>>>>> just seeing if you knew what you were talking about. >>>>> >>>>> Your question was typically vague. They you dived into some notation >>>>> which might be construed to mean "if X and X implies Y, then Y", which >>>>> is itself unproveable, and needs to be introduced as an axiom. >>>>> >>>>> None of which eliminates your need to specify the axioms in which >>>>> you're making claims about Cantor's proof. >>>>> >>>>> Sylvia. >>>> >>>> HAHAHAHA >>>> >>>> You never studied theorem provers. You're like Wally Anglesea, one of >>>> the thickest morons I've ever come across, but he has in innate ability >>>> to regurgitate >>>> the arguments of other skeptics, in the right places, imitating >>>> intelligence. >>>> >>>> Herc >>> >>> It's pattern. When someone gets too close to pinning you down, you >>> abandon any kind of argument and shift to abuse instead. >>> >>> I take it, then, that you're not willing to specify the axioms you're >>> working with, because you know very well that doing so will make your >>> claims disprovable, rather than merely undecidable, which they are in >>> the absence of axioms. >>> >>> Sylvia. >> >> >> You don't even know how a new formula is derived from an axiom. >> >> Your lights are on but no-one's home. >> >> That's why you never comprehend anything out of the ordinary, you >> just regurgitate common wisdom. No mental function though, only rudimentary >> life support. >> >> Why do I need to provide a new set of axioms for? >> >> You built a swazi symbol out of pick up sticks and want me to paint >> a mona lisa? >> >> ZFC is not proven to be correct, complete, factual, or even useful. >> >> Making your own special axiom model is just one scientific method >> I can use to take down the silly human interpreted claims that you think >> ZFC proved. > > ZFC makes claims in the context of ZFC. You can't take it down using a > different set of axioms, because ZFC doesn't make statements under those > other axioms. If you want to attack ZFC, as distinct from inventing > competing sets of axioms, your only viable course is to seek to show > that it is inconsistent.
Either inconsistent with itself, or inconsistent with reality. So?
> >> >> FUCK SYLVIA - A Trillion people for the next billion years are going to >> laugh their heads off at that stupid idiotic claim. > > That seems a tad improbable. Most of them won't get to hear about it. > >> >> The CENTRAL AXIOM is that facts, theorems, hypothesis, proofs, symbols, >> constants, >> numbers, expressions, proofs are all a computer program or output of a >> computer program >> and listable. > > So what you're saying is that under an axiom that prohibits uncountable > sets, there are no uncountable sets. Glad we cleared that up. Not that > it was very interesting, but we can move on. > > Sylvia.
There you go again, everything you claim is interesting, everything else is not.
