# 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:** 12
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [April 28, 2003, 3:09pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/221 "2003-04-28T15:09:22Z")
I also think that GEB is a bit of a dangerous book. After reading it, you don’t know that much: you’ve just been subjected to a lot of general ideas with no specifics. The subjects broached are very interesting. **TVAA** , if you want to learn the specifics, there are a couple books that I recommend wholeheartedly. They are Michael Sipser’s _Introduction to the Theory of Computation_ and Elliot Mendelson’s _Introduction to Mathematical Logic_…well, I know I got the last names right, and the titles are very close to correct. I’d recommend that you start with Sipser, as his book places more emphasis on being clear. There’s no lack of rigor, though. Mendelson’s book is very rigorous and not terribly clear, but it’s got a lot of good information. Unfortunately, neither is terribly cheap, so you may want to see if you can find used copies. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 28, 2003, 3:09pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/222 "2003-04-28T15:09:46Z")
> [@](#): > > \*Originally posted by erislover \* > \*\*I think your personal lack of rigor is forbidding you from seeing that his statements, when properly qualified, are correct. \*\* As far as I can determine, when his statements are interpreted according to his own words about them at the time and the surrounding context of the discussion, they’re wrong. There’s a reason he complained so much about my refusal to use specific mathematical languages to talk about this debate – he can’t handle the concepts otherwise. And since he repeatedly complained about my lack of rigor, his falling into error _because_ of a lack of rigor is especially damning. > [@](#): > > **We’ve got people quite skilled in mathematics on this board and there has been nothing but a minor quibble on a quite irrelevant tangent against him, except for from you.** It is unfortunately the case that many individuals skilled in mathematics are unable to discuss their knowledge except in mathematical terms. And it’s not merely from me – it’s from me _on this particular topic_. Before I noticed the significant lack of comprehension and excess of erroneousness in this debate, I regarded **Spiritus Mundi** as being one of the more rational and intelligent members of these boards. I now realize that – like some others I could mention – he does a better job of simulating intelligence than of actually manifesting it. People whose intelligence and knowledge on the subjects discussed here cannot be seriously questioned by myself have reviewed the two threads in question, and they’ve repeatedly told me that **Spiritus** does not in fact know what he’s talking about. He is not able to use words according to their definitions to transmit and receive meaning. I know that this will not convince you; it’s not intended to convince you. Whatever doubt I may have about my own judgment, I am unable to ignore the conclusions of those I know understand the issues being discussed. > [@](#): > > \*\*And I am not going to play super-knowledge guy here—I’m honestly out of my league, and found that out to my dismay in my own thread on this very topic—but knowing **Spiritus** as I do, and what I recall of his background, I think I’m deferring my judgement to him here. KNowing **ultrafilter** as I do, which is much less, but I’ve never found errors in his presentations either. Of course, again, I’m really not in the position to judge on this topic, but if you ask me, the anwer is no: I didn’t notice errors. \*\* [sigh] Your conclusions are your right and your own business. > [@](#): > > **This is, of course, not meant to be a character attack on you, but from what I’ve read here and what I gleaned from external sources I think GIT is the Quantum Mysticism of the mathematical world. I think GEB reached, a lot, and I say this with a lot of respect for Hofstader (if for no other reason than by association with another “reacher” I respect: Dennett). I’ve read some presentations on incompleteness and UTMs, and how the ITs can be formulated there and so on. And while the subject is interesting, I’ve not felt particularly compelled or motivated by any presentations of it.** Fair enough. > [@](#): > > \*\*My problem remains with your—shall we say—equivocation between abstract axiomatic structure and manifested reality. > > If the universe **is** a UTM then where does it get its input? That goes against the definition of the universe as “everything”, doesn’t it? \*\* Who said the universe is a UTM? The UTMs are merely a special case, but they demonstrate an important point: there is no fundamental difference between computer and program. They’re both informational “structures”, just on different levels of reality. If **Spiritus** ’ claim had been correct, it wouldn’t be possible for UTMs to simulate any other UTM; since we know mathematically that they can, there is a known exception to his statement and it is therefore incorrect. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 28, 2003, 3:22pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/223 "2003-04-28T15:22:21Z")
> [@](#): > > \*Originally posted by ultrafilter \* > **Yes, bring your experts here. I’d love to have a chat with them.** As I mentioned, I’m working on it. It is difficult – not only do they have more important things to do than I do (and hence can’t “waste their time reading messageboards”), they generally don’t bother wasting time trying to convince people of things. They reviewed the threads and gave me feedback only as a personal favor to me – and one expressly refused to comment on the boards, even though he said I was correct, because he found my tone throughout to be troublesome. (He has a much higher tolerance for idiots than I do.) > [@](#): > > \*\*I do think you’re intellectually dishonest, and that you have not provided any support for your any of your statements. \*\* :dubious: I can only conclude that we have vastly different standards for “support”. > [@](#): > > **1. You give precise definitions for any term, and use the term only in that manner. Furthermore, you give precise statements that are completely unambiguous.** I’ve been using the standard meanings… and ambiguity is in the eye of the beholder. I _could_ try again, I suppose… > [@](#): > > **2. You make every step explicit. No “this is trivial/obvious/easy/simple”. If it’s that easy, it shouldn’t be hard for you to write it.** [sigh] This is going to take a while. > [@](#): > > \*\*Let’s start with something very simple. I have a Turing machine that accepts all input. Bearing in mind that this machine does not have a physical realization–it exists only in the mind–how do you propose that we crash it? \*\* This is classic, and trivial. Give it a set of input equivalent to the problem “determine the truth value of the statement 'this statement cannot be proven by this TM”. It can’t generate a counter-proof. It can’t generate a proof. And no matter how many steps of computation it carries out, it will never reach any conclusion that will allow it to stop. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [April 28, 2003, 3:27pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/224 "2003-04-28T15:27:40Z")
> [@](#): > > \*Originally posted by TVAA \* > \*\*It can’t generate a counter-proof. It can’t generate a proof. And no matter how many steps of computation it carries out, it will never reach any conclusion that will allow it to stop. \*\* What are you talking about? This Turing machine just looks at its input and moves to an accept state no matter what the input is. What do proofs have to do with anything? ---
**Author:** ![erislover](https://avatars.discourse-cdn.com/v4/letter/e/71e660/32.png) [@erislover](https://boards.straightdope.com/u/erislover)\ **Post date:** [April 28, 2003, 3:53pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/225 "2003-04-28T15:53:23Z")
> [@](#): > > \*Originally posted by TVAA \* > There’s a reason he complained so much about my refusal to use specific mathematical languages to talk about this debate – he can’t handle the concepts otherwise. I disagree **strongly** here. He, frankly, will bend over backwards to adopt to someone’s use of terms. But we’re talking about a _specific_ set of concepts here. That, frankly, requires some specificity. You’ve failed to provide that. > [@](#): > > And since he repeatedly complained about my lack of rigor, his falling into error _because_ of a lack of rigor is especially damning. He’s damned if he does and damned if he doesn’t against you. If he demands and uses rigor, he’s an idiot savant who can’t understand things except in narrow contexts. If he doesn’t use rigor, he’s a hypocrite. Nice tautology you’ve got there: **Spiritus is an ass** is true in all cases. Unimpressive logically. Upsetting personally. > [@](#): > > It is unfortunately the case that many individuals skilled in mathematics are unable to discuss their knowledge except in mathematical terms. **They are mathematical concepts**! You think that mathematics and physics uses rigid symbology to make paragraphs shorter?! The English word “force” is not physic’s “F” in all cases. The symbol “F” called “force” in physics is a highly specialized and more-or-less well defined concept. It is of course no coincidence that we call “F” “force” when we speak of it. That does not mean **F** == “force[sub]English[/sub]” ! You want your talk to have all the strength of GIT with none of the development. And who, exactly, did you suppose it would convince like that? > [@](#): > > Before I noticed the significant lack of comprehension and excess of erroneousness in this debate, I regarded **Spiritus Mundi** as being one of the more rational and intelligent members of these boards. I now realize that – like some others I could mention – he does a better job of simulating intelligence than of actually manifesting it. While I am sure this is possible, and while I don’t doubt the content or character of your impressions, I do disagree. > [@](#): > > He is not able to use words according to their definitions to transmit and receive meaning. I’m afraid you’ll have to let that, and that alone, let you rest easier, because on that account you have also failed to present a compelling case. Sorry, man. Hopefully your distaste doesn’t translate over my way, but ::shrug:: we all just say what we mean the best we can. > [@](#): > > The UTMs are merely a special case, but they demonstrate an important point: there is no fundamental difference between computer and program. They’re both informational “structures”, just on different levels of reality. And being on different levels of reality does not invalidate the claim “there is no fundamental difference between them”? Fascinating. > [@](#): > > If **Spiritus** ’ claim had been correct, it wouldn’t be possible for UTMs to simulate any other UTM; since we know mathematically that they can, there is a known exception to his statement and it is therefore incorrect. Kenneth Branagh is not me. He never will be. There is a reason why the word **simulation** is not an indicator of existential equality/identity. ---
**Author:** ![g8rguy](https://avatars.discourse-cdn.com/v4/letter/g/7cd45c/32.png) [@g8rguy](https://boards.straightdope.com/u/g8rguy)\ **Post date:** [April 28, 2003, 4:11pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/226 "2003-04-28T16:11:36Z")
> [@](#): > > \*Originally posted by TVAA \* > **We’ve been talking about the preconditions for nearly nine pages of this argument, if we include the OT. There’s been no hand-waving… except possibly on the part of Spiritus, who persists in making inaccurate statements about GIT.** I’m sorry, let me clarify then: statements along the lines of “this is trivially obvious to any idiot” are hand-waving, are they not? As **ultrafilter** says, if it’s trivially obvious, it should be trivially explainable. And if it can’t be explained trivially, then it wasn’t trivially obvious in the first place. > [@](#): > > **when you don’t even seem to have a clear idea of what it _is_, no matter how much I try to explain and simplify… well.** I might suggest that if no one seems to have a clear idea what your argument is, that might reflect more upon how you’ve made it then upon the entire rest of the SDMB, no? > [@](#): > > **The technical definitions of “mass”, “acceleration”, and “force” aren’t particularly complicated. Any intelligent high school student can pick them up in a single afternoon (heck, any intelligent 4th grader should be able to understand them).** See, I don’t know too many fourth graders who grasp the concepts of “gradient,” and “second time derivative.” Perhaps the concepts of “rate of change,” or “rate of change of rate of change.” And just out of curiousity: what is the technical definition of “mass,” then? In the larger sense, though, you’ve missed my point completely. Which probably shouldn’t surprise me, as every time we actually try to engage each other in conversation, this happens, presumably on both our parts. It doesn’t matter that **F** =m **a** is simple enough for a reasonably bright high school student to grasp in some modicum of technicality. It does, however, matter that the technicality _is there_, in this as in, say, quantum field theory, and plain language variants of technical concepts must first be sure that relevant details are not glossed over, lest thine arguments be thrown into confusion. > [@](#): > > \*\*Secondly, what exactly do you mean, O great wise guy of the desert? I don’t recall _F=ma_ being shown to be wrong… It’s not even altered in either form of Relativity. Instead, it’s one of the centerpoints of Newtonian mechanics… which is sufficiently accurate to allow us to send devices millions of miles with only minor deviations for their course. > > Care to explain your wisdom? \*\* Well, if you really must know, **F** = d **p** /dt is the correct form, and is not necessarily equivalent. Note also that in relativity, one must use proper time rather than coordinate time, and the four-momentum, not the three-momentum, so that the best generalization you’re likely to come up with is F[sub][symbol]m[/symbol][/sub]=d/d[symbol]t[/symbol](m d/d[symbol]t[/symbol])x[sub][symbol]m[/symbol][/sub]. I hope that came out right; Greek letters don’t display here. Not that this is relevant, but of course it does illustrate my point, that subtleties ought be understood. ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 28, 2003, 4:59pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/227 "2003-04-28T16:59:35Z")
> [@](#): > > \*Originally posted by ultrafilter \* > \*\*What are you talking about? This Turing machine just looks at its input and moves to an accept state no matter what the input is. What do proofs have to do with anything? \*\* Grrrrr… If your TM does nothing _but_ accept data, its programming shouldn’t be sufficiently powerful for this discussion to apply. The mechanism of the TM (for example, it could be a cellular automata like the Game of Life) still determines what the behavior of the TM it’s simulating is going to be – even if that behavior is as simple (and pointless) of simply moving to an acceptance state. There are possible inputs to the underlying TM mechanism that could disrupt it – in the GoL example, virtually any glider would terminally disrupt the structure. Only a very small number of possible automata structures are “acceptable” input. Almost anything else will change the behavior of the system radically, utterly wiping out the structure that was acting as the TM. Moving from one state to another is informationally equivalent to producing a theorem from a set of axioms. You start with the initial conditions (the axioms) and produce a necessary consequence of those conditions (the theorems). Moving to a state is the same as generating a proof of the statement descibing that state from the statements describing the initial conditions. “Given these conditions, and these operations applied to them, these conditions result.” There are some states that the initial conditions can never generate, because that would be equivalent to generating a proof of a Godel statement of the system. ---
**Author:** ![FranticMad](https://avatars.discourse-cdn.com/v4/letter/f/c68b51/32.png) [@FranticMad](https://boards.straightdope.com/u/FranticMad)\ **Post date:** [April 28, 2003, 5:37pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/228 "2003-04-28T17:37:01Z")
At 5:00 we’ll come over, rip the keyboard from your hands, and then we’re gonna do some buddy-drinkin’ and then we’re gonna get **laid**. Karaoke!! ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [April 28, 2003, 5:43pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/229 "2003-04-28T17:43:26Z")
> [@](#): > > \*Originally posted by TVAA \* > \*\*Grrrrr… > > If your TM does nothing _but_ accept data, its programming shouldn’t be sufficiently powerful for this discussion to apply. > > The mechanism of the TM (for example, it could be a cellular automata like the Game of Life) still determines what the behavior of the TM it’s simulating is going to be – even if that behavior is as simple (and pointless) of simply moving to an acceptance state. > > There are possible inputs to the underlying TM mechanism that could disrupt it – in the GoL example, virtually any glider would terminally disrupt the structure. Only a very small number of possible automata structures are “acceptable” input. Almost anything else will change the behavior of the system radically, utterly wiping out the structure that was acting as the TM. > > Moving from one state to another is informationally equivalent to producing a theorem from a set of axioms. You start with the initial conditions (the axioms) and produce a necessary consequence of those conditions (the theorems). > > Moving to a state is the same as generating a proof of the statement descibing that state from the statements describing the initial conditions. “Given these conditions, and these operations applied to them, these conditions result.” > > There are some states that the initial conditions can never generate, because that would be equivalent to generating a proof of a Godel statement of the system. \*\* You claimed long ago that no computer can be built so that it never crashes. Apparently you only meant Turing-complete computers. That’s fine, but it would’ve been nice if you had said that a long time ago (if you did and I missed it, my apologies). It’s not at all obvious that that’s how we should take “computer” here. So to make this a little more specific, I dug up the [state table](http://www.rdrop.com/~half/General/UTM/UTMStateTable.html) for a UTM. Which state can it never reach? ---
**Author:** ![Ethilrist](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ethilrist/32/4604_2.png) [@Ethilrist](https://boards.straightdope.com/u/Ethilrist)\ **Post date:** [April 28, 2003, 6:07pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/230 "2003-04-28T18:07:38Z")
I’m just trying to reconcile these two statements by **TVAA** – > [@](#): > > I don’t claim to understand math. I understand only a few, relatively basic concepts. > … > GIT in its formal form is extremely complex and requires moderately heavy mathematical knowledge to understand. Sounds like either you don’t understand GIT after all, or you think it’s a relatively basic concept. And this: > [@](#): > > Just take the description of the initial condition and apply the operations that describe the interactions between the things in the system. The resulting statements will describe the new configuration of the system. Is that like writing up a list of things you did this weekend, write “To Do List” at the top, check everything, and say you’ve completed your To Do List? ---
**Author:** ![TVAA](https://avatars.discourse-cdn.com/v4/letter/t/c57346/32.png) [@TVAA](https://boards.straightdope.com/u/TVAA)\ **Post date:** [April 28, 2003, 6:34pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/231 "2003-04-28T18:34:00Z")
Wait a minute – you’re giving me a table that lists the elementary internal states of a Turing machine and then asking me to show you the configuration it can’t reach? I can’t show you the sequence of steps the machine can’t reach by manipulating the elements of that table. That’s the whole point! No, I don’t know the methods for finding a Godel statement for any particular system. **Ethilrist** : GIT _is_ relatively simple to understand; just not in its formal form. It is extremely elegant (or so I’m assured), but if it were simple it wouldn’t be regarded as one of the greatest triumphs in modern mathematics and philosophy. Every mathematician would have thought of it. The basic principles and significance of GIT… those I can understand. ---
**Author:** ![lieu](https://avatars.discourse-cdn.com/v4/letter/l/c2a13f/32.png) [@lieu](https://boards.straightdope.com/u/lieu)\ **Post date:** [April 28, 2003, 6:45pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/232 "2003-04-28T18:45:15Z")
Bwhaaa… I’ve feel like I’ve just been bitch slapped by a pocket protector. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [April 28, 2003, 6:53pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/233 "2003-04-28T18:53:50Z")
**TVAA** would you do me a favor and state every conclusion you’re trying to get us to accept? You may be right about something, but I need to see it in context. ---
**Author:** ![FranticMad](https://avatars.discourse-cdn.com/v4/letter/f/c68b51/32.png) [@FranticMad](https://boards.straightdope.com/u/FranticMad)\ **Post date:** [April 28, 2003, 8:13pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/234 "2003-04-28T20:13:00Z")
> [@](#): > > \*Originally posted by ultrafilter \* > \*\ ***TVAA** would you do me a favor and state every conclusion you’re trying to get us to accept? You may be right about something, but I need to see it in context. \*\* This is my feeling too. I tried, in GD, to envision where you are going. Somewhat clumsily I suggested that your context is anti-non-deterministic (for lack of a better word). Like ultrafilter, I would appreciate a listing of your conclusions. I know this is frustrating for you, but it is pretty common for abstract concepts to be misunderstood by others. You are bridging between a mathematical proof and English, and adding your own comments on top of that. Therefore, it strikes me a being entirely reasonable that most people would have trouble following you. On the other hand it’s about 4:15 pm where I am. Almost time for to put that keyboard down and – **Karaoke** until tomorrow! ---
**Author:** ![Measure\_for\_Measure](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/measure_for_measure/32/557_2.png) [@Measure\_for\_Measure](https://boards.straightdope.com/u/Measure_for_Measure)\ **Post date:** [April 29, 2003, 3:06am UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/235 "2003-04-29T03:06:58Z")
----- flowbark said, “I would assert that when disagreements over the meaning of the original text arise, that it is necessary to evaluate the original source, in its native (mathematical) language.” ------ TVAA replies, “Here is where I’m forced to disagree. If someone claims that elliptical orbits are not the result of an attractive force that varies with the inverse square of distance, we don’t have to go back to Newton’s Principia to resolve the dispute.” Your reply muddies the waters, I fear. If somebody says Newton says thus and so, recourse to Newton’s Principia is necessary to confirm or deny that claim. In contrast, if somebody says that, F[sub]g[/sub]=G\*(m1\*m2)/r[sup]2[/sup], one would not need to pull out any ancient text. One would, however have to 1) define his terms, 2) muster empirical evidence and 3) understand elementary algebra. Furthermore, phrases such as “inverse square” presume a certain level of mathematical knowledge. If you are not familiar with exponents, you really can’t evaluate such a claim. ----- I’ve read lots and lots of standard-English explanations of what GIT is and what it implies. ## Uh, great. But you can’t judge the accuracy of your standard-English explanations of GIT without recourse to the original mathematical argument. (Secondary sources are ok, provided they contain sufficient mathematical rigor, or so I claim). You see, there is the problem of trendiness. If “Potential-energy” was a trendy concept, I could imagine all sorts of plausible applications of it. One could say that somebody with a good night’s sleep has more potential energy than a hypercaffeinated insomniac. Those who are more awake can get more work done, right? Furthermore, I could argue potential energy is directly related to the square of the amount of sleep displaced. Provided I defined my terms and was willing to test them directly, that would even be acceptable, if a little weird. ## But I wouldn’t want to make to much of the connections between “Potential sleep energy” and U=.5kx[sup]2[/sup], as defined in mechanics (kinetics?). Still, you have my sympathies. There are lots of people who have read about Heisenberg’s Uncertainty Principle and rather fewer who have grasped its relationship to frequency distributions. ---
**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, 7:20am UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/236 "2003-04-29T07:20:19Z")
So. How many examples of deceitful posting does it take to make a pattern? 3? 4? 5? EXHIBIT 1: Deliberate repetition of false claims Please note the dates and times in the following sequence of posts, some of them in the GD Godel thread and some of them in this thread. > [@](#): > > **Spiritus: 04-18-2003 04:26 AM** Perhaps here we are hitting a difference of usage, though. You may be thinking of things like the ability to prove that a Peano Axiomatization is consistent by alternate axiomatic sets (such as Gentzen’s transnfinite induction). I can see how that might lead you to say that “The system defined by a P. A. is consistent” would be a statement true in a P. A. that has been proved in an extended (alternate, in this case) axiomatic set. That isn’t really correct, though. > > “The system defined by a P. A. is consistent” has not been proven to be a true statement **within a Peano Axiomatization**. It has been proven true in a different logic altogether. The truth of the statement within a P. A. remains unknown. To illustrate, consider the axiom of choice. It is very easy to extend ZF in order to prove that the axiom of choice holds. But it is also easy to prove the converse. Obviously, we cannot take either proof as a demonstration that the axiom of choice is or is not true in ZF > > \*\*Spiritus: 04-18-2003 09:52 AM \*\* [ul][li]We both agree that the implication of GIT is that no proof within a P. A. can exist for all true statements in a P. A. That is where GIT ends.[/li][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] > **TVAA: 04-18-2003 10:58 AM** Ah, I see the problem. I’m not talking about the ways to prove within the PA that the statement is true. I’m talking about the ways to prove that the statement is true within a PA. > > **TVAA: 04-26-2003 03:07 AM** **SM** , among other stupid claims, insists that GIT merely demonstrates that there are some things that can’t be proven ever. . . This is just plain dumb. . . If you add extra axioms to the system, it may be possible to prove a formerly unprovable statement, but there will then be new statements that can’t be proven. > > **Spiritus: 04-26-2003 04:08 AM** My actual claim as that GIT implies that certain statements cannot be proven to be true in a Peano Axiomatization. You can prove those statements by using extended (or simply different) sets of axioms, but that does not imply that the truth holds in the Peano Axiomatization. Our confidence in that conclusion can only be as great as our confidence in the new axiom set. I even provided an illustration by referencing the axiom of choice and ZF set theory. Perhaps you can get one of your invisible experts in mathematics to explain the reference for you. > > **TVAA: 04-26-2003 01:40 PM** Read this, you moron. As it points out, GIT applies for any set of axioms that are at least as strong as Peano’s. The extended or alternate set of axioms may be able to prove the formerly unprovable statements, but there will then be NEW unprovable statements to contend with. > > **Spiritus: 04-26-2003 05:07 PM** **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. > > **TVAA: 04-26-2003 05:48 PM** **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.” > > **Spiritus: 04-27-2003 12:45 AM** _[I quote the GD post of (04-18-2003 09:52 AM) and the PIT post of (04-26-2003 05:07 PM), both of which show clearly that I am not saying that statements cannot be proved in an extended axiom system]_ Yet **TVAA** continues to spew shit about “ **Spiritus** says there is no proof. He’s an idiot.” > > **TVAA: 04-28-2003 10:08 AM** (After **Erl** posted, _”I still don’t see where you’ve pointed out any errors of Spiritus’s._”) You didn’t see that he couldn’t tell the difference between showing that something is true in (with) a system and showing that something is true in (about) a system? So you keep repeating the same dishonest claim more than a week after acknowledging that our disagreement had to do with the proper application of the word “proof” to demonstrations in extended logical systems. This has nothing to do with understanding GIT. Q.E.D. EXHIBIT 2: Hypocritical aplication of a double standard **TVAA** has taken great glee in screaming that I must be ignorant about GIT because after 7 pages of discussion about GIT I neglected to specify that a system must be meet specific requirements in order for GIT to reply. What I said was: [ul][li] Here’s another point that you don’t understand: a system cannot be proven to be consistent from within itself. That is GIT[sup]2[/sup]. Thus, you can never demonstrate your claim that the Universe itself is a consistent axiomatic system.[/ul][/li] **TVAA** has taken great relish in slamming me for not supplying the habitual specification upon when GIT[sup]1 or 2[/sup] applies. He calls me stupid for omitting it, and goes on to argue that this omission means that I obviously do not understand the theory. But let’s take a look at how **TVAA** himself introduced GIT in his GD thread > [@](#): > > \*\*TVAA: \*\*Anything that can be accurately described by a formal mathematical system is subject to the Incompleteness Theorem. > > \*\*TVAA: \*\*(After **Orbifold** corrects the mistake above) You’re quite correct; I meant to include that, but forgot. Strangely enough, he doesn’t immediately declare himself stupid and conclude that he obviouslt knows nothign about GIT. How interesting. Q.E.D. EXHIBIT 3: Deliberate distortion of another poster’s position (with an added dash of hypocricy.) **TVAA** has berated me for demanding that all discussions of GIT be held in a formal symbolic language. His most recent repetition of that claim was: > [@](#): > > There’s a reason he complained so much about my refusal to use specific mathematical languages to talk about this debate – he can’t handle the concepts otherwise. Of course, I have never demanded any such thing. The disagreement that we have had over language begins on page 3 of the GD thread. There, in a part of our discussion relating to computers and computer theory, I question his use of the words “model” and “complexity”. Because the “model” discussion dragged on a _very_ long time, I’ll just repost the “complexity” exchange here. Anyone interested can follow **TVAA’s** twisting of the word “model” in the other thread. > [@](#): > > \*\*Spiritus: \*\* As a side issue: are you actually intending to argue that complexity is a measure of the number of elements in a system? > > \*\*TVAA: \*\* If by “elements” you mean relationships, yes. The number of realtionships within the system determine how much information it contains. > > \*\*Spiritus: \*\* This strikes me as an odd usage of “complexity”. It certainly is at odds with the standard complexity theory in computer science, which would seem to be the appropriate context from which to discuss complexity in the game of life (and in TMs [or non-deterministic computers] in general). > > \*\*TVAA: \*\* It’s a mathematical fact [that one level of the game “life” is more complex than another.] . . . No – it has everything to do with both [complexity in the math/computer sci use of the term and GIT]. > > \*\*Spiritus: \*\* Complexity theory in computer science addresses the resources required to solve a problem. It has nothing to do with how much information is contained within a system. The standard notation for his is the big O notation. Life and “meta life” have identical complexity under standard usage. > > \*\*TVAA: \*\* Incorrect. There are always ways to make the computation more complex – if complexity were merely the resources required to solve a problem, it would be undefined, as any solution implies the existence of a more complex solution with unnecessary steps. Complexity theory concerns itself with the minimum required resources to solve a problem, and this is directly concerned with the amount of information contained within the system. > > \*\*Spiritus: \*\* No, it is not. In mathematics, as in computer science, complexity has a specific meaning. You are using the term improperly. Did you even bother to follow the link I provided? An order N algorithm with 2 pieces of input has exactly the same complexity as an order N algorithm with 2 million pieces of input. It serves no useful purpose for you to misuse terminology and then make pronouncements of fact based upon your variant meanings for words. > > \*\*TVAA: \*\* you claim that the meta-grid that can be constructed with the standard grid of Life is as complex as the grid itself. This is not only incorrect, it’s **stupid**. However many resources are necessary to simulate a basic square, the resources for a meta-square are necessarily greater . . . The words I’m using all have well-defined meanings in standard English. If you can’t handle that, get off the boards. I’m quite serious – if you can’t rationally consider arguments made in everyday language, you have no place on boards where the arguments are presented in that format. > . > . > . > Complexity: the amount of data required to perfectly define a system. This is a greatly condensed version of the general language definition of “complex”. > > \*\*Spiritus: \*\* You have a theorem in mathematics and a construct of computer science. If you want to draw meaningful conclusions from those things it is a good idea to use the terminology appropriate to those fields. For instance, the “common everyday meaning” of “complexity” is of absolutely no use in showing that set of elements that model a system is necessarily bound by the limitations of the system being modeled. There is no hard connection between those two concepts, and saying “complexity” does not draw a line of either mathematical or logical implication. > . > . > . > I have shown that your statements are untrue using the terminology appropriate to the field. You say that you have no interest in using appropriate terminology. > > Okay, then the onus is very much upon you to draw the lines **in specific detail**. The reason that fields of stufy develop specialized usage is so that many things can be communicated subtextually. Since you reject the conventions appropriate to your subject, you don’t have access to any such contextual information. Personally, it seems a silly choice on your part, but if that’s the way you want to proceed then it is certainly your right to do so. > > \*\*TVAA: \*\* You’re being stupid because you’re acting as if I’m using it, then claiming that my statements are wrong because they’re inconsistent with the terminology. Okay. so what do we see here: [ol][li]At no time did I demand that GIT be discussed only in formal mathematical language.[/li][li]I did assume, upon seeing terms like “complexity” in a discussion about computer theory that the terms were being used to descrive the recognized concepts of computer theory. [/li][li] **TVAA** _initially_ claimed that his usage was in accord with the definition of “complexity” in computer theory.[/li][li] **TVAA** then changed tactics and declared that he was not using “complexity” in a manner consistent with the context of computer theory. And, of course, I was stupid for thinking that he was.[/li][li]Even then, I did not demand that he use the terminology appropriate to the field, I simply asked him to explicitely and clearly define his terms.[/li][li]Which got me called stupid again.[/ol][/li]And now for the dash of irony. Consider this exchange: > [@](#): > > **TVAA** Obviously natural-language formulations of mathematical concepts aren’t valid. “Force equals mass times acceleration” isn’t at all the same as F=ma, is it? > > **g8rguy** This example also illustrates, however, the problem with using common language for mathematical concepts. Because, ignoring the fact that the equation isn’t even true (which was obvious to someone of your vast intellect), it’s not useful until you’ve defined “force,” “mass,” and “acceleration.” Which was obvious to someone of your vast intellect. Each of these things, of course, has a specific technical definition, which is why we use equations to communicate in technical fields to begin with: one doesn’t lose the technical definitions with equations the way one might with everyday English reformulations of the same concepts. > > **TVAA** The technical definitions of “mass”, “acceleration”, and “force” aren’t particularly complicated. Any intelligent high school student can pick them up in a single afternoon (heck, any intelligent 4th grader should be able to understand them). Notice: [ul][li] **TVAA** doesn’t say it is stupid to expect the terms to be used in their technically specific sense (else it would destroy his little example).[/li][li] **TVAA** doesn’t rant and rage that only someone who didn’t understand physics would expect the terms to be used in their technically specific sense.[/li][li] **TVAA** , in fact, appears to very much support the idea that it is not too much to ask that someone use terms in their technically specific sense when discussing ideas in a specific context.[/ul][/li] Q.E.D. ---
**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, 7:24am UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/237 "2003-04-29T07:24:22Z")
EXHIBIT 4: Equivocation in argument: changing the charges as evidence shifts **TVAA** and I have been round a bit on whether GIT deals with the truth or falsehood of statements. Witness the exchange: > [@](#): > > \*\*Spiritus: \*\* 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**. > > \*\*TVAA: \*\* 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 . . . 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. > > \*\*Spiritus: \*\* 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. > > \*\*TVAA: \*\* 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. > > \*\*Spiritus: \*\* 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. . . [I then point out the note from the very cite he offered] 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. > > \*\*TVAA: \*\* 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 > . > . > . > 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. > . > . > . > 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. So we see that: [ul][li]I initially pointed out that “truth” was not really required by GIT but is often used as a gloss by people sriting about GIT in natural language. GIT is, in fact, entirely mute on the cubject of truth, caring only about consistency and completeness. [/li][li] **TVAA** disagreed, saying that GIT specifically required that some unproveable statements be true.[/li][li] **TVAA** posted a cite to back up his claim.[/li][li]I showed that the cite actually specifically refuted his claim in a note.[/ul][/li]Now, some might think that this would inspire **TVAA** to acknowledge that my initial statement was correct. But such folks fail to recon with the power of cognitive dossonance personified. It cannot be possible that my statement was correct, because then it would weaken his vehement belief that I am an idiot who doesn’t know what I am talking about. Thus . . . **TVAA** shifts tactics and says that he knew all along that GIT did not require some unproveable statements to be true, but that I was misusing, “soundness”. (I will address the factual claim later. It is unrelated to this exhibit of **TVAA’s** dishonesty in argument.) Q.E.D. EXHIBIT 5: Repeated offensive claims offered without substantiation I’ll keep this one short. This is **TVAA** on a very simple issue of fact: > [@](#): > > \*\*Spiritus: \*\*[after posting the full exchange of posts about a truly trivial issue] 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. > > \*\*TVAA: \*\* 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. > > \*\*Spiritus: \*\*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. > > \*\*TVAA: \*\* I’ve already done that. Pay attention, dolt. Now, his claim here is plain: **he has already posted something that specifically cites a passage of mine that introduces symbology into our debate.** Of course, he doesn’t deign to post it again, even though it would be an easy way to demonstrate that I actually amm in error. No, he simply says: **I already did it** and caps it with an insult. Why not simply quote the relevant post? I think we can all figure out why. Q.E.D. Questions of fact Just a couple, since this is too long already. > [@](#): > > Hey, **Spiritus** , remember a few weeks ago when you said GIT says nothing about the nature of the universe but only something about human conceptualizations of it? > > Why are you now saying (correctly) that the universe’s consistency cannot be proven within itself? > > Putz. [ol][li]Because whether or not consistency can be proved does not change the nature of the Universe.[/li][li]Because I am not even saying that the consistency cannot be proved within the Universe. I am saying that it cannot be proved _ **IF** _ the Universe is a deductive system powerful enough to invoke GIT. [/li][li]:wally[/ol][/li] > [@](#): > > You’ve repeatedly said that truth is related to soundness. This is backwards: soundness is related to truth. I could have chosen any number of others, but the basic assertion is that I am misusing soundness because something can be true but not proveable. Well, in the general sense you are absolutely correct that somethign can be true but not proveable. What that means for a statement in a deductive system, though, is that there is an external, non-deductive model to which the system maps and the isomorphic partner for the statement is present in the model. Absent the correspondence with such a model (and I use the term here in the symbolic logic sense, not in the **TVAA** sense), the only way to demonstrate truth is through deduction from sound axioms. Think about that for a second, and recall that this entire argument about “truth” and “soundness” took place within the very specific context of how one could sat that something is true “in a Peano Axiomatization.” So, if you can tell me what serves as an external, non-deductive model for a Peano Axiomatization, then I might have to change my mind and agree with you that a statement can be erifiably true “in a Peano axiomatization” without being proveable “in a Peano Axiomatization”. Until then, I stand by my statements that in the precise context that we are discussing, there is no non-deductive external model from which to infer truth, so the only statements that can be properly called “true within the system” are those which can be proven within the system. “Statements can be true without being proveable” is certainly true of many systems to which GIT applies, but it is not true of all systems to which GIT applies. GIT is a very fundamental theorem. It applies to many, many systems–not just those for which an external model of truth exists. \*\*Now, having said that, I have no intention of engaging in any further discussion of GIT with you. I will address the examples I gave above of your dishonesty and deceitfulness, since I think it is unfair to level charges without being prepared to support them. But the pattern of those examples is clear: you lack either the intention or the capability to debate with me honestly. You may continue to hurl invectives and level false charges as you wish, but do so only for masturbatory self-gratification. I am through dignifying them with responses. As I said before: Your esteem was worhtless then. Your contempt is insignificant now. You lack the integrity to make either a concern.\*\* ---
**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, 12:46pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/238 "2003-04-29T12:46:20Z")
Oh, brother. **Spiritus** picks up a misconception, forces me to beat it to death over several pages, and then claims I’m changing my argument when I cease referencing his inanities? 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… ---
**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, 1:04pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/239 "2003-04-29T13:04:07Z")
And for the last time, we don’t even need to use a PA, only an axiomatic system at least as powerful as PA! > [@](#): > > \*\*So, if you can tell me what serves as an external, non-deductive model for a Peano Axiomatization, then I might have to change my mind and agree with you that a statement can be erifiably true “in a Peano axiomatization” without being proveable “in a Peano Axiomatization”. \*\* Oi. Remember[this site](http://www.math.hawaii.edu/~dale/godel/godel.html#FirstIncompleteness) ? Where it’s shown that a general Godel statement is true in a proof by contradiction? Where it’s clearly stated that the statement is true in the theory but cannot be proven (shown to be true) within the theory? If you want the statement to be “verifiably” true, then you’re demanding a proof of its truth. But we’ve already established that there can be no proof of **G** within the system we’re discussing… so to verify the statement, we’ll have to use a different set of axioms (or extend the ones we have) to do so, which is just what that site does. Thus, another system can show that the statement is true within the first system, but there can be no such demonstration using only the first system. It’s true within the system without being provable within the system. Do you understand _now_, or do I have to explain this yet again and in even simpler language? ---
**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, 1:23pm UTC](https://boards.straightdope.com/t/spiritus-mundi/171273/240 "2003-04-29T13:23:45Z")
> [@](#): > > And for the last time, we don’t even need to use a PA, only an axiomatic system at least as powerful as PA! You say this like it was in dispute. [Previous page](https://boards.straightdope.com/t/spiritus-mundi/171273.md?page=11) [Next page](https://boards.straightdope.com/t/spiritus-mundi/171273.md?page=13)