"Sylvia Else" <sylvia@not.here.invalid> wrote ... > 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. >
Why? You prefer your discussion points to be derived from axioms, not axioms themselves?
