# 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:** 16
**Author:** ![London\_Calling](https://avatars.discourse-cdn.com/v4/letter/l/49beb7/32.png) [@London\_Calling](https://boards.straightdope.com/u/London_Calling)\ **Post date:** [May 1, 2003, 2:56pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/301 "2003-05-01T14:56:53Z")
> [@](#): > > \*Originally posted by Spiritus Mundi \* > London\_calling, I will single you out for the **Phaedrus** riff. Nothing like a little historical perspective to take the sting out of the current crop of loon. This **Spiritus Mundi** he is like a wild donkey, I triple guarantee you. We will push this gangster, this mercenary back into the swamp. He is a dog and we will beat his drunken, druggy nose with shoes and all the world will dance in joy! This is a lesson which will not be forgotten by history. Truly Now we will go and surround this **Spiritus** at the airport where he will be beheaded and I will bring his head to this place in ……… _\_ ps. Thank you **Spiritus** , but I fear you have invoked the ‘P’ word and that there may be no going back …… ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [May 1, 2003, 3:31pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/302 "2003-05-01T15:31:38Z")
Repeat a lie often enough, and people will begin believing it. **London\_Calling** is clearly familiar with this concept… probably because he falls for the trick so often. ---
**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:** [May 1, 2003, 3:42pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/303 "2003-05-01T15:42:15Z")
[ul][li]I have provided many specific arguments that indicate why you are wrong. [/li][li]I have linked to discussion about GIT that delve beyond the merely surface presentations often offered for mass consumption. [/li][li]I have even bolded for you Godel’s own words about the implications that a general and formal proof of the undecideablitiy of G would have on _inhaltlich richtig_.[/ul][/li]You might have taken the effort to actuall read and understand such things, or even to ask informed questions about them. Instead, you continue to embrace your ignorance. You cling to your delusion that I am a moron making “stupid mistakes” and “obvious errors” about GIT because you can’t be bothered to interrupt your masturbatory cycle of analingual pleasure long enough to educate yourself about what GIT _ **actually** _ says. You claim you have experts whose credentials in these fields are beyond doubt, yet you continue to make errors in interpretation and definition that even a reasonably educated layman would avoid. And you say that your **"invisile experts[sup]Tm[/sup]**" confirm that you are right while people that actually present the concepts surrounding GIT in an accurate form are “too stupid to be worth talking to.” You have on multiple occassions been caught making clear factual mistakes, both about what I have said and about such basic things as the proper definition of **consistency**. But you are such an ooze-dripping pustule of intellectual insecurity that you cannot bring yourself to admit: [color-blue]“hey, I never knew that wasn’t the real definition of consistency”.[/color] Instead you pretend that your ignorance somehow defines the proper set of systems to which GIT applies. In short, you are one of the more pathetic examples of poor and dishonest argumentation that has ever graced this board. No doubt you suffer from some unfortunate combination of : [ul][li]Poor parenting[/li][li]Substandard education[/li][li]A social environment that rewards alpha aggression above intellectual accomplishment[/li][li]Personality disorders that interfere with your ability to admit fault[/li][li]Social/personal/sexual insecurites that drive you to overcompensate[/li][li]Whatever.[/ul][/li]It really doesn’t matter. You’re an adult, now, responsible for your own behavior. Stop being a pathetic asshole. > [@](#): > > You may complain that this explanation doesn’t use specific terminology, but its meaning is correct. Wrong again. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [May 1, 2003, 3:44pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/304 "2003-05-01T15:44:03Z")
That _is_ what truth means, and it _is_ what the implications of GIT are. You can repeat your mantra of “wrong, wrong, wrong” as much as you like, but it won’t change anything. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [May 1, 2003, 3:46pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/305 "2003-05-01T15:46:28Z")
**Spiritus** , I have websites and textbooks galore which show that your standard-language “explanations” about what certain mathematical terms mean are grossly incorrect. I don’t know what’s more pathetic: that you think you can convince people that you’re right and I’m simply lying about what the words mean, or that you actually can. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [May 1, 2003, 3:51pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/306 "2003-05-01T15:51:03Z")
Your citations so far have been pretty pathetic. ---
**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:** [May 1, 2003, 5:18pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/307 "2003-05-01T17:18:26Z")
> [@](#): > > For any sufficiently powerful system S, the statement “this statement cannot be proven in S” (later referred to as G) cannot be proven or disproven Let’s see . . . following the **TVAA** mode of argument I should now immediately begin declaring that **TVAA** is an idiot who obviously hasn’t the first clue about GIT. He forgot to include the restriction **“omega-consistent”** [sup]1[/sup] for his “sufficiently powerful” systemns. What a moron! Only an absolute clueless imbecile would make such an obvious mistake about GIT! :rolleyes: > [@](#): > > Spiritus, I have websites and textbooks galore which show that your standard-language “explanations” about what certain mathematical terms mean are grossly incorrect. **TVAA** , that why _Argumentum ad Numerum_ is a logical fallacy. The fact that a lot of folks who write websites, or even introductory textbooks, say something does not mean that it is so. For the textbook writers, we can charitably assume that they know better but are simplifying things for an intro level class. (Though if you truly have a textbook that says the proper definition for **consistency** is “grossly incorrect” then you should immediately complain to whatever professor forced you to spend good money an a bad book.) Any kook can publish a website. And any loser can cling to ignorance rather than opening his mind to the truth. > [@](#): > > I don’t know what’s more pathetic: that you think you can convince people that you’re right and I’m simply lying about what the words mean, or that you actually can. What’s more pathetic is that you are so fundamentally lacking in intellectual integrity that you are unable to confront even the most basic and obvious mistakes. I am right about what the words mean. Any good treatment of GIT will address the historical context enough to show both that godel’s original result held only for omega-consistent systems and that the proper (and less restrictive) definition of consistency is not the _“Idiot’s Guide to Mathematical Logic”_ version that you think is gospel. I know that it will make you feel ridiculous to admit, after 12 pages of ranting about how you knew so much more about GIT than I or **ultrafilter** or **orbifold** or . . ., that you don’t even understand the class of systems to which GIT rigoously applies. But guess what–you already look ridiculous. This willfully blind devotion to ignorance only makes you look ridiculous _ **and** _ dishonest. Of course, that’s nothing new for you, either. [sup]1[/sup][sub]Yes, “omega-consistent” is proper, here, since **TVAA** is using a form of Godel’s original, less powerful, and no longer standard Godel statement. Had he shown the wit, awareness, or learning capacity to use the more powerful Rosser form of G, then the proper restriction would have been “consistent”.[/sub] ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [May 1, 2003, 5:24pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/308 "2003-05-01T17:24:46Z")
> [@](#): > > \*Originally posted by Spiritus Mundi \* > \*\*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.) > \*\* Those are utterly different definitions. In the first case, if there’s a single statement that isn’t a theorem in the system, the system is consistent. In the second case, if there’re no statements in the system whose negations are also in the system, the system is consistent. The first definition of “consistency” has little to do with this debate. It’s a completely different concept that happens to be described by a similar word. ---
**Author:** ![hawthorne](https://avatars.discourse-cdn.com/v4/letter/h/c89c15/32.png) [@hawthorne](https://boards.straightdope.com/u/hawthorne)\ **Post date:** [May 1, 2003, 5:27pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/309 "2003-05-01T17:27:24Z")
> [@](#): > > _Spiritus Mundi_ > But guess what–you already look ridiculous. Yes, he does. And has done for several pages. So why don’t you declare victory? ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [May 1, 2003, 5:29pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/310 "2003-05-01T17:29:33Z")
> [@](#): > > \*Originally posted by Spiritus Mundi \* > \*\*Let’s see . . . following the **TVAA** mode of argument I should now immediately begin declaring that **TVAA** is an idiot who obviously hasn’t the first clue about GIT. He forgot to include the restriction **“omega-consistent”** [sup]1[/sup] for his “sufficiently powerful” systemns. What a moron! Only an absolute clueless imbecile would make such an obvious mistake about GIT! > :rolleyes: \*\* The restriction I included implies everything omega-consistentency does. It’s obviously quite a bit stronger, in fact. > [@](#): > > \*\ ***TVAA** , that why _Argumentum ad Numerum_ is a logical fallacy. The fact that a lot of folks who write websites, or even introductory textbooks, say something does not mean that it is so. For the textbook writers, we can charitably assume that they know better but are simplifying things for an intro level class. (Though if you truly have a textbook that says the proper definition for **consistency** is “grossly incorrect” then you should immediately complain to whatever professor forced you to spend good money an a bad book.) Any kook can publish a website. \*\* And any kook can post on the Straight Dope claiming to understand higher math, right **Spiritus**? > [@](#): > > \*\*What’s more pathetic is that you are so fundamentally lacking in intellectual integrity that you are unable to confront even the most basic and obvious mistakes. I am right about what the words mean. Any good treatment of GIT will address the historical context enough to show both that godel’s original result held only for omega-consistent systems and that the proper (and less restrictive) definition of consistency is not the _“Idiot’s Guide to Mathematical Logic”_ version that you think is gospel. \*\* Your “less restrictive” definition of consistency allows for contradictions. I am not impressed. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [May 1, 2003, 5:37pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/311 "2003-05-01T17:37:08Z")
If, as you claim, I’m using an outdated and less powerful form of GIT, then it follows that the updated and more powerful version can show anything the first did and more. If the first version of GIT shows something, then the second will as well. It’s simply the case that conclusions demonstrable from the second might not hold in the first. Poor reasoning, **Spiritus**. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [May 1, 2003, 5:44pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/312 "2003-05-01T17:44:08Z")
> [@](#): > > \*Originally posted by TVAA \* > **And any kook can post on the Straight Dope claiming to understand higher math, right Spiritus?** It’s a good thing I’m not afraid of irony. I don’t think I could get out of bed in the morning. \*\* > [@](#): > > Your “less restrictive” definition of consistency allows for contradictions. I am not impressed. \*\* Some systems are consistent even though they contain contradictions. Why is it so hard for you to grasp this concept? You don’t need to answer that. I think I’ve got a pretty good idea as to what the answer is. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [May 1, 2003, 5:48pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/313 "2003-05-01T17:48:20Z")
> [@](#): > > \*Originally posted by ultrafilter \* > **Some systems are consistent even though they contain contradictions. Why is it so hard for you to grasp this concept?** Not according to the definition of ‘consistency’. Tell me, **ultrafilter** , why was it necessary to qualify ‘consistency’ with the prefix ‘omega’ in the link you provided? If the definition given for ‘omega-consistency’ is indedd what ‘consistency’ means, why is it necessary to put a greek letter in front of the term? ---
**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:** [May 1, 2003, 6:41pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/314 "2003-05-01T18:41:01Z")
Are you incapable of reading, is that teh problem? The proper definition of consistency _ **does not** _ require the qualifier “omega”. It is the **TVAA** definition of consistency that is _almost_ equivalent to **omega-consistency**. The difference, as **ubltrafilter** pointed out and I implied in my definition for the three types, is subtle. Do you understand yet, **TVAA**? How many more times do we have to tell it to you before the concept will penetrate? How many more sites with a rigorous approach to mathematical logic will help you to at least **UNDERSTAND** what we are saying the proper definitions of consistency and omega-consistency are? Just read the damn words! I know that’s hard with your head planted so firmly up your ass, but try to pretend that your mind is not locked down like the White House on 9-12. > [@](#): > > Those are utterly different definitions. No shit. And only one of them is correct. The other is a simpification given to folks who like to think about mathematical logic without stressing any neurons. > [@](#): > > In the first case, if there’s a single statement that isn’t a theorem in the system, the system is consistent. > > In the second case, if there’re no statements in the system whose negations are also in the system, the system is consistent. Congratulations. You have actually managed to get something right. > [@](#): > > The first definition of “consistency” has little to do with this debate. It’s a completely different concept that happens to be described by a similar word. But, of course, it could not last. The first definition is **the rigorously correct definition of consistency.** It defines precisely the set of systems to which GIT applies. Historically, Godel’s original sketch of a proof held only for omega-consistent systems. Rosser fixed this more than 60 years ago, which is why the Godel-Rosser version of GIT is now standard. If your piles and piles of bullshit popularization haven’t managed to convey that simple truth to you, then you should stop wasting your money on bad books. Or at least stop pretending that bad books make you an expert on GIT. > [@](#): > > The restriction I included implies everything omega-consistentency does. It’s obviously quite a bit stronger, in fact. :rolleyes: Whooooooooooooooooooosh > [@](#): > > And any kook can post on the Straight Dope claiming to understand higher math, right Spiritus? Actually, I believe you have posted that you know almost nothing about higher math. This is obviously correct, though it just as obviously does not stop you from saying many, many ignorant things about math. > [@](#): > > Your “less restrictive” definition of consistency allows for contradictions. I am not impressed. As it turns out, mathematics and logicians don’t give a rat’s dangling testicle whether you are impressed or not. The definition remains the same. > [@](#): > > If, as you claim, I’m using an outdated and less powerful form of GIT, then it follows that the updated and more powerful version can show anything the first did and more. [ul][li]There is no doubt about my “claim”. Any good treatment of GIT (which obviously excludes those that you rely upon) will address Rosser’s work.[/li][li]What follows is that the standard version of GIT is more general. It applies to more systems. That is the sens in which it is more powerful.[/li][li]Your version proves the same thing for a smaller set of systems. There is a proper subset of that smaller set of systems for which the implication fo truth value that you so desire also holds. In the smaller set of omega-consistent systems, the only additional qualifer required for the truth implication to hold is that a binary truth value be defined for all statements.[/ul][/li] > [@](#): > > If the first version of GIT shows something, then the second will as well. It’s simply the case that conclusions demonstrable from the second might not hold in the first. No. The “weakness” and “strength” are inherent in the distinction between consistent and omega-consistent. Thus, the implication of a proof holding in one or another context is explicitely and solely the breadth of systems across which GIT can be properly applied. The point that you apparently find so personally upsetting is that with the proper definition of consistency it becomes apparent that the semantic consequences for truth value, which depend upon qualities found only in a proper subset of systems powerful enough to invoke GIT, is shown to be irrelevant to the proof of GIT. GIT says nothing about truth. GIT implies nothing about truth. GIT is a general result. The truth you are looking for is a proerty of specific deductive systems. It does not hold over the general class of systems subject to GIT. > [@](#): > > Poor reasoning, **Spiritus** Pure ignorance, **TVAA**. ---
**Author:** ![mallocks](https://avatars.discourse-cdn.com/v4/letter/m/f4b2a3/32.png) [@mallocks](https://boards.straightdope.com/u/mallocks)\ **Post date:** [May 1, 2003, 6:42pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/315 "2003-05-01T18:42:21Z")
this is clearly an argument that can only be solved by one side dying. I honestly don’t know who’s right and who’s wrong, and to be honest after 7 pages I think the only thing that is obvious is that neither TVAA nor Spiritus et. al. is going to accept that the other is right, nor is going to stop feeding the other with more posts. Surely one of you could simply leave with a post saying “I’m right” and simply ignore the replies from the other… ---
**Author:** ![3trew](https://avatars.discourse-cdn.com/v4/letter/3/13edae/32.png) [@3trew](https://boards.straightdope.com/u/3trew)\ **Post date:** [May 1, 2003, 6:49pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/316 "2003-05-01T18:49:42Z")
Next week, GIT versus Time Cube! ---
**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:** [May 1, 2003, 6:50pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/317 "2003-05-01T18:50:53Z")
**TVAA** , since you were obviously too involved in a your feedback loop of ignorance and anal gratification to read these words the first time, I am going to repost (in layman’s terms so you will be able to understand teh symbols if not the content) the proper definitions for consistency and omega-consistency. > [@](#): > > [ul][li]\*\*Consistency: \*\*For some well-formed statement P, § is not a theorem of A.[/li] > [li]\*\*TVAA-consistency: \*\*If § is a theorem of system A then (~P) is not a theorem of A. This is _almost_ equivalent to omega-consistency and in the converse is often used as a method for showing omega-inconsistency. [/li] > [li]\*\*omega-inconsistency: \*\*A system is omega-inconsistent when all wffs in a certain infinite series are theorems while the negation of the summarizing quantified statement is a theorem. [/ul][/li] **Hawthorne** Despite all evidence, I actually hold out a miniscule slive of hope that **TVAA’s** intellect might sometime peak out from his anal cavity of hubris (perhaps in a moment of accidental slippage) long enough for him to actually **learn something** about GIT. It is obviously a subject that he is passionate about, despite his dogmatic determination to accept simplified popular presentations rather instaed of trying to educate himself about the actual theorems. Besides, the asshole called me out by name in one of the most lame and ill-coinsidered PIT threads ever perpetuated upon this board. It would be poor policy for me to not give **TVAA** the full respect to which he is entitled. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [May 1, 2003, 7:13pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/318 "2003-05-01T19:13:32Z")
> [@](#): > > \*Originally posted by TVAA \* > \*\*Not according to the definition of ‘consistency’. > > Tell me, **ultrafilter** , why was it necessary to qualify ‘consistency’ with the prefix ‘omega’ in the link you provided? If the definition given for ‘omega-consistency’ is indedd what ‘consistency’ means, why is it necessary to put a greek letter in front of the term? \*\* If you think that I or **Spiritus** has said that [symbol]w[/symbol]-consistency is the same as consistency, please tell us where, so that we may laugh at you for your poor reading comprehension. [symbol]w[/symbol]-consistency is not the same as consistency. There are consistent but [symbol]w[/symbol]-inconsistent systems out there. Consider a theory with the constant 0, the successor function (denoted '), one unary predicate letter P, and the usual rules of inference and logical axioms. We have the following proper axioms: 1. ([symbol]$[/symbol]x)(P(x)) 2. ~P(0) 3. ([symbol]"[/symbol]x)(P(x’) -\> P(x)) Now there are two things that we can prove here: First, some natural number has property P. Second, for any natural number n, n does not have property P. However, we can’t prove ([symbol]"[/symbol]x)(~P(x’)), because proofs are required to be finitely long. Therefore, the theory is consistent, but [symbol]w[/symbol]-inconsistent. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [May 1, 2003, 9:19pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/319 "2003-05-01T21:19:00Z")
> [@](#): > > consistent > > \Con\*sist"ent, a. [L. consistens, p. pr.: cf. F. consistant.] 1. Possessing firmness or fixedness; firm; hard; solid. > > The humoral and consistent parts of the body. --Harvey. > > **2. Having agreement with itself or with something else; having harmony among its parts; possesing unity; accordant; harmonious; congruous; compatible; uniform; not contradictory.** Remind me again how consistency permits contradiction. [shakes head] **ultrafilter** ’s “consistency” is not consistent. If that word is the name given to a particular concept in a particular branch of mathematics, that’s just peachy keen – _but that is not what I am talking about_. A system is consistent when it cannot prove both a statement and its negation. Allowing contradiction means the system is not consistent. Do you understand? ---
**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:** [May 1, 2003, 9:49pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/320 "2003-05-01T21:49:01Z")
I understand that you are not now nor have you ever been talking about GIT. I understand that from all appearances you are fundamentally incapable of considering a problem rigorously. I understand that you still have not learned what even your **“invisible experts[sup]Tm[/sup]”** told you: precision in language is important when discussing the implications of formal theorems. I understand that you will probably never understand GIT. [Previous page](https://boards.straightdope.com/t/spiritus-mundi/171273.md?page=15) [Next page](https://boards.straightdope.com/t/spiritus-mundi/171273.md?page=17)