# 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:** 13
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 29, 2003, 1:36pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/241 "2003-04-29T13:36:30Z")
**Spiritus** seems to think so. At least, instead of discussing “sufficiently powerful” systems long after we’ve established what “sufficiently powerful” means, he keeps referring to a specific axiomatic system instead. I realize that showing something is true in the most basic axiomatic system we’re discussing shows it in all of them… But he’s ignoring a principle that’s been demonstrated by mathematicians far more competent than either of us. I’ve shown examples where a statement can be proven true relative to a system yet unprovable in that system. That’s all I need to do to show that’s possible. The important point is that truth does not depend on provability… yet **Spiritus** doesn’t seem to grasp this. All things that are provable within a consistent system are true, but not all true things are provable. That point _is_ is dispute… or at least, **SM** keeps disputing it. ---
**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\ **Post date:** [April 29, 2003, 2:41pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/242 "2003-04-29T14:41:14Z")
> [@](#): > > I realize that showing something is true in the most basic axiomatic system we’re discussing shows it in all of them… Really? ---
**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\ **Post date:** [April 29, 2003, 2:45pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/243 "2003-04-29T14:45:03Z")
> [@](#): > > The important point is that truth does not depend on provability… yet Spiritus doesn’t seem to grasp this. I’m sorry but you must completely ignore everything he posts if you think so. For ease of speech in terms of the topic I recall him hypothesizing the soundness of the axioms in a sidenote to **ultrafilter** , in which case, as you say, all provable things are true, but not all true things are provable, in a sufficiently powerful system. He emphasized, repeatedly, and pointed out to you very early on in fact, that GIT was completely unconcerned with soundness. Why are you continuing to do this? ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 29, 2003, 4:13pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/244 "2003-04-29T16:13:06Z")
He was the one who _brought_ up soundness. **Spiritus Mundi** continues to dispute the idea that a statement can be true within a PA without being demonstrable. I’ve pointed out that mathematicians know this is true in general… but the demands keep coming. If he does understand, why does he keep asking? If he doesn’t understand, why isn’t that enough reason to continue? ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 29, 2003, 4:21pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/245 "2003-04-29T16:21:32Z")
Just to make this completely clear: **SM** is talking about _maybe_ accepting a statement that is precisely what was proven by Godel. GIT shows that soundness has inherent limitations; people once imagined that everything that was true might be sound. GIT demolished that hope. Why is it relevant? Because **SM** brought it up, and because we can’t argue about what GIT implies until we’ve established what GIT says. Does anyone wish to continue? I’d like to get back to insulting **Spiritus** if you don’t mind… ---
**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\ **Post date:** [April 29, 2003, 4:24pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/246 "2003-04-29T16:24:33Z")
Your OP said this: > [@](#): > > It does mean that no finite system can ever derive all **truths**. No computer can be made that cannot be crashed. Mathematics is necessarily incomplete: there will always be **“true”** statements that cannot be proven within a given system. Emphasis added. Who brought up soundness? ---
**Author:** ![Diane](https://avatars.discourse-cdn.com/v4/letter/d/2acd7d/32.png) [@Diane](https://boards.straightdope.com/u/Diane)\ **Post date:** [April 29, 2003, 4:26pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/247 "2003-04-29T16:26:31Z")
I think you broke my brain. Happy now? ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 29, 2003, 4:37pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/248 "2003-04-29T16:37:54Z")
**SM** did. I’m fairly certain he was the first to use the word. My OP just states the consequences of GIT… and, as you’ve pointed out, GIT doesn’t change or contradict the definition of soundness one bit. I could check to make sure that **SM** first brought up the issue of soundness, but I don’t think it’s worth the effort at this point. Sorry, Diane. ---
**Author:** ![FranticMad](https://avatars.discourse-cdn.com/v4/letter/f/c68b51/32.png) [@FranticMad](https://boards.straightdope.com/u/FranticMad)\ **Post date:** [April 29, 2003, 4:45pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/249 "2003-04-29T16:45:02Z")
> [@](#): > > \*Originally posted by TVAA \* > Remarkably, for all that **Spiritus** claims to be well-educated in the fields of mathematical logic and computer science, he missed the obvious weakness in my argument – one place that he might actually be able to mount a successful attack against. > > Will he notice it, folks? Only time will tell. Let’s watch… I think you should just say what the weakness in your argument is. That way, you will either demonstrate that **Spiritus** missed it, and that he is incompetent at mathematics. Or he will be forced to prove you were wrong about the weakness in your argument, and therefore end up supporting your original position. Either way, you can’t lose. Otherwise, keep the truth a secret if you like – and this whole thread will be nothing more than a waving of prosthetic dick implants to show who’s is bigger. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 29, 2003, 5:02pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/250 "2003-04-29T17:02:13Z")
He neglected to pick up on the point that it’s not the case for every type of system that a contradiction leads to all possible statements becoming valid. That was one of the first things my sources noticed and complained about… Oh yeah, **Spiritus** is an expert on mathematical logic, all right… ---
**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 29, 2003, 9:01pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/251 "2003-04-29T21:01:14Z")
> [@](#): > > **Spiritus Mundi: 04-27-2003 12:19 AM** > 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.) You’re an idiot. ---
**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 29, 2003, 9:07pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/252 "2003-04-29T21:07:11Z")
Great time for a thread wrap. :rolleyes: The above was in response to **TVAA** posting" > [@](#): > > He neglected to pick up on the point that it’s not the case for every type of system that a contradiction leads to all possible statements becoming valid. > > That was one of the first things my sources noticed and complained about… > > Oh yeah, Spiritus is an expert on mathematical logic, all right… ---
**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:** [April 29, 2003, 10:18pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/253 "2003-04-29T22:18:30Z")
Well, I just read the first three pages and thought, to begin with, **TVVA** was parodying Legomancer’s ‘Ask the Dalek’ thread. But then I realised **TVVA** is actually the Iraqi Information Minister with a new gig; Hi dude, how’s the beret ? You folks sure were a little slow on the uptake there … ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 29, 2003, 10:28pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/254 "2003-04-29T22:28:59Z")
It’s “TV **A** A”, first of all. Speaking of slow on the uptake… And do you actually have any understanding of what we’re talking about? If you can logically support either side with a reasoned argument, you’re more than welcome to do so… but otherwise, kindly shut your pie hole. ---
**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 29, 2003, 10:36pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/255 "2003-04-29T22:36:18Z")
From wikpedia > [@](#): > > Here, the word “true” has been used naively, assuming that every statement about natural numbers is either true or false in an absolute sense, independent of our feeble axiomatization attempts. While Gödel would have agreed, modern logicians do not use this notion of “truth” since it is notoriously hard to define. > . > . > . > Note that, if the axiomatic system is consistent, Gödel’s proof shows that p (and its negation) cannot be proven in the system. Therefore it can be argued that p is “true” in some sense: after all, p claims not to be provable, and it isn’t. Gödel himself adopted this interpretation: he believed the Peano axioms to be consistent and for him, p was a true statement about natural numbers that could not be proven from those axioms. Nowadays, mathematical logicians often prefer to avoid speaking about truth altogether. Perhaps you should run that one by your “invisible experts” and your collection of common language discussion of GIT. ---
**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:** [April 29, 2003, 10:41pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/256 "2003-04-29T22:41:11Z")
Hey, I’m with you dude. God will roast their stomachs in hell at the hands of Godel’s Incompleteness Theorem ! ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 29, 2003, 10:45pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/257 "2003-04-29T22:45:50Z")
The encyclopedia didn’t say the position was wrong, they said mathematicians tended to avoid it because it was difficult. Much the same way you’ve dealt this my position throughout this argument… ---
**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:** [April 29, 2003, 10:51pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/258 "2003-04-29T22:51:03Z")
Do not fear, **TVAA** (did I get that right ?), we will placed them in a quagmire from which they can never emerge … except dead! ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 29, 2003, 10:53pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/259 "2003-04-29T22:53:49Z")
I rather enjoyed the more creative insults that were thrown about in the earlier portion of this thread, but they’re starting to lose their savor. And in any case, **Spiritus** , we can’t rule out the possibility that we could show it to be true in regard to the original axioms set by adding more axioms. I believe I’ve linked an example earlier where this is demonstrated? But of course you won’t actually _refute_ that example. You’ll probably just call me an idiot again. ---
**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:** [April 29, 2003, 11:07pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/260 "2003-04-29T23:07:28Z")
NO ! We do have savor. We have very much savor. It is **Spiritus Mundi** who has none because he is a liar and an infidel. I will show you he is a lying dog, not a lying down dog. IN ONE HOUR! [Previous page](https://boards.straightdope.com/t/spiritus-mundi/171273.md?page=12) [Next page](https://boards.straightdope.com/t/spiritus-mundi/171273.md?page=14)