:dubious:
Do you have idea what’s going on in this thread?
Karaoke!
This is not a sufficient response, IMO. Judging from this thread, you appear to have a habit of mischaracterizing the remarks of others (homonucleus indeed). Now, impressionistic thinking is one thing. Combining that with abusiveness is less acceptable.
He may have made such claims, but I have never seen them. Frankly I’ve read a number of his posts though and Spiritus does not strike me a braggart.
TVAA, on the other hand does. It would be unfair to make such an assertion without examples, however:
Gems from TVAA, from the past couple of days
“I don’t know more about the workings of the human brain than anyone else, living or dead – but I know a LOT more than you do.”
" I am certain they’re [Spiritus and ultrafilter!] making very stupid mistakes, though."
“I am under no obligation to respect pastawits who can’t think.”
…
Flowbark: What about those who can’t make a well substantiated argument (as opposed to a half-assed and often abusive characterizations)?
For the sake of accuracy, I must stress that “Braggart” is probably not the best characterization of TVAA. Vain Pretender to Knowledge would be a better one, as far as I can tell.
Ok, invective aside, I should note that TVAA has too much verbal acuity to be considered a total idiot.
His errors are those of hubris. I somehow suspect that his invisible experts have a better sense of what they know and don’t know. Perhaps TVAA could focus less on the conclusions he apparently shares with them and more on their methods of investigation and discourse.
To take a hypothetical example, if somebody had read both The Tao of Physics and A Brief History of Time, I wouldn’t say that they had mastered Quantum Mechanics at even an Introductory Level. Popular treatments are different and I would argue more superficial (and often more speculative) than those in textbooks.
That’s ok. We all have to start somewhere. I myself do not claim to understand physics, though I read popular treatments (and occasionally textbooks) with some interest.
However, if my hypothetical person called any decent physics major an idiot, my likely response would be first dubiousness, then laughter.
Can’t rule it out!!!
You pathetic little worm. I thought that the climax of your personal implosion of credibility occurred a few posts ago when you disdained to address five detailed examples of your dishonest posting style with a mewling,
That one had potential, since it assumes that every person reading this thread is somehow too stupid to actually read and understand the exhibit of your dishonesty. One might imagine that it would be difficult for even you to demonstrate more clearly the utter lack of personal integrity with which you engage in debate. Perish the thought! The disfunctional pathology that is TVAA has deeper troughs to slink through.
You tease us with an appetizer, next. Gleefully proclaiming that I must sureley be a fraud for not pointing out the difference between a complete system and a non-contradictory system. You waft the stench of that charge through the thread, tantalizing us with the idea that you might actually (finally!) have a charge of some merit. But no, as a confection it proves but a trifle, lacking both zest and complexity. It is simply another example of you asserting something that is patently false. It takes but a moment for me to demonstrate, yet again, that you are clearly and unequivocally wrong.
Not the you have the integrity to acknowledge the error, of course, The TVAA method is to ignore, insult, and hope that nobody notices.
Ah–but the masterpiece was yet to come, wasn’t it? For now TVAA somehow manages to ooze himself into a nearly upright posture amongst the sewage of this thread and post, as if with a straight face, we can’t rule out the possibility that we could show it to be true by extending the axiom set. But how can that be? Have not TVAA and his band of invisible experts[sup]Tm[/sup] declared that:
Always! there can be no doubt, for TVAA and his band of experts invisible[sup]Tm[/sup] cannot be doubted. Why, one of them is at least three degrees of separation removed from the stupid people who post on this board. And verily, from the height of their invisible prominence they have decreed (through TVAA: prophet plenipotentiary of the invisible realm)
There will be! And so, it must be so. No meally-mouthed can’t rule out’s here–why that would be almost as perfidious as daring to say that
But that cannot be, for to utter such heresy would be to invite bitter scorn and outrageous insults. Verily the vilest PIT of SDMB is th inevitable destination for any who dare suggest that GIT does not demand TRUTH be found amongst the unproveable statements. We know this, because the experts ineffable[sup]Tm[/sup] have deemed it so. Oh, not in person for they would ne’er sully their exalted fingers by dipping them into the shallow and dank pool of the SDMB. Yet they graciously allow their bountious wisdom to grace our porr soulds through the Turret’s twitching of TVAA: presto-digitator of the sages. And lo, the sacred fingers have t-a-p-p-e-d o-u-t
The fingers have spoken, and they leave no room for doubt. The specialists supraliminal[sup]Tm[/sup] have spoken (through the ecstatic seizures of TVAA: drooling mouthpiece of the master mathematicians.) Let no man speak against them, lest the epithets fall as the locusts upon Egypt. Stupid. Idiot. Spiritus. Mundi. For TVAA is an angry prohpet. He has a BIG IDEA[sup]c[/sup], and he has no patience for disagreement. After all, has he not said
Of course, the notes to that very cite indicated that the TRUTH was unnecessary, but that would hardly be sufficent to disuade TVAA and his posse of poseur’s penultimate[sup]Tm[/sup]. Notes be damned, they say. And "Damn the notes! Full ignorance ahead!
[ul][li]Proven! [/li][li]we can’t rule it out. [/ul][/li]One of these things is not like the other. But, of course, TVAA is still certain that I am both stupid and absolutely clueless about Godel’s Theorems. After all, his invisible friends[sup]Tm[/sup] told him so.
Then again, TVAA is a dishonest little prick. He’s not shy about it, though. He paces his character flaws on full display for all to see.
More’s the pity. :wally
It’s “homunculus”, first of all.
Secondly, do you know what “homunculus” means in regards to theories of mind? I ask because you claim I’m misrepresenting the argument I’m responding to… and yet I don’t think I am.
And none of those statements are bragging. The first is accurate, the second is debatable, and the last is simply true.
I would agree that a person who had merely read The Tao of Physics and A Brief History of Time is almost certainly not competent to discuss physics with a major.
If that person were having a discussion with a physics major regarding quantum computation, and the physics major insisted that quantum computers were capable of tasks normal computational devices were incapable of, the reader would be justified in calling him stupid. If he isn’t stupid because of a lack of intelligence, he’s stupid for making a claim that contradicts knowledge he’s expected to have.
That’s your counter-argument? You insult my friends and repeat my statements over and over (as if repetition would falsify them)?
Spiritus, the definitions of completeness and truth are probably the most effective ways you could defuse my argument. Mocking the possibility isn’t going to help your case any.
And indeed, the statement cannot be proven, can it?
You haven’t bothered to actually refute anything in quite some time, SM. Your constant cry of “Aha! Behold the pretender’s error!” doesn’t disguise your inability to actually state your point.
I’ve read this thread and the other straight through several times, and the only one I can show is making “patently false” statements is you. (Of course, they’re correct when “properly interpreted” in such a way as to include the vital points you were leaving out… convenient, no?)
Face it, Spiritus: this stopped being about the argument about eight pages ago. If you wanted to point out the relative problems with the word “truth”, you should have done so at the beginning. Instead you kept making statements about “soundness”, which is utterly irrelevant to this topic.
Well, you are certainly an idiot if you think I need to refute a special case of GIT in order to defend a general principle of GIT.
GIT says nothing about the truth of the statements that it declares unproveable. That does not stop someone from adding additional criteria to the general proof, such as a Tarskian truth condition, and demonstrating that GIT still holds. One could also show that GIT holds for first-order predicate calculus, which demands a binary truth relationship and thus that some (exactly half) of the Godel statements be true. Both of those proofs result in a weaker formulation than the standard GIT (which is not actually the form proven by Godel, as I am sure you and your invisible experts are well aware.)
[ol][li]The standard formulation of GIT is the most powerful one that anybody has yet demonstrated. It is quite cear and quite generic and it does not require that a Godel statement be “true”. [/li]
[li]It is possible to show that GIT holds in any number of more specific contexts than the generic Peano Axiomatization, such as a predicate calculus, that will necessitate a truth condition for some G statements.[/li]
[li](2) has absolutely no effect on (1).[/ol][/li]Do your invisible experts understand that yet?
I’m not claiming that a Godel statement must be true. You’ve claimed that I’ve claimed this for what, six pages now?
GIT shows that some statements will always be unprovable. These statements can be either true or false.
GIT does not state that the unprovable statements are true – that’s not a conclusion of Godel’s argument. We can still discuss its consequences – and one of those consequences is that there are unprovable statements in sufficiently poweful axiomatic systems (some of which happen to be true).
Do you understand that?
Repetition does not falsify them. The wikpedia citation falsified them. Your pathetic attempt to dodge from “GIT proves it” into, “we can’t rule it out” is simply another example of your unfamiliarity with intellectual integrity.
And if your friends would like to express to me personally what offense they feel, I will be happy to discuss the matter with them.
But that is my point, asshole. This is a PIT thread that you opened specifically to call me names and demonstrate that I know nothing about GIT. So far, you have simply proven that you are both dishonest and unable to demonstrate my “obvious stupidity”. If you had wanted to discuss GIT like an honest and resonable man, then you should have:
[ul][li]Stayed in GD.[/li][li]Managed to refrain from calling people idiots and such while in the GD thread[/li][li]Had a role model sometime, somewhere teach you about personal integrity.[/ul][/li]
Yet you have been strangely unable, after 5 pages of straiing and trying, to demonstrate such a statement.
No.
[ul][li]It stopped being a polite argument when you stopped being polite. [/li][li]It stopped being an honest argument when you stopped being honest.[/li][li]But it is still an argument. [/li][li]It’s just a pathetically one-sided argument since you have displayed both your dishonesty and your ignorance to such great effect.[/ul][/li]
BTW, this has to be one the most pathetic moments in PIT history. You come to the PIT, call me by name, start spraying shit on me, ultrafilter, and whoever the hell you think my “superfirends” are. Then a few pages later you start whining that I am insulting your frineds and not “stating my point”. Okay. Here’s my point.
YOU ARE A PATHETIC, DISHONEST, WHINY, LITTLE BOIL DRIPPING PUSS DOWN THE ASS-CRACK OF THE SDMB.
I trust we are clear?
Damn you’re a pathetic little liar.
I never said that you claimed
[ul][li]“a Godel statement (as in all Godel statements)” must be true.[/ul][/li]I have said and showed through direct quotations of your own statements (heplfully highlighted for the just plain dishonest) that you have claimed
[ul][li]“some Godel statements must always be true” in any given system.[/ul][/li]Of course, you suddenly backed off of this claim and declared that we **“can’t rule it out”. **
Strangely enough, you did not suddenly admit that maybe I wasn’t totally clueless about GIT after all when I said that GIT implied nothing about the truth value of Godel statements.
Strangely enough, you apparently think that nobody reading this thread can actually read your words and see you for the sad caricature that you have become.
Once again, you are wrong.
We can’t rule out the possibility that any specific Godel statement might be true… until we actually find out whether it is by extending or changing the axioms.
But the truth of a statement does not depend on whether we know whether it is true or not. Some Godel statements can be shown to be true: “This statement cannot be proven in system S” is one of them. It’s not the same as generating a proof for the statement; in any case, no matter whether we’re able to show that some such statements are true (by considering axioms not present in the systems we were looking at), there will always be more than we can’t determine.
They’re still true or false!
You really are incredible, Spiritus. You persist in leaping to unjustified conclusions and claiming you’ve disproven my whole argument with them.
Which shows you only that the statement is true (or not) in your new axiom set.
No matter how many times you ignore the obvious, it remains the case that proving somehting in one axiom set does not imply that it is true in a non-equivalent axiomatixc system. A proof is valid ony within the axiomatic system from which it is derived. Period. No matter how many time you assert the contrary.
You read popular treatments of abstruse concepts and imagine that somehow this makes you knowledgable enough to ignore 70 years of continued work in the field of mathematical logic. Kurt Godel called his statement “true”, but his use of that term was naive. Treatments of GIT that require truth are actualy weaker than the standard form, because they can apply only to systems where an external standard of truth can be applied. That standard of truth, BTW, is comparison to a model. It is not, and has never been, "can be proved with a different system of axioms."
Do you think that the Axiom of Choice is true in ZF Set theory?
That depends upon one’s theory of truth, but of course it would be too much ot expect you to actually know something about the fields in which you make such assertions.
Regardless, this is a red herring anyway. The question here is exactly can we know it since you are asserting that it must be so that some Godel statements are true for any system. That is a statement of knowledge.
Godel said “it is true”. 70 years of study later mathematicians and logicians work in the field carefully avoid injecting “truth” into the argument because it is:
[ul][li]Unnecessary.[/li][li]Irrelevant to any rigorous application of GIT as a general theorem[/li][li]Not defined precisely enough to be useful in many systems[/ul][/li]TVAA, puffed up with the wisdom of science writers and public websites declares that “truth” must be present and offers a weak version of “G” that has not been standard for more than 60 years. But TVAA must be right because he has absolute conviction that any who disagree with him are uneducated, ill-infomed, idiots who know nothing about a field in which TVAA cannot even be bothered to learn the language.
Yeah. That’s one possibility. :rolleyes:
Only in a system that requires a binary truth relationship and has a relationship to an external model that allows “truth” to be meaningful without a sound and valid proof!
Do you honestly believe that GIT only applies to such systems?
[ol][li]There is a very well defined set of systems in which GIT applies. [/li][li]There is a different set of systems in which the type of truth relationships you argue for applies.[/li][li]There is a non-empty intersection of these two sets in which your weaker version of an incompletenes theorem would apply.[/li][li]The intersection defined in (3) is a proper subset of both of the sets defined in (1) and (2).[/li][li]So, perhaps you should simply stop talking about GIT and start talking about TVAA’s Incompleteness Theorem (TIT). That way not only would your statements about “truth” be correct[sup]1[/sup], but so would your declarations that everyone else on this board is clueless about the theorem. I, at least, will blissfully remain so. What you and TIT do in the privacy of your own mind is between you and your invisible experts[sup]Tm[/sup][/ol][/li]
[ul][li]You are dishonest.[/li][li]Your charges are both untrue and unsubstantiated.[/li][li]You post distorted “summaries” of my positions.[/li][li]You apply hypocritical standards of rigor in argument.[/li][li]You arrogantly assert that any who disagree with your non-rigorous and naive declarations about GIT are “idiots” who know nothing about GIT.[/li][li]You make stupid challenges based upon either an inability to read or an ignorance of mathematical logic[/li][li]You lack the intellectual integrity to answer specific evidence of your deceitful tactics[/ul][/li]Each of the conclusions above have been justified with specific detail. The contrast with your own preference for statements of unsupported slander and dishonest evasions is quite striking.
Do you really imagine that nobody notices your distortions?
Do you really think that people are blind to your evasions?
Do you realy delude yourself that not answering a question makes people forget that it was asked?
Do you really hope that saying “Spiritus is an idiot” enough times will confuse people into thinking that you have substantiated any of your charges?
Probably. We already know you and your "Experts ineffable[sup]Tm[/sup] have a low opinion of the intelligence of your fellow dopers. This is yet another area where I find your position to be overflowing with ignorance and unjustified arrogance.
[sup]1[/sup][sub]Except for your absurd idea that proving a result in one axiomatic system necessarily implis that it is true in another. Given a line and a point not on the line, how many lines through the point can be drawn parallel to the line?[/sub]
An apology
This thread is six pages long and I have been lax in acknowledging the many Dopers who have spoken up in my defense. Even though TVAA’s attacks have been uniformly absurd and esaily dispatched, I still appreciate the words of support.
When the loonies start singling you out for their obsessive delusions, it’s always nice to see confirmation that the world still has plenty of (mostly ;)) sane, intelligent, and honest people.
I’m not going to try listing you all by name, because I would invariably leave one person off and feel bad about it afterward. But thanks to you all.
you didn’t list my name - I feel badly!!!
(seriously, I haven’t studied math in a significant number of years, however, especially w/that last post, you posted clearly enough that I got it… 
)
I fucking quoted the OP in GD and added emphasis.
I will rerepost it just in case.
That’s right. We’ve been mentioning that for fucking pages upon pages now. Nice that you’ve caught up finally.
Are you going to cite Spiritus’s posts for that, or pretend like you’ve been saying this all along?
**
No, Spiritus. The truth of a statement is defined only in terms of an axiomatic system. Not all statements that are true relative to a specific axiomatic system can be proven by that system, but they are still true in that system. It might be possible to use another system to show that they are in fact true relative to the first system. The proof of this would be in the second system. The statements would now be known to be true relative to, or ‘in’, the first system.
The second set does not need to be capable of proving the statement in question, only the statement that the first statement is true in the specific system.
Your response shows that you’re becoming confused about what we’re proving in what system. Read more carefully before you accuse others of error.
** Another model can show that the statement is true relative to the first model, SM.
** NO, I AM NOT CLAIMING THAT SOME STATEMENTS ARE TRUE FOR ANY SYSTEM! I am claiming that for any system, some of the Godel statements will be true.
You’re the only person here who has made statements claiming that GIT shows that some statements must be false in all systems – and that was in a twisted and false “summarization” of my argument.
** That view isn’t wrong: it hasn’t been disproven, falsified, or refuted. As you’ve pointed out, the truth of the Godel statements isn’t relevant to most of GIT’s implications.
So?
How is your point relevant to the OT’s OP? How does it contradict or invalidate anything I said?
** No. It’s simply the case that the implications of calling a statement “unprovably true” are somewhat ambiguous.
You’ve lied, deceived, ignored points, brought up irrelevant points, constantly made claims that arguments were wrong without explaining yourself or justifying your statements. You’re either utterly unable to read English statements and derive meaning from them or you’ve deliberately distorted my position into strawmen; either way, you’re not worthy of even elementary respect.
No, you idiot! I am not claiming that the statement can be proven in the second system, so it must be true in the first! I’m saying that it can be proven in the second system that the statement is true in the first!
The statement that can be proven in the second system is not the first’s Godel statement, it’s the statement about whether the Godel statement is true relative to the first system.
Is your sense of self-worth so based on appearing correct before the people on this message board that you’re unable to even recognize you’re not arguing against the statements I’ve actually made? Are you genuinely convinced that the things you’ve disproven have anything to do with my points?
Perhaps you’re not stupid after all – you’re outright delusional.
See, wring, I knew that would happen. 
London_calling, I will single you out for the Phaedrus riff. Nothing like a little historical perspective to take the sting out of the current crop of loon.
TVAA
Pleae read this carefully. There are ambiguities possible in English phrasing so I am going to make this as clear as I possibly can.
[ol][li]You say that for any system to which GIT applies some of the unproveable statements are necessarily true.[/li][li]You are wrong.[/li][li]You say that proving “G is true in sytstem A” in system B has necessary implications for “G” in system A.[/li][li]You are wrong.[/li][li]For illumination on point (4), do some research upon whether a Peano Axiomization is considered by mathematicians to be necessarily consistent.[/li][li]For further illumination on point (4) consider the following proof.[/li]Axiom: Everything Spiritus Mundi says is true.
Premise: Spiritus Mundi says that TVAA knows in his heart of hearts that TVAA is below average in intellect, integrity, and personal hygeine.
Conclusion: TVAA knows in his heart of hearts that TVAA is below average in intellect, integrity, and personal hygeine.
Voila. I have just proven that in whatever system of knowledge is you heart of hearts it is true that TVAA is below average in intellect, integrity, and personal hygeine. After all, you say this is a valid method for demonstrating truth.
[li]I am using terminology appropriate to the field of mathematical logic. The words “model” and “system” are not interchgangeable in that context. You say: “Another model can show that the statement is true relative to the first model”.[/li][li]You are misusing the term “model”.[/li][li]You say that I have claimed “some Godel statements must be false for all systems.”[/li][li]You are wrong. But it is true that some Godel statements must be false for any system to which GIT applies that maps to an external model in which truth can be verified or requires a binary truth operation be defined for all statements.[/li][li]You think that “truth” being irrelevant to most implications of GIT somehow supports your mistaken assertion that for any system to which GIT applies some Godel statements must be true.[/li][li]You are wrong. Truth is irrelevant to most implications of GIT because truth is not an element of GIT. GIT says nothing about “truth”. You might as well argue that “side-angle-side” proves that some triangles are “true” relative to each other.[/li][li]You think that it is simply “ambiguous” to talk about statemnts being “unproveably true” in a system that allows for no external verification of truth.[/li][li]You are wrong.[/li][li]You say that I have: " lied, deceived, ignored points, brought up irrelevant points, constantly made claims that arguments were wrong without explaining yourself or justifying your statements."[/li][li]You are wrong.[/li][li]You are also a shameless hypocrite. The record in this thread is quite clear about who has been deceptive, who has ignored points, who has issued slanderous charges without providing justification. [/li][/ol]
Yes.
And so are you, unless it is just a startling coincidence that you have suddenly stopped saying things like:
[ul][li][Spiritus] neglected to pick up on the point that it’s not the case for every type of system that a contradiction leads to all possible statements becoming valid.[/li][li]SM, among other stupid claims, insists that GIT merely demonstrates that there are some things that can’t be proven ever. . . This is just plain dumb. . . If you add extra axioms to the system, it may be possible to prove a formerly unprovable statement[/li][li]SM said GIT shows that there are statements that have no proofs, and that this was trivial because they were simply statements that are always wrong. [/li][li]Spiritus, remember a few weeks ago when you said GIT says nothing about the nature of the universe but only something about human conceptualizations of it? Why are you now saying (correctly) that the universe’s consistency cannot be proven within itself?[/li][/ul]
Of course, you have never explicitely retracted/corrected the above. That would require a degree of intellectual integrity with which you are obviously unfamiliar.
I’m gonna hate myself for this, but TVAA is right about one point. First, I’m saying that statement G is undecideable in theory K iff there is no proof in K of G and no proof of ~G. I think this is the definition TVAA wants to use, although there’s really no way to tell.
If G is an undecideable statement, then ~G is also undecideable. They can’t both be true or both be false, so in any theory with at least one undecideable statement, there is at least one true undecidable statement and at least one false one.
None of that changes the fact that TVAA is dishonest, arrogant, and in general unpleasant.
ultrafilter, as I have been pointing out to TVAA that conclusion holds only in systems that require a binary truth operation to hold for all statemnts. It fails to hold for systems that do not map to an external model for truth, systems that do not define truth as a binary operation, or systems that do not require a defined truth value for all statements.
The argument you just used is the one standardly applied for a predicate calculus, but GIT holds for many systems that are not equivalent to a predicate calculus.
ultrafilter, as an example, consider a system which is consistent yet allows for valid proofs of both § and (~P). Which of those statments would you say is necessarily true and which is necessarily false?