Enough with the technobabble. You’ve already discredited yourself to the point where I wouldn’t trust a recipe for egg salad you posted. Tell me more about how smart you are.
Shhhh… Listen…
You hear that noise?
That’s the sound of the baby Jesus crying.
What technobabble?
If you don’t understand my position or Spiritus’, why are you drawing conclusions about them?
I am not particularly smart. I’m didn’t detect the gross and obvious errors in Spiritus’ position because I’m smarter than he is. In terms of raw computing power, he’s probably smarter than I am.
He’s still wrong. His arguments are wrong, and in many cases, they’re outright stupid. A spade is a spade, and dumb is dumb, and my opponents are being really, really dumb.
Or maybe I’ve just had a stroke.
<I really want to stop posting, I do have things to do today, but I just can’t help myself… it’s like a never ending train wreck that I can’t stop watching>
It’s not a matter of “credibility”. Credibility is what we rely on when we have no other way of determining truth. There are objective standards for evaluating my claims and my opponents’ counter-claims. Theirs happen to be incorrect, and mine happen to be correct.
There is no escape.
You say I’ve discredited myself? How?
Have you looked at Spiritus’ inaccurate and inconsistent statements? Why aren’t you suggesting that he’s discredited himself?
That you are presenting his side unfairly, perhaps?
Forgive me for saying so, but you are the only one who has voiced significant disagreement. I think Spiritus is quite flexible in discussing most ideas in everyday terms, but some things, like GIT, are actually not only well-defined concepts but highly localized to certain frames. This requires additional rigor that you’ve failed to provide.
Admittedly, I once empathized with your point and I think the thread I started on this same topic was linked to in your thread. ultrafilter, among others, helped me understand the difficulties I was facing.
They read the threads in question, eris. I don’t think anything could present his case better than his case.
I’m afraid I have to disagree with you here. It is possible for these concepts to be discussed in everyday terms. Spiritus can’t do this – not only can’t he understand statements made in that language, but he can’t describe important mathematical concepts without error.
Should I repost his errors separately?
You are entitled to your opinions, and I respect your judgment, but I suspect ultrafilter has confused matters more than he’s clarified them.
I could be mistaken.
The point I’m making is that the underlying physical system responsible for the set of interactions we consider to be a computer is subject to the same restrictions as the programs the computer runs.
Spiritus has repeatedly claimed that there are differences between programs and computers. In truth, there aren’t any – that’s why any Universal Turing Machine can simulate the behavior of any other. All it needs to do is run a program that duplicates the interactions that would take place within the second UTM.
He’s also wrong about his emphasis on Peano Axiomatization. If he’d read the links I’d provided, he’d find professional mathematicians talking about what’s necessary for GIT to apply. The axiomatic systems in question need only to be as “strong” as PA is – that is, they need to imply what PA does at minimum. PA is the bare minimum to define operations among the natural numbers, and it’s operations that are necessary for GIT.
We know empirically that the physics underlying computers is stronger than PA. That’s why it’s possible to make systems that can represent arithmetic in the first place.
I think the essence of an everyday language rebuttal is summarized thusly (which he did say, actually).
Take your UTM that has the ability to perform all the string operations that PA can. Take the (a) Godel number—G—that the arithmetic theory is undecided on and feed it into the machine.
Add 1.
What happens?
Double G. What happens?
In short, what operations on the G are forbidden? Specifically.
Gosh, if your team of experts read the threads and indicated that you were in the right, why not have them post here and explain (in precise terms) why you are right?
lucwarm TVAA already stated that their panel of experts declined to do that 'cause the folks here were too stupid to understand (or something to that effect)>
So you’re saying that this UTM is programmed to perform basic arithmetic, and it’s given a Godel number for basic PA?
As far as I know, the UTM would perform basic operations on it.
So what?
The UTM in question necessarily has more axioms defining its nature than mere PA. Adding more axioms (or switching axiomatic systems) changes the nature of Godel statements: a statement that was previously unprovable can become provable. A numerical sequence that was formerly a Godel statement will no longer (necessarily) be one when the system changes.
This is one of the things that Spiritus repeatedly got wrong.
My argument has never been that giving G to the system would cause problems. Rather, GIT shows that there’s some statement that the computer won’t be able to handle.
No, they said Spiritus was too stupid to understand. At least accurately report what I said, will you?
SO it’s only Spiritus who’s too stupid?
well that’s even lamer then. “gee, we’d explain it to those other smart folks but that Spiritus guy, he’s too stupid and we’d hate for him to have an opportunity to learn, too”
Of couse, ‘all the rest’ apparently were agreeing w/Spiritus, so once again, we’re back to that problem - if all *including *Spiritus think you’re wrong, then why is it only Spriitus who’s ‘too stupid’ to have it explained to??
I’m just going to hit your first couple of nonsense points, the rest repeat some patterns that have already become tiresome.
You have again and again proven incapable of following an ongoing topic of discussion. You post like an epileptic four-year-old with an etch-a-sketch. Every line drops from your pen as if unconnected to all that has gone before. Here is the context of this particular little bit of nonsense.
Stop twitching and pay attention.
Above is the progress of our conversation on this absurd little hijack. I NEVER CLAIMED THAT YOU HAD MADE A CONTRADICTION. I said that your initial statemend (I put it in blue above so that even you would be able to pick it out) failed to account for all possibilities, such as the case when a definition for “good” contains a contradiction.
This is PATTERN 1 of a TVAA post: pathetic inability to actually follow the progress of a discussion leading nonsense declarations and stupid misrepresentations.
The question I asked was: you consider ethics to be a sub-discipline of physics?
This is PATERN 2 of a TVAA post: a stunning inability to answer simple question no matter how often they are asked of him. TVAA much prefers to reiterate the preconceptions of hiw world-view, apparently because then he doesn’t risk the possibility of actually thinking a new thought.
This is a repeat of PATTERN 1. For completeness, I will once again (I did this in the GD thread) post the progress of our conversation on this bit of inanity. I’ll also add the bits from this thread
Again, I have highlighted in blue for the comprehension-deficient.
Again, this has to be the most pathetic focus of a juvenile argument that I have witnessed in 2 decades. The only time I claimed that you were talking about labels was right after you talked about labels. See if one of your experts can parse the blue statements for you. No need for a full diagram. Just ask them to identify the subject of the restrictive clause in the first sentence.
This is PATTERN 3 of a TVAA post. He makes a claim about logic. Someone points out to him that he has failed to actually make an argument that supports such a statement. He responds: it’s not particularly difficult, and it all follows.
:rolleyes:
Right. You will notice, or at least I wil notice, that what TVAA does not do. . . . ever . . . even after being asked to repeatedly . . . even if he promises that he will . . . is provide an actual argument that reaches his asserted conclusion.
This is PATTERN 4 of a TVAA post. Because he uses words so carelessly and reasons without rigor, he apparently canno imagine that anyone else would actually compose a sentence that means exactly what it says and not what it does not say. For instance, I did not say attempting to survive is the best/only ethic in TVAA’s presentation. Yet he responds with an extraneous argument based upon whether an organism should attempt to survive. What I said was survival is the best/only ethic in TVAA’s presentation. And, in his final sentence (again, in blue for the comprehension impaired) he confirms exactly that.
Of course, even that doesn not make an impact on the twitching puddle of cognitive dissonance that is TVAA. Somehow, at the same time that he posts a confirmation of what I said he manages to imagine that he has refuted what I said.
:wally
There are some factual errors in TVAA’s next snippets, but I’m not going to revisit them again. I think it has been well-demonstrated that TVAA’s capacity for ignoring a factual refutation is unmatched among recent posters. One has to go back to the height of bj0rn to find a similar blend of overbearing arrogance and blind-devotion to personal ignorance. If anyone cares about his factual erros, please visit the GIT thread.
TVAA’s next trick will be to try and distort or twist my posts to fit the random firing of neurons inflicted upon him by cruel fate. The claim was:
So, TVAA sets himself off to prove that I made the claim highlighted (again, in blue for the comprehension impaired) above. He comes up with:[ul]
[li]Any inconsistent system can derive all truths, as well as all falsehoods. Getting a system that can prove all truths and nothing else is impossible, although GIT itself does not prove that.[/li] (That was someone else. Now my words:) Well, I think we can give this one to GIT by assuming that some of the unproveable theorems in a Peano axiomatization are, in fact, true. Obviously, GIT does not guarnatee this (being unconcerned with soundness), but I don’t think it is a horrible assumptive leap to make.
Notice that this passage says absolutely nothing about GIT being trivial because all statements are wrong. The problem here is that TVAA has read a few common language presentations of GIT and thinks that means he understands the theorem. In fact, GIT says absolutely nothing about soundness (which is how a valid derivation is determined to be true). Writers often speak of “true” statements, and in fact I have done so myself in an attempt to communicate basic ideas about GIT, but GIT itself is entirely mute upon the subject of truth. GIT is entirely an implication of the properties completeness and consistency. It does not address soundness.
Of course, what makes TVAA’s misreading even mor egregious is that in the passage above I am explicitely granting that I think we can safely assume soundness for some system to which GIT applies. In other words, I am saying that even though GIT does not require it, I think we can talk meaningfully about the “truth” of the unproveable statements in some system to which GIT applies. This is exactly opposite to the claim above.
TVAA follows with: We don’t need to “assume” that they’re true. Statements are either true or false relative to the axioms in a consistent system. Principles of mathematics MUCH more basic than GIT show this to be the case.
This is simply another expression of TVAA’s ignorance with regard to logical terminology. A statement is “valid” or “proveable” or even “demonstrable” relative to an axiomatic set. A statement is “true” if it is “valid” and the axiom set is “sound”. Common language presentations of GIT often blur the line between “true” and “valid”, which is one reason why people who truly want to understand GIT do not rely upon common language presentations.
Next TVAA twitches upon:
[li]**Spiritus: **The only thing GIT tells us about marks on a paper is that there is no way to ever interpret marks on paper to be a proof of certain valid number theoretic statements because no such proofs can exist. This is a limitation of math, not a limitation of pencil and paper.[/li]this sentence of mine actually does contain one common-language error. I should not have said “valid number theoretic statements” I should have said “consistent number theoretic statements” (because the only way to show that they ar valid would be to prove them, and GIT tells us that that cannot be done.). Apart from that, the statement is rigorously correct. It does indeed recognize that GIT tells us there are some statments that have no proof. But it does not in any way support TVAA’s claim that I said: this was trivial because they were simply statements that are always wrong.
After his next random seizure, TVAA sees:
[li]**spiritus: **GIT says nothing about “possibilities not capable of being manifested within a system”. You appear to be suffering from the misunderstanding that every true statement in a Peano Axiomatization has a “possible proof”, but GIT just won’t let us manifest them. This is incorrect. GIT says that no possible proof exists for some true statements.[/li]Here I am guilty of the same common language equivocation of “truth” for “consistent with the axioms”. Of course, that isn’t what TVAA has a problem with, because that isn’t a distinction that he understands. TVAA wants to talk about the fact that th estatements can be proved in soe other axiom system. Now, in the thread in question we went over the distinction about what significance adheres to the context (system of axioms) under which a proof can be demonstrated. Anyone who cares to can read that discussion in the GD thread. In this thread, the only quesiotn is whether htis statement in any way supports TVAA’s claim that I 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. Now, since the passage above atually references “true” statements, it obviously does not support the claim that I say the statements identified by GIT are ALWAYS WRONG.
[/ul]
PATTERN 4 in all it’s [in]glory. TVAA is very fond of this one. Call it a strawman. Call it willful misrepresentation. Call it drooling idiocy by a man incapable of reading with comprehension. Labels don’t really matter. The concept is clear. TVAA wouldn’t know a rigorous discussion of GIT if it materialized in front of his eyes in a colorful pattern of glowing rectangles.
So, that’s it. Repeat those four patterns at intervals dictated by a spamodic neurology, sprinkle with occassional helpings of personal insult and a fanatic dedication to personal ignorance and you too can make a TVAA post.
But please don’t. One TVAA is more than enough.
erislover:
If G is unprovable in the axiomatic system underlying the working of the computer, the computer’s output will never match G.
It doesn’t matter what series of operations are performed, or what the initial input is… as long as the axioms of the system remain unchanged, the physical system of the computer will not be able to reach that configuration.
Of course, it’s possible that interactions with the external world could change the nature of the computer’s behavior – but then there would be other statements that the new system couldn’t handle.
Even if the computer were so reduced in power that it could no longer handle arithmetic, the system underlying the computer hasn’t changed. This “system” is a UTM that is simulating the first UTM – it’s necessarily consistent, as an inconsistent system can’t simulate anything, and we know empirically that its axioms are more than sufficiently powerful.
- If the concept of “good” includes a contradiction, it’s not a valid concept, is it?
Why in the world would we even discuss self-contradictory theories? No one could follow them if they were subjective, and they couldn’t possibly be determined objectively – so why bother?
-
I was responding to a point you brought up, Spiritus. My arguments up to the point you brought symbology into the debate did not discuss the concept. I’m not talking about the symbols used to represent “good”, I’m talking about the definition of good that is independent of the specific groups of symbols used in order for us to communicate our thoughts about the concept.
-
Most of your “simple questions” are simply irrelevant. The rest are usually questions that have already been answered or whose answers can be deduced from previous statements.
I see that you haven’t responded to my pointing out your errors, Spiritus. How long will you allow that challenge to go unanswered? Would you like me to repost them?
-
I simply do not understand what you mean when you say I haven’t demonstrated something logically. I’ve made statements with logical significance. These statements can be evaluated and logical conclusions as to their validity and consistency can be made. You don’t do this – you merely state, over and over again, that they’re not “logic”.
-
I think you’ve amply demonstrated that standard English is too complex for you to handle. You state that my position is that “survival is the best ethic”. No, that would only be the case if I claimed that ethical systems that held that survival is the most important of all goals are the best. What I’m saying is that the ethics that result in the survival of the organisms that have them are the best – I’m not making any specific claims about what the systems actually say, just what the overall properties of the system are.
Okay – I said that I would pass by TVAA’s simple errors in fact in this thread, but this one is simply too ironic to let slide:
[ul][li]First, and most obvious, you are not quoting Godel’s Second Incompleteness Theorem. You are quoting somebody’s common language interpretation of GIT[sup]2[/sup][/li]
[li]Second, yes it applies only to “sufficiently powerful” systems. Was it really necessary for me to specify that since you have been explicitely arguing that the Universe meets exactly those criteria in order to justify your application of GIT? [/li]
Put down the etch-a-sketch. Take some ritalin. Stop pretending that each post in a conversation is uninformed by the preceeding context.
[li]Third, if you are going to insist that GIT must be spoken about in common language terms, then you lose the right to call people “stupid” for not listing all of the restrictions upon an application of GIT every time the subject comes up, you raging hypocrite. [/li]
[li]Fourth, despite the rage with which you quibble, you have not actually offered any rebutal to the conclusion. Either the Universe is not sufficiently powerful for GIT & GIT[sup]2[/sup] to hold, or you cannot ever demonstrate that the Universe is consistent. Do you think that me names somehow erases evrybody’s memory of the point under discussion? [/li]
That is stupid.
[/ul]
Basic error. Soundness is the property of models and statements. Specifically, if a statement is sound, then if it can be proven in an axiomatic system it is true in that system. Completeness is a property of logical systems such that, for any statement P, there exists a proof of P or not P that can be derived from the system.
GIT indeed does not deal with soundness. It doesn’t have to. If a statement is sound within a system, it is true. It is not the case that statements that are not sound are not true. (If A then B does not imply that If Not A then Not B.)
** This is irrelevant. GIT shows that there are statements in the system that are not sound, as they can’t be proven, but are nevertheless true.
By extending the system of axioms, it’s (often) possible to demonstrate that a previously unprovable statement is in fact true in regard to the original system of axioms. We don’t need to “grant” this. It doesn’t matter if Spiritus feels it can be safely assumed. It has been demonstrated to be the case that it can be done, by mathematicians more competent than anyone on these boards including myself and Spiritus.
** This is incorrect.
I will say it again: the property of axioms called soundness means only that, if the axioms are true, the conclusions that can be drawn from these axioms are true. GIT shows that there are conclusions that cannot be drawn from the axioms that are nevertheless true relative to them.
From this site : The most important result along these lines are Gödel’s incompleteness theorems which essentially show that every sufficiently powerful logical system does contain sentences which can be neither proved nor refuted from within the system.
From this site :
This clearly shows that the truth of a statement relative to an axiomatic set is not dependent on whether it can be proven within that set.
Spiritus next point, in which he points out a common language error, is still incorrect. GIT does NOT show that certain statements have no proofs. It shows that certain statements have no proofs within specific axiomatic systems. In his analysis, Spiritus repeats his error, saying “It does indeed recognize that GIT tells us there are some statments that have no proof.”
There are ways in which any statement can be proven. The whole point that statements can be proven in an axiomatic system in which they’re false only if that system is inconsistent.
Spiritus, just admit that you don’t understand the implications of GIT and we can end this. Continue to spread your misunderstandings and I’ll be forced to continue.
The next point hinges upon the same incorrect claim about GIT as before; it’s already been refuted.