This is high praise considering who it is coming from and in what thread. I thank you. Sorry, but you have lost and will always lose this debate.
Who votes that TVAA has won?
It would help if you’d stop using mathematical terminology in a way inconsistent with standard usage.
Actually, you never did get around to demonstrating the definition of ‘consistency’, did you? All you did was provide links to a variety of definitions listed under the word.
** Check the dictionaries. They have these things, called ‘definitions’, that describe the proper meaning and usage of words. I find them incredibly useful! 
Define ‘formal’.
**
Prove it? Prove it?! It’s been shown, Spiritus. Don’t you recall the link? No – I’m sure it wasn’t formal enough for you.
**
Just fascinating, Spiritus. This page that discusses Godel’s invention of the Theorem claims that the reason Godel found a way to use an numerical way to represent statements so that he’d have a “standard model in which we can consider whether a closed formula is true or false.” Oops – there’s those nasty words again!
They also bring up good ol’ Peano Arithmetic. Have fun reading…
Godel’s Second Incompleteness Theorem shows that a consistent system must contain statements it can’t prove… and yet that statement will be true relative to the axioms, or otherwise the system wouldn’t be consistent.
But, of course, it doesn’t matter if those statements are necessarily true! Spiritus says logicians have given up the concept of truth, and his word is law!
You’ve claimed that ‘truth’ isn’t particularly important to this debate and that mathematicians have stopped commonly referring to the concept. The second part is correct, although you misrepresent the reasons why they stopped… the first is wrong. I’ll find that exact quotation later.
While we’re at it, why don’t we discuss all those places where you claimed GIT says nothing about the truth of statements.
** Ignore their meanings and it doesn’t matter how long your replies are – they signify little.
** I’ve provided plenty of examples; you denied them, and tried to shift attention to my supposed misrepresentations.
** Not all of them; just some.
You have lacked: the intelligence to notice the tiny problems in your claims;
the common courtesy to acknowledge the meanings of words in the context they’re being used, instead citing unrelated and irrelevant definitions that you’ve never actually demonstrated;
the intellectual honesty to admit that you just don’t like being told you’re wrong.
Classic Spiritus.
[ol][li]This is why Godel needed to formulate omega-inconsistency.[/li][/ol]
** What’s this?
The mathematical definition of ‘consistency’ actually is ‘simple consistency’?! Who would have known? Consistency is a consequence of omega-consistency?! Who could have imagined?
Try actually reading the sources you use… you might have an idea of what you’re talking about.
** I don’t think you can understand any case not couched in mathematical symbols. That would explain why your sources seem to contradict your claims. I take it they’re imperfect presentations to the ignorant, yes?
** I would have admitted that if you’d asked. (Not that I think you know much about Tarski’s work, if your understanding of GIT is any indication.)
** Not really. It was supposed to make you realize that that method of defining ‘truth’ is useful.
** If it were accurate enough, it would be me, stupid. That’s the whole point. You’re the one who seems to think this idea implies voodoo… although that’s about the mentality you’d be able to grasp, isn’t it?
** It’s fairly obvious. Oh, wait – I forgot nothing is obvious to you except the mistaken beliefs you hold. My pardon.
Wow,
After 9 pages, I gotta say that TVAA’s perverse insistence that, contrary to all evidence, he is right and all his opponents are wrong makes the Iraqi Minister of Information look positively reasonable by comparison.
Crikey!
What evidence would that be?
The unsubstantiated claims of Dopers isn’t evidence. The linked sites that contradict Spiritus’ claims: now that’s evidence.
One “nay” vote from the bemused delegate from Puddletown.
Unless putting your fingers in your ears and going “I’m right and you’re an idiot la la la la” over and over counts as winning…
There are no refutations in this thread. Spiritus has been surrounded ALLLLLLL over the board. First, we are going to kill him and then we are going to put him in prison for crimes of rhetoric. There is no evidence. I will take you to a thread where Spiritus has been soundly defeated. I will do this in ONE HOUR. And then, I will do something surprising. Something unconventional. You will see.
Look, it doesn’t matter… as long as he simulates what it is like to win a debate then there is no fundamental difference between the two and we can say that he’s right. Because there’s no difference in the way a right person acts and he does. So he’s right.
Duh.
::applause:: 
eris, I expected at least an intelligent complaint from you.
Oh well…
(I mean, don’t actually bother to read the new site… it’s not worth it to note that it points out that Spiritus is wrong. And don’t go trying to actually figure out what I mean – you’ll just confuse yourself with the rantings of a madman, right?)
I’m hurt.
Actually, I took the time last night to read the translation and overview of Godel’s proof that he linked to. I saw no problems.
Care to be more specific?
But you didn’t read my link?
http://www.andrew.cmu.edu/~cebrown/notes/vonHeijenoort.html#Godel2 The sections on Godel are quite a ways down the page… between 2/3rds and 3/4ths of the way, I’d guess.
Please note that the site points out that omega-consistency was eventually discarded, that the consistency of arithmetic can actually be proven ( when GIT shows that it can neither be proven nor disproven within arithmetic), et cetera.
And you didn’t notice that Spiritus’ link identifies ‘consistency’ with ‘simple consistency’ and claims the simple consistency of a system is a consequences of its omega-consistency?
Or the part where they show that if a system is consistent, its consistency cannot be proved or disproved within itself (in other words, the statement ‘that system is consistent’ is true but a godel statement of the system)?
Please reread your link.
I would say that passage is not something that refutes Spiritus’s claims at all.
For what? I would appreciate you to illustrate what Rosser did in extending the incompleteness theorems without using omega-consistency. In doing so, I would like you to quote portions of the text that support your statements, and also quote portions of Spiritus’s text that show how he was being silly, factually incorrect, et cetera.
In short: make an argument.
** He claims that considering the ‘truth’ of this statements is inappropriate. Those links do so. He claims that it is not necessarily the case that some Godel statements are necessarily true but not provable within the system; this is clearly false, as those links demonstrate a statement which can never be proven within a system but is true nevertheless in all of the sufficiently powerful systems it discusses.
** How?
Neither you nor I are sufficiently capable mathematicians that we could actually understand such an argument. I frankly don’t know exactly what Rosser did. I don’t need to. Spiritus’ link states that the consistency of the systems Godel used is a consequence of their omega-consistency. Basically, Spiritus’ claims about what ‘consistency’ means are grossly incorrect AND omega-consistency doesn’t need to be used for the Incompleteness Theorems to apply: plain old consistency works just fine. Mathematicians must better than anyone here have already done it – all I need to do is point out that they have done it, I don’t need to reinvent the wheel from scratch.
Are you unable to remember claims Spiritus had repeated over and over for nearly thirteen pages of messge board?
That’s precisely what he’s relying on: he knows that nobody will ever read this thread all the way through, so his inaccuracies, misstatements, and lies will eventually be buried in text.
For you, I’ll see what I can manage. But you shouldn’t need me to point out the inconsistencies. Where have you been all this time?
In the meantime, consider this:
When I say that the different levels of reality are fundamentally the same, I mean that there’s no property that allows anyone to objectively identify any particular level as ‘real’ or ‘virtual’. If ‘reality’ is just the level in which you exist, then by generating simulations of yourself you can enter previously ‘virtual’ systems and make them real. You might also find a way to bring yourself into the levels underlying your ‘reality’, becoming even more real.
Whether this universe is real or virtual is ultimately not a meaningful question to ask. No information is ever really conveyed by any proper response.
I enjoy Spiritus very much, TVAA. He is a favorite poster of mine, and a semi-personal friend as far as the internet goes. I read everything he writes. It is my pet fucking hobby to prove him wrong.
YOU DO NOT JUST WAVE YOUR HANDS AND SAY HE’S WRONG OR DIDN’T YOU READ MY SHIT TO CONSTRUCT AN ARGUMENT FOR ME, YOU MAKE A FUCKING ARGUMENT YOURSELF.
I’m done. At the very least, you are right and cannot present a case to save your life, in which case I am piss-all interested in anything your millions of links have to say. Children’s books about the perils of theft have done a better job than this in the same amount of pages but with more pictures. At the very worst, you are as dishonest as so many have claimed here.
You’re asking me to prove that Spiritus said something that was being argued about not three pages ago?
No kidding you’re done.
I made my arguments at the beginning of these threads – all the rest of this has been Spiritus’ trying to make counterarguments and my trying to refute them.
He’s demanded that I “do what Godel couldn’t do” and demonstrate that some Godel statements are necessarily true. It’s been done by other people. All I need to do is reference sources that show it’s been done.
I’m not asking anyone to “construct my argument for me”. I HAVE BETTER THINGS TO DO THAN REMIND YOU OF WHAT SPIRITUS SAID SEVERAL PAGES AGO. Am I supposed to not only prove what he said was wrong but repost each and every time he made the claim?
He’s repeatedly stated that I’m using the word ‘consistency’ improperly and that it has a specific meaning in mathematics. The source he then links to four pages later states precisely what ‘consistency’ means in regards to Godel’s arguments – and it’s what I said, not what he said. He’s never offered a source that gives a precise defintion of ‘consistency’ that matches his description – he’s offered sites that define much weaker concepts but never actually state what ‘consistency’ is.
He’s said that the concept of ‘truth’ is improper for a discussion of GIT – but the sources we’ve both linked to include discussions of truth.
He’s said repeatedly that this discussion should focus on omega consistency instead of simple consistency – but the link he offered states that simple consistency is a consequence of omega consistency, and links I offer show that mathematicians have demonstrated GIT while discarding omega consistency.
And you can’t find any problems?
And the votes for TVAA having won are rolling in folks! Can the internet keep up with the deluge of data???
If TVAA wants a review of the last few pages I’m more than happy to oblige him.
What I’ve learned from this thread is that on top of being a deluded crackpot possibly worshiping a variant of Kyrptonian Scientology TVAA is also quite a tenacious little bugger as well. When his skewed rationalizations, piss poor analogies, and outright inaccuracies fail to convince an audience he resorts to an incessant torrent of “nu uh’s!” For some reason I always imagine they should be read in the voice of Hal 9000 with just the faintest tinge of deranged pity, “I’m sorry Dave, I have specialists who say you’re wrong, <long pause> moron.”
Naturally one would immediately wonder who these nondescript specialists are. Maybe we are horribly mistaken and owe TVAA our deepest apologizes for questioning both his massive intellect and his access to leading authorities on GIT. Would the real expert please stand up? But alas a new twist arises…
Logical statements expressed by our exceptionally feeble minds actually make them physically ill? That’s some trick! Boy they must really be some smart guys, the kind of people who need custom hats for their freakishly huge craniums and have pulsing veins in their foreheads that beat out the digits of pi. Either that or we’re all huge idiots and no one bothered to tell us. Hmmm…. It’s and interesting proposition, but I’m going to go with c) TVAA grew up in a nuclear power plant and has a taste for paint chips.
With the commanding backing of his experts called into question, and further investigation mounting TVAA falls back onto and old favorite of charlatans and hustlers…
Hence…
When obfuscation fails to throw his pursuers off the trail he pulls out the big guns, the most potent debating tactic in the history of verbal confrontation… the mom joke…
…and there you have TVAA in this thread in a nutshell. Clearly we are in the presence of brilliance the likes of which this planet has never known.
So little time. Just a few highlights.
:rolleyes:
I use mathematical terminology in a manner consistent with mathematic. That’s what it is for. The whole “meaning of consistency” digression consists of two things:
[ul][li]Your arrogant pronouncements that only TVAA knows the “true” meaning of consistency.[/li][li]Your ignorant pronouncements that Godel’s original work help for simply (negation) consistent systems rather then omega-consistent systems.[/ul][/li]
:rolleyes:
Right, because it hasn’t been made clear over and over and over that neither ultrafilter nor I were referencing “comoon language” definitions of ‘consistency’.
:rolleyes:
As I suspected: chickenshit.
:rolleyes:
No, the argument you linked to includes the additional restrictions necessary to invoke Tarskian truth conditions. Here, let me put this in excruciatingly simple terms.
[ul][li]Few restrictions => broad application of theorem == GOOD[/li][li]More restrictions => narrow application of theorem == LESS GOOD.[/li][li]Godel, and folks who extended his work, wanted GIT to be as GOOD as possible.[/li][li]Adding extra restrictions, that are not required to acheive the same result, makes GIT LESS GOOD.[/li][/ul]
:rolleyes:
Yes, and there’s the words “standard model”. Trust me, you really don’t want to get into issues of teh standard model of arithmetic and how we can use it to argue that somethiung must be true in an arithmetic system. Godel himself said: “the exact statement of the proof [of the undecidability of g], which now follows, will have among others the task of substituting for the second of these assumptions [that every provable formula is also correct as regards content] a purely formal and much weaker one”. In other words, he used truth in his semi-formal presentation of method, but Godel understood that the formal result should and could be dervied from a more secure and weaker quality.
Godel wanted his proof to be as powerful as possible. Adding a requirement that some Godel statements be “true” weakens the applicability of the theorem. That is a LESS GOOD thing.
:rolleyes:
You’re an idiot. “Simple consistency” is what Godel was aiming for. He couldn’t get there from his original Godel statement.
The phrase you are too stupid to understand is: the ‘consistency’ (sometimes called ‘simple consistency’) of P is a consequence of its ‘w-consistency’ Here is what that means:
[ol][li]{omega-consistent systems} is a subset of {simply consistent systems}. (Actually, this places some restrictions on the allowed rules of infeence, but there is little hope that you would understand such nuances.}[/li]li implies that if a system is omega-consistent, it is also simply consistent.[/li][li]The converse is not true. A system may be consistent without being omega-consistent.[/li][li]Thus, Godel’s proof, which holds for all omega-consistent systems, does not have implications for all simply consistent systems.[/ol][/li]
I do read the sources that I post. I cannot change the fact that you are both too poorly educated to read the material with comprehension and too ignorant to realize your own limitations. BTW, the passage that you should have tried to understand is:
That quote both shows how Godel’s proof is invoked through omega-consistency and why simple consistency was insufficient for the purpose. Perhaps you should ask one oyf your “invisible experts[supTm[/sup]” to explain it to you.
Have to run – I’ll catch up on the other nonsense as time permits.