On 20/06/2010 6:15 AM, |-|ercules wrote: > "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?
Reality? Show me even one infinity in reality.
> > > >> >>> >>> 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.
Hardly. I'm just saying that it's uninteresting that a statement is true under an axiom when it's just a restatement of the axiom.
