Spiritus Mundi

[TVAA]

The record player that couldn’t actually play all records, because if it played certain records the sonic resonance would cause the player to break?

[Spiritus_Mundi]

TVAA, the spastic colon of the SDMB.

No way am I going to try to combat every stupid, dishonest, or just plain nonsensical claim that you have made. You quite literally are not worth that much time. Actually, you arent’ worh thte time I have already spent on you, but there is some amusement value in pointing out the deficiencies of your character.

One post at a time, then.

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?

Aren’t you the moron who just a little while ago posted that contradictions could be subjected to logical analysis? that’s rught, you are. And, of course, I didn’t say that I wanted to discuss one. I said that your statement did not deal with the possibility that one might exist. You made a categorical statement. That statement wsa wrong. I pointed it out to you.

This has been an ongoing pattern in our exchanges.

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 posted the relevant pieces of our exchange. Post the specific statement of mine that you are misreading as an introduciotn of symbology into the debate or admit that you are the most pathetic coprophage to infest this board since Captain Foreskin got the snip.

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.

:rolleyes:

Right. What a perfectly reasonable reason for ignoring questions in a debate.

I see that you haven’t responded to my pointing out your errors, Spiritus. How long will you allow that challenge to go unanswered?

The answers can be deduced from previous statments, you illiterate fuck.

Alternative: PATTERN 4, you illiterate fuck.

Would you like me to repost them?

Please do. I can never get enough of people presenting absurd strawmen and then claiming they are mine. I always take it as a sign of both desperation and intellectual bankrupcy.

I simply do not understand what you mean when you say I haven’t demonstrated something logically.

Because you have not. Logical arguments, even informal logical arguments, have certain structural requirements. You have not met those requirements. You have not een come close. You simply wave your hand and say: GIT. When asked specific questions, you respond: The answers can be deduced from previous statments.

That is not a logical demonstration. That is TVAA twitching to the beat of his own ego.

I’ve made statements with logical significance. These statements can be evaluated and logical conclusions as to their validity and consistency can be made.

When can be becomes has been shown then perhaps you will have made a logical argument. A string of assertions and a charge that people are stupid if they don’t understand is not a logical demonstration.

What kind of an insufferable prick would imagine that it was . . oh, right. TVAA, spasmodic shitsack of the SDMB.

You don’t do this – you merely state, over and over again, that they’re not “logic”.

It’s not my job to fill in the blanks of your argument, especially because your arguments are misguided towers of ignorance and misconception. It’s your job to support your argument. That you are pathetically inept in the attempt is evidnet. Sucks to be you.

By the way, this post is not a sonnet. Even if I call it a sonnet and say that the metre and rhyme can be deduced from my words, this post is not a sonnet. The “why” of that statement is implied in the observation itself: this post does not possess the structural elements of a sonnet.

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.

We covered this already. Apparently it is you who have a hard time with English.
[ul][li]What I said: survival[/li][li]What I did not say: Attempt to survive, value survival, strive for survival, or any of numerous other possible misreadings by knuckledragging buffons.[/ul][/li]You claim that no matter what other elements an ethoc might have, the best ethos isthe one that survives. Thus, survival itself becomes the only ethical value in your view. Only that which survives (not “values survival”, not “tries to survive”, not “spews incoherent shit about survival”) is ethical, in the twisted world of TVAA, twitching turd thrower of teh SDMB.

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.

Yes. I got that. In your view the contents of an ethical system are entirely irrelevant to whether it is “good”. Of course, that itself is an ethical valuation on thepart of TVAA. In TVAA-ethics, only survival marks something as good.

Gee, now where have I heard that before?

[Spiritus_Mundi]

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.

Error? Where. here is what I said:
[ul][li]GIT is entirely an implication of the properties completeness and consistency. It does not address soundness.[/ul][/li]How, exactly, do you imagine that linking to a definition of soundness indicates an error on my part? (BTW, I notice that you misrepresent the content of that site to pass over the fact that soundness is a property ascribed to arguments, and thus to systems derived from a single set of axioms. I wonder why you would do that?) What I said of GIT is rigorously correct. If you disagree, then you should try to actually address the content of my statement.
:rolleyes:

GIT indeed does not deal with soundness.

Yes, I know that. I am the one who told you, remember. It happened just before you started shaking your etch-a-sketch.

It doesn’t have to.

Right, because it is not saying anything about truth. If it wants to say somethign about truth, then ot would have to address soundness.

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.)

Goodness, then it’s a really good thing that I never tried to pretend that all unsound statements are untue, isn’t it?

This is pathetic. GIT does not address soundness. GIT does not require soundness. GIT is, in fact, entirely uninterested in soundness. But soundness is the only way that we can declare valid theorems to be “true”. Therefore, if we want to use “truth” in our arguments, we must assume that the system being examined has sound axioms.

You call that a “basic error”.

That’s because you haven’t clue one about either GIT or logic.

This is irrelevant.

IRRELEVANT?

You claim I said “X”. I show that I did not say “X”. You say “irrelevant”. PAY ATTENTION TO THE CONTEXT OF OUR ARGUMENT!!!

Forget, for the moment, who is right about GIT. In this passage, I am simply showing that I never made the stupid statement that you attributed to me. I am also showing that you are too stupid to know whether the quotations you choose actually support the claims that you make.

Both of those things have been well demonstrated. That is not irrelevant. It is a rather important thing to note, since you keep making ridiculous assertions.

GIT shows that there are statements in the system that are not sound, as they can’t be proven, but are nevertheless true.

Okay – back to why you are an ignorant fuckwit who hasn’t a clue as to what GIT actually says. GIT doesn’t say anything about truth. It is only writers trying to gloss GIT for a lay audience that talk about truth. GIT says that well formed statments exist such that neither the statement nor the negation of the statement can be proved within a consistent axiomatic system of sufficient power. Period.

GIT doesn’t care whether the statements are true or not, but in any system that excludes only binary truth values it is necessary that one or the other be true. It is not the case, however, that every axiomatic system of sufficient power to invoke GIT must necessarily treat truth as a binary quality. In fact, it is not necessary that such a system concern itself with truth at all. GIT is a statement about what is proveable, not necessarily about what is 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.

No, it is not. It is possible to prove that the statement is true in the new axiomatic system. That does not imply that the staement is true in the original axiomatic system. Ask one of your invisible experts to explain the axiom of choice to you.

Here is a really really really simplified example. Perhaps it is even simple enough for you to understand.
SYSTEM A
[ol][li]Axiom: People who don’t understand logic should not pretend that they do.[/li]
[li]Assertion: TVAA should not pretend that he understands logic.[/li]
[li]Proof: oops – neither this statement nor it’s negation can be proved in system A.[/ol][/li]
SYSTEM B
[ol][li]Axiom: People who don’t understand logic should not pretend that they do.[/li][li]Axiom: TVAA does not understant logic.[/li]
[li]Assertion: TVAA should not pretend that he understands logic.[/li]
[li]Proof: modus ponens from (1) and (2).[/ol][/li]So, have I know proven that “TVAA should not pretend that he understands logic.” is true in system A?
:wally

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.

You are wrong. Your dicussion of soundness is fine. But the highlighted sentence is incorrect. GIT doesn’t care whether the statements are true.
[ol][li]COMPLETENESS: For any statement P, either § or (not P) is a theorem.[/li][li]CONSISTENCY: For some statement P, § is not a theorem. (Often, a less rigorous version of consistency is given: "For any statement P, § and (not P) are not both theorems.)[/ol][/li]Godel’s Incompleteness theorem states that both (1) and (2) cannot hold for any axiomatic system that meets certain specifications.

That’s it. Period. Full stop. Do not pass go. Do not insert unnecessary statements about truth. Do not spew ignorant shit and imagine that it smells like wisdom.

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.

Yes. Notice that it does not say “true sentences” or “sound sentences”. It says “sentences”. Stop. End of story. Do not pass go. Do not insert unnecessary statements about truth. Do not spew ignorant shit and imagine that it smells like wisdom.

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.

Actually, it clearly shows that:
[ul][li]You are stupid enough to post a proof without reading the notes that accompany it.[sup]1[/sup][/li][li]And you apparently have little to no familiarity with tarski’s theories of language and truth.[/ul][/li][sup]1[/sup]
From the very same site, immediately beneath the passage quoted by TVAA.

Note 1. An analysis of the proof shows that the axioms don’t have to be true. It suffices that (a) the system is consistent and (b) it can prove the basic facts needed to do arithmetical computations, e.g., prove that 2+2=4. The latter is needed to encode sequences of numbers and insure that computable sets are definable.

Any chance that you will believe the words when they come from your own site? Or is that little bit of intellectual honesty beyond the capacity of the ecstatic excrescence that is TVAA.

That’s it. Wading through 2 of your posts in one sitting is all that I can stomach. The rest will just have to wait until I drink enough whiskey to clear the stench.

[alice_in_wonderland]

Wowsers.

I don’t know much about math, but it looks like yer losing, TVAA.

Quickly - you must fetch the “experts” to save the day!

*cue superhero music

::Here they come to save the day…::*

[Spiritus_Mundi]

I’ll just down this glass and . . .

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.”

Here is what I said in this thread:
[ul][li]TVAA wants to talk about the fact that the statements can be proved in some 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.[/ul][/li]Here is what I said in the GD thread:
[ul][li]We both agee that it is possible to prove the statements that are unproveable in a P. A. by extending the axiom set. That has nothing to do with GIT, but we both agree on it anyway.[/li]
[li]We disagree on whether those proofs in extended languages can be rigorously said to prove results “in a Peano Axiomatization”, but that is irrelevant to your proof since you are arguing that the Universe itself is a system that is bound by GIT. Since the whole Universe is your system, and you argue that any property the system emulates is a property of the system as a whole, there is no “axiom outside the box” that could be used to extend the language and prove an “unprovable in the Universe” statement.[/ul][/li]
Yet TVAA continues to spew shit about “Spiritus says there is no proof. He’s an idiot.”

You are a liar, TVAA. You cannot argue well, so you argue with deceit, insult, and evasion. You cheapen this board with every characer you post.

[ultrafilter]

I’ve read GEB. I’ve also read Mendelson and Sipser. And now I’ve read the ravings of a lunatic.

[Spiritus_Mundi]

There’s really no difference.

There really IS a difference. Honest people do not say they are quoting when they are actually paraphrasing.

Again, if you’re not capable of using words to signify meaning, please just say so.

If you ever chose to stop lying, please just say so.

It’s very important. Subsystems of the universe are not necessarily sufficiently powerful; leaving out one of the vital requirements of GIT does not strike me as a good way to debate about it.

Here is what I said:
[ul][li]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? [/ul][/li]Here is what you said, right before the post I am responding to:
[ul][li]The universe is necessarily a sufficiently powerful system because time exists. To put in another way: one configuration of the universe leads to another. That’s causality.[/ul][/li]Yet here you are pretending that it is important for me to specifically eliminate the possibility that we are talking about subsystems of the universe .
:rolleyes:
If you ever chose to stop lying, please just say so.

One of the problems in this “debate” is that you’ve consistently ignored points made within its context. You keep demanding explanations that have already been given, and you make inaccurate and incomplete statements about what you mean.

Anytime you want to actually support such charges with specific detail, let me know. If you’d like to know how, see any number of my posts where I quote your actual words and then use them to support my assertions.

Until then: :wally

It seems to me that I’ve been citing those restrictions and requirements over and over again. I fail to see the problem. If people wished, they can always return to the original thread, yes?

Right. Each and every time you have mentioned GIT or its implications you have taken the text to explicitely reference the specific requirements for GIT to hold . . . Or else you’re a delusional loony.

Gentlemen, place your bets. I have 9 pages of TVAA talking about GIT for anyone who wishes to place his money on the delusional loony.

For some remarkable reason, you’re ignoring the flaws, errors, and inaccuracies I keep pointing out in your statements and focusing on the aspects of my statements you don’t understand. It’s a reasonable strategy, and one I would expect from a thinker of your caliber.

Ah – I love irony.

The passage above immediately follows my pointing out that GIT[sup]2[/sup] precludes TVAA from proving that the Universe is consistent (if it is consistent). But for GIT[sup]1[/sup] to necessarily apply, TVAA must demonstrate that the Universe is consistent.

Strangely enough, TVAA managed to completely ignore that fact in making his reply above. Instead, he tries to deflect attention from it by charging that I ignore flaws, errors, etc. hmmmmmmmmmmmmmm

Can anyone out there say “intellectually bankrupt”?

If nothing else, these threads have been eye-openers for me. I actually respected you before these discussions began.

I recall.
[ul][li]Two weeks ago you said: “Spiritus: I am generally awestruck by the levels of rationality and intelligence you demonstrate in your posts.” [/li]
[li]Now you say: Spiritus is “an idiot”, “a moron”, “stupid”, “not capable of using words to signify meaning”.[/ul][/li]Why? Because I disagree with your interpretation about a metalogical theory. You cheapen the word “respect” to use it so. Your esteem was worhtless then. Your contempt is insignificant now. You lack the integrity to make either a concern.

[Liberal]

Again, if you’re not capable of using words to signify meaning, please just say so.

It’s almost pitiful, Vorlon trying to win a point. Sorta like Bud Bundy trying to get a date.

[iampunha]

It’s like bj0rn’s twin … bj0rn can’t string together a coherent sentence, and TVAA can’t string together a coherent argument/premise—>conclusion logic set. But it is so adorable the way he sets up all those little “this might be a logical argument!” decoys.

Someone with a deeper knowledge of SDMB history want to tell me who their bastard child would be?

[Desmostylus]

*Originally posted by iampunha *
Someone with a deeper knowledge of SDMB history…

In the top ten poster list, you’re number nine, so there shouldn’t be too many people with a deeper knowledge than you, should there?

[Drastic]

I remember the episode where Bud impressed his friends with his smoove ways by dating a store mannequin. The highlight of the episode was when it was time to go upstairs ([Isaac Hayes]Ohhh yeah[/Isaac Hayes]) and on the way up all her limbs and head came off. That was a great episode.

[The_Great_Unwashed]

*Originally posted by TVAA *
**Have any of you ever read Godel, Escher, Bach? **

and then

**Have any of you ever read Godel, Escher, Bach? **

What? Did you read my post on the first page of the original thread? Where I said:

[QUOTE]
**I find the general idea quite appealing, and even believable – that for a given computer of sufficient complexity there exists a sequence of inputs that will cause it to fail catastrophically (like the record players in Godel, Escher, Bach (maybe you’ve read it?)). **

[QUOTE]

It seems extraordinarily perverse of you to bring it up now given that you failed to respond to the question at the time.

Anyway…

Yes, I’ve read it.

Yes, I remember the record players.
Give me chapter and page where Hofstadter says these record players are subject to GIT?

[FranticMad]

I think we should find where TVAA lives, and treat him to a night on the town. Get him slightly drunk and then get him laid and then get him properly drunk at a karaoke. The only rule is “no talking about GIT while getting french kissed.”

[Fenris]

*Originally posted by iampunha *
**Someone with a deeper knowledge of SDMB history want to tell me who their bastard child would be? **

Yeah…whatshisname…th’ one who was scared of women and had long incomprehensible posts where he was trying to disprove the idea that since he couldn’t get lucky, women were pretty damn smart…or something.

Th’ hell was his name…?

Justhink!

(At least, I hink it was. )

Fenris

[TVAA]

*Originally posted by Spiritus Mundi *
**No way am I going to try to combat every stupid, dishonest, or just plain nonsensical claim that you have made. You quite literally are not worth that much time. Actually, you arent’ worh thte time I have already spent on you, but there is some amusement value in pointing out the deficiencies of your character.

** That’s it, SM. Ignore the errors and contradictions I’ve pointed out in your argument and instead accuse me of committing those same mistakes.

Aren’t you the moron who just a little while ago posted that contradictions could be subjected to logical analysis? that’s rught, you are. And, of course, I didn’t say that I wanted to discuss one. I said that your statement did not deal with the possibility that one might exist. You made a categorical statement. That statement wsa wrong. I pointed it out to you.

How stupid. First, they are indeed subject to logical analysis. Watch.

“This definition is self-contradictory. Therefore it cannot represent any consistent or coherent set of behaviors; as such, we have no reason to consider it further.”

Perhaps you’d like to argue that we should take the time to consider definitions that are merely inherently wrong instead of inherently contradictory?

**I posted the relevant pieces of our exchange. Post the specific statement of mine that you are misreading as an introduciotn of symbology into the debate or admit that you are the most pathetic coprophage to infest this board since Captain Foreskin got the snip.

** I’ve already done that. Pay attention, dolt.

**Right. What a perfectly reasonable reason for ignoring questions in a debate. **

They’re stupid and pointless. If I answered every question you’ve thrown into the ring, these threads would be twice as long.

**Because you have not. Logical arguments, even informal logical arguments, have certain structural requirements. You have not met those requirements. You have not een come close. You simply wave your hand and say: GIT. When asked specific questions, you respond: The answers can be deduced from previous statments.

** No, the answers have been given. You’ve either ignored those answers, or failed to understand them. I’m not surprised.

You can’t even explain what GIT implies without making elementary errors. Your claims about “soundness and completeness” alone would get you a failing grade in a paper for introductory mathematical logic. If the soundness of a system can be demonstrated, then the truth of its statements can be shown merely by showing that they can be derived from its axioms – but that is not the only way truth is determined, and it’s impossible to use that method on statements that cannot be derived from the system.

Didn’t you take a look at the links I presented? One demonstrates that the classic Godel statement is true in a system S while not provable in system S.

**When can be becomes has been shown then perhaps you will have made a logical argument. A string of assertions and a charge that people are stupid if they don’t understand is not a logical demonstration.

** It HAS been shown, fool. That’s why I know it CAN be done. The whole point is that at some point, you have to be able to think about them yourself.

If I give an explanation, you’ll simply demand an explanation for the explanation. “You haven’t proven your point, TVAA, you’ve merely made assertions.”

GIT applies to those things that are sufficiently powerful to generate the theorems of arithmetic (if it can demonstrate that 2+2 really does equal 4, it’s sufficiently powerful) and that are consistent. It’s trivially obvious that computers are within GIT’s realm. While the programs run by the computer may not be consistent, the configuration of the computer is, as we’ve established that it can simulate things, which only a consistent system can do. Thus even if the computer is running a program that isn’t sufficiently powerful, the mechanism of the computer is a system vulnerable to GIT.

Hello… this is a series of points that you haven’t been able to grasp for what, eight pages of SD board?

The argument has been supported quite thoroughly, thanks. At no point in the discussion of it have you shown the least glimmer of comprehension.

At least those reading this thread have the record of your misstatements and misunderstandings to show them you’re incorrect.

Oh, and your dismissal of the evidence that contradicts your statements because “it’s not a mathmatical statement, just a natural-language statement about math” is pathetic. We use unnatural languages to perform mathematics because they allow a more concise and precise representation of the concepts at hand, but standard languages can still generate meaningful and rigorous statements about math. I’m not personally capable of doing this well, but professional mathematicians are – and professional mathematicians wrote the things I’ve quoted and linked.

You poorly-named excuse for a revelation!

By the way, this post is not a sonnet. Even if I call it a sonnet and say that the metre and rhyme can be deduced from my words, this post is not a sonnet. The “why” of that statement is implied in the observation itself: this post does not possess the structural elements of a sonnet.

Correct. Luckily for me, the structural requirements of a logical argument are somewhat broader.

Sucks to be you.

[quote]
**What I said: survival
[li]What I did not say: **Attempt to survive, value survival, strive for survival, or any of numerous other possible misreadings by knuckledragging buffons.You claim that no matter what other elements an ethoc might have, the best ethos isthe one that survives. Thus, survival itself becomes the only ethical value in your view.[/li][/quote]
No, stupid.

In order to be an ethical value, a principle must be a stated within an ethical system. I’m saying that the ethical systems as a whole will possess a property: they’ll be the ones that persist and “win” the battle of evolutionary competition. “Survival” does not need to be a value within their systems – in fact, I cannot rule out the possibility that these systems will explicitly disregard survival as valuable.

You have no conception of the meaning of the word “value”.

**Yes. I got that. In your view the contents of an ethical system are entirely irrelevant to whether it is “good”. Of course, that itself is an ethical valuation on thepart of TVAA. In TVAA-ethics, only survival marks something as good.

** Not “good”: correct. Those things that are correct will determine the nature of “good”. Perhaps “good” is objecively determinable – in which case the ethical systems that continue to exist indefinitely will inevitably come to reflect them. Perhaps “good” is subjective – in which case the principles that determine what subjective states are posible will determine it.

[TVAA]

Ooh – I just foundthis article at Scientific American.

I suggest you all read it – it has some important implications for the necessity of using specific mathematical language to discuss GIT.

[TVAA]

*Originally posted by Spiritus Mundi *
**How, exactly, do you imagine that linking to a definition of soundness indicates an error on my part?

**

It doesn’t. I linked to the definition to show you were misusing the term.

(What kind of an idiot would suggest that a linking would itself demonstrate an error?)

**(BTW, I notice that you misrepresent the content of that site to pass over the fact that soundness is a property ascribed to arguments, and thus to systems derived from a single set of axioms. I wonder why you would do that?)

** BTW, I notice that you misrepresent the content of that site to pass over the fact that for an argument to be sound, the system in which it is evaluated must be true. Soundness therefore makes statements about the system as well.

No, I take back my earlier statement: GIT doesn’t take soundness for granted, since the axioms of the systems GIT applied to don’t need to be true. GIT is more fundamental than soundness is – it applies to statements that aren’t sound.

My mistake. Too bad it’s not one you pointed out…

What I said of GIT is rigorously correct. If you disagree, then you should try to actually address the content of my statement.

I did so, fool. Remember when I pointed out your error in saying that GIT showed that some statements have no proofs?

Right, because it is not saying anything about truth. If it wants to say somethign about truth, then ot would have to address soundness.

No, it doesn’t. Soundness is not a prerequisite for truth. Truth is in fact a prerequisite for soundness. All things that are sound are true, but not all things that are true are sound.

Reread the definition of “soundness”, SM.

**Goodness, then it’s a really good thing that I never tried to pretend that all unsound statements are untue, isn’t it?

** You’ve repeatedly said that truth is related to soundness. This is backwards: soundness is related to truth.

Talking about the truth of statements doens’t actually require addressing their soundness. In fact, soundness refers only to arguments, which involve taking intial statements and deriving necessary consequences of them. GIT addresses those statements that specific initial assumptions cannot derive – given the specific axiomatic set, there’s no argument that can be made that will produce those statements.

Stop beating about the bush.

**This is pathetic. GIT does not address soundness. GIT does not require soundness. GIT is, in fact, entirely uninterested in soundness. But soundness is the only way that we can declare valid theorems to be “true”. Therefore, if we want to use “truth” in our arguments, we must assume that the system being examined has sound axioms.

**

Um, no.

First: I thought you said “soundness” was only applicable to arguments. Why are you using it to refer to axioms? (Maybe because it’s considered useful, if not technically correct, to refer to consistent axioms that can be used in a sound argument as “sound”?)

And no we don’t. We need concern ourselves with soundness only if we want to demonstrate the truth of a statement. Whether it is true is a question that doesn’t require soundness.

We consider cases where the axioms of a system are “true”, yet by definition the truth of axioms can never be derived from the axioms. Why then do we call them true? Because the truth of a statement is not dependent on whether we can generate a demonstration of that proof in a specific system.

**You claim I said “X”. I show that I did not say “X”. You say “irrelevant”. PAY ATTENTION TO THE CONTEXT OF OUR ARGUMENT!!!

Your words speak for themselves. We don’t need your apologetics to explain to us what they really meant.

**Forget, for the moment, who is right about GIT. In this passage, I am simply showing that I never made the stupid statement that you attributed to me. I am also showing that you are too stupid to know whether the quotations you choose actually support the claims that you make.

** sigh Your ego blinds you, Spiritus.

**Okay – back to why you are an ignorant fuckwit who hasn’t a clue as to what GIT actually says. GIT doesn’t say anything about truth. It is only writers trying to gloss GIT for a lay audience that talk about truth. GIT says that well formed statments exist such that neither the statement nor the negation of the statement can be proved within a consistent axiomatic system of sufficient power. Period.

** Correct. We cannot show that all unprovable statements are true. However, statements that are true can be shown to be unprovable.

What’s your point, again?

**GIT doesn’t care whether the statements are true or not, but in any system that excludes only binary truth values it is necessary that one or the other be true. It is not the case, however, that every axiomatic system of sufficient power to invoke GIT must necessarily treat truth as a binary quality. In fact, it is not necessary that such a system concern itself with truth at all. GIT is a statement about what is proveable, not necessarily about what is true.

** It’s not about whether the statements referenced are true… it’s all about whether a meta-statement about mathematics is true. Get it right, Spiritus.

**No, it is not. It is possible to prove that the statement is true in the new axiomatic system. That does not imply that the staement is true in the original axiomatic system. Ask one of your invisible experts to explain the axiom of choice to you.

** No, here’s the important thing:

The new axiomatic system proves that the statement is “true in the previous system”. It cannot show that it’s “true” in the previous system.

Syntax is everything, Spiritus. Order of operations applies in English as well as arithmetic.

If you knew more about Godel, you’d know that he was a strong proponent of the principle that things are true regardless of whether they can be demonstrated so. Other mathematicians prefer a more conservative view. Regardless, it can be shown that statements that cannot be proven within a system are still true relative to that system. READ THE LINK PROVIDED WHERE THIS IS DONE.

**You are wrong. Your dicussion of soundness is fine. But the highlighted sentence is incorrect. GIT doesn’t care whether the statements are true.

** I never said GIT “cares”. It doesn’t matter one bit.

GIT doesn’t make any claims about the truth of the statements, yes. It does show that statements that are true can be unprovable. Statements that are false can also be unprovable.

[TVAA]

*Originally posted by alice_in_wonderland *
**Wowsers.

I don’t know much about math, but it looks like yer losing, TVAA. **

If you don’t know much about the math involved, how do you know who’s losing and who’s winning?

[TVAA]

[QUOTE]
*Originally posted by Spiritus Mundi *
**Here is what I said in this thread:
[ul][li]TVAA wants to talk about the fact that the statements can be proved in some 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.[/ul][/li]Here is what I said in the GD thread:
[list][li]We both agee that it is possible to prove the statements that are unproveable in a P. A. by extending the axiom set. That has nothing to do with GIT, but we both agree on it anyway.[/li][/quote]
** It has a great deal to do with GIT, as that means that some of the statements GIT shows to be unprovable in a system are true.

**We disagree on whether those proofs in extended languages can be rigorously said to prove results “in a Peano Axiomatization”, but that is irrelevant to your proof since you are arguing that the Universe itself is a system that is bound by GIT. Since the whole Universe is your system, and you argue that any property the system emulates is a property of the system as a whole, there is no “axiom outside the box” that could be used to extend the language and prove an “unprovable in the Universe” statement.

** PA isn’t important. All that matters is whether the system of axioms is at least as powerful as PA. PA itself doesn’t need to be explicitly part of the axiom set.

**You are a liar, TVAA. You cannot argue well, so you argue with deceit, insult, and evasion. You cheapen this board with every characer you post. **

You’re the one who’s misrepresented the nature of GIT, lied about what they’ve said, and continually ignored the other side.

[TVAA]

*Originally posted by ultrafilter *
**I’ve read GEB. I’ve also read Mendelson and Sipser. And now I’ve read the ravings of a lunatic. **

Yes, Spiritus Mundi’s posts are rather “strange”, aren’t they?

Refuting points I’ve never made or implied… claiming his incorrect statements were just “misinterpreted”… failing to deal with the argument at hand, then claiming to have shown it’s false…

Clearly the work of a disturbed mind.