This Spiritus Mundi he is like a wild donkey, I triple guarantee you. We will push this gangster, this mercenary back into the swamp. He is a dog and we will beat his drunken, druggy nose with shoes and all the world will dance in joy!
This is a lesson which will not be forgotten by history. Truly
Now we will go and surround this Spiritus at the airport where he will be beheaded and I will bring his head to this place in ……… <you all know the rest … >
ps. Thank you Spiritus, but I fear you have invoked the ‘P’ word and that there may be no going back ……
[ul][li]I have provided many specific arguments that indicate why you are wrong. [/li][li]I have linked to discussion about GIT that delve beyond the merely surface presentations often offered for mass consumption. [/li][li]I have even bolded for you Godel’s own words about the implications that a general and formal proof of the undecideablitiy of G would have on inhaltlich richtig.[/ul][/li]You might have taken the effort to actuall read and understand such things, or even to ask informed questions about them. Instead, you continue to embrace your ignorance. You cling to your delusion that I am a moron making “stupid mistakes” and “obvious errors” about GIT because you can’t be bothered to interrupt your masturbatory cycle of analingual pleasure long enough to educate yourself about what GIT actually says.
You claim you have experts whose credentials in these fields are beyond doubt, yet you continue to make errors in interpretation and definition that even a reasonably educated layman would avoid. And you say that your "invisile experts[sup]Tm[/sup]" confirm that you are right while people that actually present the concepts surrounding GIT in an accurate form are “too stupid to be worth talking to.”
You have on multiple occassions been caught making clear factual mistakes, both about what I have said and about such basic things as the proper definition of consistency. But you are such an ooze-dripping pustule of intellectual insecurity that you cannot bring yourself to admit: [color-blue]“hey, I never knew that wasn’t the real definition of consistency”.[/color] Instead you pretend that your ignorance somehow defines the proper set of systems to which GIT applies.
In short, you are one of the more pathetic examples of poor and dishonest argumentation that has ever graced this board. No doubt you suffer from some unfortunate combination of :
[ul][li]Poor parenting[/li][li]Substandard education[/li][li]A social environment that rewards alpha aggression above intellectual accomplishment[/li][li]Personality disorders that interfere with your ability to admit fault[/li][li]Social/personal/sexual insecurites that drive you to overcompensate[/li][li]Whatever.[/ul][/li]It really doesn’t matter. You’re an adult, now, responsible for your own behavior. Stop being a pathetic asshole.
Spiritus, I have websites and textbooks galore which show that your standard-language “explanations” about what certain mathematical terms mean are grossly incorrect.
I don’t know what’s more pathetic: that you think you can convince people that you’re right and I’m simply lying about what the words mean, or that you actually can.
Let’s see . . . following the TVAA mode of argument I should now immediately begin declaring that TVAA is an idiot who obviously hasn’t the first clue about GIT. He forgot to include the restriction “omega-consistent”[sup]1[/sup] for his “sufficiently powerful” systemns. What a moron! Only an absolute clueless imbecile would make such an obvious mistake about GIT!
:rolleyes:
TVAA, that why Argumentum ad Numerum is a logical fallacy. The fact that a lot of folks who write websites, or even introductory textbooks, say something does not mean that it is so. For the textbook writers, we can charitably assume that they know better but are simplifying things for an intro level class. (Though if you truly have a textbook that says the proper definition for consistency is “grossly incorrect” then you should immediately complain to whatever professor forced you to spend good money an a bad book.) Any kook can publish a website.
And any loser can cling to ignorance rather than opening his mind to the truth.
What’s more pathetic is that you are so fundamentally lacking in intellectual integrity that you are unable to confront even the most basic and obvious mistakes. I am right about what the words mean. Any good treatment of GIT will address the historical context enough to show both that godel’s original result held only for omega-consistent systems and that the proper (and less restrictive) definition of consistency is not the “Idiot’s Guide to Mathematical Logic” version that you think is gospel.
I know that it will make you feel ridiculous to admit, after 12 pages of ranting about how you knew so much more about GIT than I or ultrafilter or orbifold or . . ., that you don’t even understand the class of systems to which GIT rigoously applies. But guess what–you already look ridiculous. This willfully blind devotion to ignorance only makes you look ridiculous and dishonest.
Of course, that’s nothing new for you, either.
[sup]1[/sup][sub]Yes, “omega-consistent” is proper, here, since TVAA is using a form of Godel’s original, less powerful, and no longer standard Godel statement. Had he shown the wit, awareness, or learning capacity to use the more powerful Rosser form of G, then the proper restriction would have been “consistent”.[/sub]
In the first case, if there’s a single statement that isn’t a theorem in the system, the system is consistent.
In the second case, if there’re no statements in the system whose negations are also in the system, the system is consistent.
The first definition of “consistency” has little to do with this debate. It’s a completely different concept that happens to be described by a similar word.
If, as you claim, I’m using an outdated and less powerful form of GIT, then it follows that the updated and more powerful version can show anything the first did and more.
If the first version of GIT shows something, then the second will as well. It’s simply the case that conclusions demonstrable from the second might not hold in the first.
Tell me, ultrafilter, why was it necessary to qualify ‘consistency’ with the prefix ‘omega’ in the link you provided? If the definition given for ‘omega-consistency’ is indedd what ‘consistency’ means, why is it necessary to put a greek letter in front of the term?
Are you incapable of reading, is that teh problem? The proper definition of consistency does not require the qualifier “omega”. It is the TVAA definition of consistency that is almost equivalent to omega-consistency. The difference, as ubltrafilter pointed out and I implied in my definition for the three types, is subtle.
Do you understand yet, TVAA? How many more times do we have to tell it to you before the concept will penetrate? How many more sites with a rigorous approach to mathematical logic will help you to at least UNDERSTAND what we are saying the proper definitions of consistency and omega-consistency are?
Just read the damn words! I know that’s hard with your head planted so firmly up your ass, but try to pretend that your mind is not locked down like the White House on 9-12.
No shit. And only one of them is correct. The other is a simpification given to folks who like to think about mathematical logic without stressing any neurons.
Congratulations. You have actually managed to get something right.
But, of course, it could not last. The first definition is the rigorously correct definition of consistency. It defines precisely the set of systems to which GIT applies.
Historically, Godel’s original sketch of a proof held only for omega-consistent systems. Rosser fixed this more than 60 years ago, which is why the Godel-Rosser version of GIT is now standard. If your piles and piles of bullshit popularization haven’t managed to convey that simple truth to you, then you should stop wasting your money on bad books. Or at least stop pretending that bad books make you an expert on GIT.
:rolleyes:
Whooooooooooooooooooosh
Actually, I believe you have posted that you know almost nothing about higher math. This is obviously correct, though it just as obviously does not stop you from saying many, many ignorant things about math.
As it turns out, mathematics and logicians don’t give a rat’s dangling testicle whether you are impressed or not. The definition remains the same.
[ul][li]There is no doubt about my “claim”. Any good treatment of GIT (which obviously excludes those that you rely upon) will address Rosser’s work.[/li][li]What follows is that the standard version of GIT is more general. It applies to more systems. That is the sens in which it is more powerful.[/li][li]Your version proves the same thing for a smaller set of systems. There is a proper subset of that smaller set of systems for which the implication fo truth value that you so desire also holds. In the smaller set of omega-consistent systems, the only additional qualifer required for the truth implication to hold is that a binary truth value be defined for all statements.[/ul][/li]
No. The “weakness” and “strength” are inherent in the distinction between consistent and omega-consistent. Thus, the implication of a proof holding in one or another context is explicitely and solely the breadth of systems across which GIT can be properly applied.
The point that you apparently find so personally upsetting is that with the proper definition of consistency it becomes apparent that the semantic consequences for truth value, which depend upon qualities found only in a proper subset of systems powerful enough to invoke GIT, is shown to be irrelevant to the proof of GIT. GIT says nothing about truth. GIT implies nothing about truth. GIT is a general result. The truth you are looking for is a proerty of specific deductive systems. It does not hold over the general class of systems subject to GIT.
this is clearly an argument that can only be solved by one side dying. I honestly don’t know who’s right and who’s wrong, and to be honest after 7 pages I think the only thing that is obvious is that neither TVAA nor Spiritus et. al. is going to accept that the other is right, nor is going to stop feeding the other with more posts. Surely one of you could simply leave with a post saying “I’m right” and simply ignore the replies from the other…
TVAA, since you were obviously too involved in a your feedback loop of ignorance and anal gratification to read these words the first time, I am going to repost (in layman’s terms so you will be able to understand teh symbols if not the content) the proper definitions for consistency and omega-consistency.
Hawthorne
Despite all evidence, I actually hold out a miniscule slive of hope that TVAA’s intellect might sometime peak out from his anal cavity of hubris (perhaps in a moment of accidental slippage) long enough for him to actually learn something about GIT. It is obviously a subject that he is passionate about, despite his dogmatic determination to accept simplified popular presentations rather instaed of trying to educate himself about the actual theorems.
Besides, the asshole called me out by name in one of the most lame and ill-coinsidered PIT threads ever perpetuated upon this board. It would be poor policy for me to not give TVAA the full respect to which he is entitled.
If you think that I or Spiritus has said that [symbol]w[/symbol]-consistency is the same as consistency, please tell us where, so that we may laugh at you for your poor reading comprehension.
[symbol]w[/symbol]-consistency is not the same as consistency. There are consistent but [symbol]w[/symbol]-inconsistent systems out there.
Consider a theory with the constant 0, the successor function (denoted '), one unary predicate letter P, and the usual rules of inference and logical axioms. We have the following proper axioms:
([symbol]$[/symbol]x)(P(x))
~P(0)
([symbol]"[/symbol]x)(P(x’) -> P(x))
Now there are two things that we can prove here: First, some natural number has property P. Second, for any natural number n, n does not have property P. However, we can’t prove ([symbol]"[/symbol]x)(~P(x’)), because proofs are required to be finitely long. Therefore, the theory is consistent, but [symbol]w[/symbol]-inconsistent.
Remind me again how consistency permits contradiction.
[shakes head]
ultrafilter’s “consistency” is not consistent. If that word is the name given to a particular concept in a particular branch of mathematics, that’s just peachy keen – but that is not what I am talking about.
A system is consistent when it cannot prove both a statement and its negation. Allowing contradiction means the system is not consistent.
I understand that you are not now nor have you ever been talking about GIT.
I understand that from all appearances you are fundamentally incapable of considering a problem rigorously.
I understand that you still have not learned what even your “invisible experts[sup]Tm[/sup]” told you: precision in language is important when discussing the implications of formal theorems.
I understand that you will probably never understand GIT.