# Spiritus Mundi **URL:** \ **Category:** The BBQ Pit\ **Created:** [April 26, 2003, 5:09am UTC](https://boards.straightdope.com/t/spiritus-mundi/171273 "2003-04-26T05:09:07Z")\ **Posts on this page:** 20\ **Page:** 7
**Author:** ![cainxinth](https://avatars.discourse-cdn.com/v4/letter/c/7bcc69/32.png) [@cainxinth](https://boards.straightdope.com/u/cainxinth)\ **Post date:** [April 26, 2003, 7:09pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/121 "2003-04-26T19:09:35Z")
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. ---
**Author:** ![Kal](https://avatars.discourse-cdn.com/v4/letter/k/9de053/32.png) [@Kal](https://boards.straightdope.com/u/Kal)\ **Post date:** [April 26, 2003, 7:11pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/122 "2003-04-26T19:11:21Z")
Shhhh… Listen… You hear that noise? That’s the sound of the baby Jesus crying. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 26, 2003, 7:12pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/123 "2003-04-26T19:12:21Z")
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. ---
**Author:** ![Kal](https://avatars.discourse-cdn.com/v4/letter/k/9de053/32.png) [@Kal](https://boards.straightdope.com/u/Kal)\ **Post date:** [April 26, 2003, 7:12pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/124 "2003-04-26T19:12:26Z")
Or maybe I’ve just had a stroke. ---
**Author:** ![cainxinth](https://avatars.discourse-cdn.com/v4/letter/c/7bcc69/32.png) [@cainxinth](https://boards.straightdope.com/u/cainxinth)\ **Post date:** [April 26, 2003, 7:13pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/125 "2003-04-26T19:13:22Z")
\ ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 26, 2003, 7:16pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/126 "2003-04-26T19:16:31Z")
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? ---
**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\ **Post date:** [April 26, 2003, 7:31pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/127 "2003-04-26T19:31:02Z")
> [@](#): > > \*Originally posted by TVAA \* > I’ve spoken with people with those prerequisites, and they say **Spiritus** is wrong. What other conclusion can I draw? That you are presenting his side unfairly, perhaps? > [@](#): > > The problem is that **Spiritus** not only doesn’t consider arguments not couched in special terms to be worthy of consideration, he’s unable to discuss mathematical ideas in everyday English without getting them wrong. 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. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 26, 2003, 8:46pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/128 "2003-04-26T20:46:43Z")
> [@](#): > > \*Originally posted by erislover \* > **That you are presenting his side unfairly, perhaps?** They read the threads in question, **eris**. I don’t think anything could present his case better than his case. > [@](#): > > **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.** 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? > [@](#): > > \*\*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. \*\* 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. ---
**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\ **Post date:** [April 26, 2003, 8:53pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/129 "2003-04-26T20:53:07Z")
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. ---
**Author:** ![lucwarm](https://avatars.discourse-cdn.com/v4/letter/l/e19adc/32.png) [@lucwarm](https://boards.straightdope.com/u/lucwarm)\ **Post date:** [April 26, 2003, 8:58pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/130 "2003-04-26T20:58:50Z")
> [@](#): > > \*Originally posted by TVAA \* > \*\*They read the threads in question, \*\* 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? ---
**Author:** ![wring](https://avatars.discourse-cdn.com/v4/letter/w/838e76/32.png) [@wring](https://boards.straightdope.com/u/wring)\ **Post date:** [April 26, 2003, 9:00pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/131 "2003-04-26T21:00:35Z")
**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)\> ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 26, 2003, 9:01pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/132 "2003-04-26T21:01:58Z")
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. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 26, 2003, 9:04pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/133 "2003-04-26T21:04:00Z")
No, they said **Spiritus** was too stupid to understand. At least accurately report what I said, will you? ---
**Author:** ![wring](https://avatars.discourse-cdn.com/v4/letter/w/838e76/32.png) [@wring](https://boards.straightdope.com/u/wring)\ **Post date:** [April 26, 2003, 9:07pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/134 "2003-04-26T21:07:03Z")
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?? ---
**Author:** ![Spiritus\_Mundi](https://avatars.discourse-cdn.com/v4/letter/s/c68b51/32.png) [@Spiritus\_Mundi](https://boards.straightdope.com/u/Spiritus_Mundi)\ **Post date:** [April 26, 2003, 9:07pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/135 "2003-04-26T21:07:14Z")
I’m just going to hit your first couple of nonsense points, the rest repeat some patterns that have already become tiresome. > [@](#): > > Where, exactly, was I using a contradiction to reliably derive an ethos? What contradiction are you talking about? 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. > [@](#): > > \*\*TVAA: \*\*Logic does not demand that any particular set of conditions be called ‘good’ only if ‘good’ has no definition. > > \*\*Spiritus: \*\*Not necessarily. I don’t think that you can make the implication biconditional. It is certainly true that if “good” has no definition then logic cannot tell you what is good. However, it is entirely possible for good to have a definition that does not admit to logical analysis. (Or perhaps just not one or another method of logical analysis.) > > \*\*TVAA: \*\*Only if you throw out the concept of “definition”. > > \*\*Spiritus: \*\*Not at all. You only have to allow definitions to express ideas that make logical analysis problematical. Examples of this are: self-contradiction, paradox, non-determism, etc. > > \*\*TVAA: \*\*[you fail] to realize that the only way the concept couldn’t be analyzed logically would be if it had no properties. He suggests that the concept could have properties like “self-contradictory” or “non-deteministic”, but these concepts and related-concepts ARE analyzed logically frequently. > > \*\*Spiritus: \*\*You wanted to derive an ethical system from logic. Under most logical systems, a contradiction can be used to prove all things. That makea it a little difficult for you to use a contradiction to reliably derive an ethos. > > \*\*TVAA: \*\*Where, exactly, was I using a contradiction to reliably derive an ethos? What contradiction are you talking about? 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. > [@](#): > > Ethical systems that aren’t evolutionarily adaptive will cease to exist – regardless of whether an ethical system is meant to describe a property of the world or merely define “proper” behavior, it will eventually develop significance in regards to the world. 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. > [@](#): > > But you keep claiming that I’m talking about the label. Then you deny that you’re misrepresenting arguments… 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 > [@](#): > > **Spiritus Mundi:** You just shouldn’t fool yourself into thinking that logic is determining what is “good” and what is “evil”. > > **TVAA:** I agree that the word-sound ‘good’ is arbitrary: we could use ‘grafnoinkel’ instead if we wished. > > **Spiritus Mundi:** There is no dispute on this point. You are misunderstanding if you imagine that I am saying anything about the specific symbol chosen to represent the concept “good”. > > **TVAA:** I’m not saying anything about the symbol chosen to represent any concept. I’m saying something about the concept, and anything that can act as the embodiment of the concept in a language. > > **Spiritus Mundi:** Nor am I, which is why I told you that the issue was not under dispute when you brought it up. > > **TVAA:** But I didn’t bring it up. I don’t know what you’re reading into my arguments, but I have never discussed “symbols used to represent good”, or symbols used to represent any other concept. > > **Spiritus Mundi:** How pathetic do you have to be to keep going back to an argument over who said “the label doesn’t matter” first. > > **TVAA:** But you keep claiming that I’m talking about the label. Then you deny that you’re misrepresenting arguments… 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. > [@](#): > > It’s not particularly difficult to understand how living things might arise, and it’s not particularly difficult to understand that they’ll have preferences. Everything else follows. 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.** > [@](#): > > I’VE NEVER CLAIMED THAT SURVIVAL IS THE BEST ETHIC! It may be the case that the most successful ethic actually instructs its carriers to attempt NOT to survive. Haven’t you ever heard of the Selfish Gene hypothesis? Survival isn’t the best ethic, but the best ethic is the one that survives. 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: > [@](#): > > \*\*TVAA: \*\*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. This is NOT what GIT says. > > **Spiritus:** You are correct that that is not what GIT says. It is also not something that I have ever said. Perhaps you would be so kind as to post my actual words instead of your summaries of my words. Your summaries lack a certain . . . shall we say “desirable accuracy”. 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. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 26, 2003, 9:09pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/136 "2003-04-26T21:09:55Z")
**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. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 26, 2003, 9:21pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/137 "2003-04-26T21:21:25Z")
1. 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? 1. 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. 2. 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? 1. 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”. 2. 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. ---
**Author:** ![Spiritus\_Mundi](https://avatars.discourse-cdn.com/v4/letter/s/c68b51/32.png) [@Spiritus\_Mundi](https://boards.straightdope.com/u/Spiritus_Mundi)\ **Post date:** [April 26, 2003, 9:27pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/138 "2003-04-26T21:27:57Z")
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: > [@](#): > > **spiritus:** Here’s another point that you don’t understand: a system cannot be proven to be consistent from within itself. That is GIT2. Thus, you can never demonstrate your claim that the Universe itself is a consistent axiomatic system. (Asuming you ever manage to demonstrate that it is an axiomatic system at all.) > > **TVAA"** Godel’s Second Incompleteness Theorem states that, and I quote, “in any consistent axiomatizable theory (axiomatizable means the axioms can be computably generated) which can encode sequences of numbers (and thus the syntactic notions of “formula”, “sentence”, “proof”) the consistency of the system in not provable in the system.” > > This does NOT apply to all systems, only to sufficiently powerful and complete systems. > > Stupid. [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] ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 26, 2003, 9:44pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/139 "2003-04-26T21:44:00Z")
> [@](#): > > **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.** Basic error. [Soundness](http://www.wikipedia.org/wiki/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](http://www.wikipedia.org/wiki/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_.) > [@](#): > > \*\*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. \*\* 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 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. \*\* 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](http://www.wikipedia.org/wiki/Mathematical_logic) : 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](http://www.math.hawaii.edu/~dale/godel/godel.html#FirstIncompleteness) : > [@](#): > > Godel’s First Incompleteness Theorem. Any adequate axiomatizable theory is incomplete. In particular the sentence “This sentence is not provable” is true but not provable in the theory. > Proof. Given a computably generated set of axioms, let PROVABLE be the set of numbers which encode sentences which are provable from the given axioms. > Thus for any sentence s, > (1) \< s \> is in PROVABLE iff s is provable. > Since the set of axioms is computably generable, > so is the set of proofs which use these axioms and > so is the set of provable theorems and hence > so is PROVABLE, the set of encodings of provable theorems. > Since computable implies definable in adequate theories, PROVABLE is definable. > Let s be the sentence “This sentence is unprovable”. > By Tarski, s exists since it is the solution of: > (2) s iff \< s \> is not in PROVABLE. > Thus > (3) s iff \< s \> is not in PROVABLE iff s is not provable. > Now (excluded middle again) s is either true or false. > If s is false, then by (3), s is provable. > This is impossible since provable sentences are true. > Thus s is true. > Thus by (3), s is not provable. > Hence s is true but unprovable. 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. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 26, 2003, 9:48pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/140 "2003-04-26T21:48:37Z")
**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. [Previous page](https://boards.straightdope.com/t/spiritus-mundi/171273.md?page=6) [Next page](https://boards.straightdope.com/t/spiritus-mundi/171273.md?page=8)