** Could you point out where I paraphrased when I said I was quoting?
That’d be great…
** We’re talking about whether computers are subject to GIT. Their behavior shows that they’re sufficiently powerful. Their underlying description is consistent, or else they wouldn’t exist in a fundamental way – therefore, GIT applies.
Are you going to actually respond to this argument?
**
The laws underlying computers, and the entire physical world, are necessarily consistent – we wouldn’t exist otherwise. The real question is whether the Tao is consistent. I have no idea.
** No. What changed is that you stopped demonstrating rationality and intelligence in your posts.
I’m always willing to correct my initial impressions of people.
[sigh] Y’know, The Great Unwashed, there was a reason I didn’t bother to respond to your question the first time.
The record player’s behavior must be consistent, or it couldn’t be said to “play” the records. The record player’s behavior is admittedly complex enough to generate arithmetic – its actions are consistent with them. Ergo…
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.
Now, here’s an interesting point: inconsistent systems can allow anything to be proven. What if the most basic level of reality is like Borges’ library, containing all possible statements? It would therefore include all possible groupings of those statements, consistent and inconsistent alike. Our universe could coexist with a multitude of other consistent universes and hordes of inconsistent “things”…
What you don’t seem to grasp, Spiritus, is that there are things that do not exist in the universe.
How do you intend to demonstrate the universe is consistent?
Contrariwise, how do you intend to demonstrate the universe is complete?
As an actor, Kenneth Branagh can imitate me, he can exhibit characteristic similarities in mannerisms, choice of words, inflection, and given enough time probably even my appearance (he’d have to put on a few pounds though :p). Thus, by what I could sort from your ideas on the verb “model”, he can model me. I can solve first order linear differential equations: can he? I cannot recall Hamlet’s “bool theQuestion=(2b||!2B)” speech line by line: can he? In short, in what way are you justified in saying that my limitations necessarily imply anything about him? And in what way do his limitations necessarily reflect on me?
TVAA, thanks for bailing me out in the sticky thread here.
I had a nice post for this thread all typed out and stuff, and then the hamsters ate it.
While I can roughly follow the argument, my days of Computational theory and reading and thinking about GEB and GIT are a long time ago. I find it hard to pinpoint the exact disagreement. And I’m sorry to see that GD’ers whom I respect (if not always agree with are vehemently taking it out on each other.
It looks as if people agree on GIT meaning that for every consistent axiomatic system there is at least one statement that cannot be proven true or false in it. The debate is on the consequences.
I must say I’m not sure whether you can meaningfully speak about the ‘Godel Statement’ is true in itself. That presumes the existence of a pre-axiomatic standard of truth. I’ve never seen such a beast in math. But since I haven’t been following the thread and the one in GD, I guess I should shut up now.
Spiritus, you are triply a fool. Have you never considered the implications of the universe’s being inconsistent?
You couldn’t use Godel’s Second Incompleteness Theorem to show that the universe can’t be proven to be consistent, because its opposite could also be shown to be true.
The very concepts of “truth” (a statement reflects the behavior of the world) and “false” (a statement does not reflect the behavior of the world) would be destroyed.
Nothing would have any properties – which is equivalent to saying that – everything would have all properties.
There would be no ‘you’ – all 'you’s and non’you’s would be and not be. You’d make all arguments and not make all arguments.
In order to disagree with the claim that the universe is consistent, you must first acknowledge that the universe is consistent – otherwise you’d agree and disagree.
The more you struggle against me, the more you become subject to my arguments.
It is impossible to generate a proof that the universe is consistent.
It is impossible not to assume that the universe is consistent.
In fact, if we choose “reality” to represent the world in which we exist, and “universe” as the total system in which that reality exists (these are somewhat non-standard choices, but I think they are defensible), then we’re forced to the conclusion that:
Reality is necessarily consistent, but the proof of this lies outside reality in the wider universe.
Or we can simply call our reality “the universe” and call what’s outside – something.
If I may be so bold as to make an allusion: “for lack of a better name, I call it the Tao.”
I, as a subsystem of the universe (or reality, or whatever), cannot possibly show that it’s complete.
Showing that a system is complete is only possible in another system that’s more complex than the first… and as a subsystem, I’m necessarily less complex than the universe.
The most complex system that the universe can simulate is… itself. It can’t simulate any other system that’s as complex as it is, either. Only systems less complex.
And that’s why nothing in the universe can generate a proof that the universe is either consistent or complete.
This has nothing to do with whether the universe is consistent – it obviously is. At least, the reality in which we exist is. We cannot doubt it – and by this, I mean we cannot doubt it.
Completeness? As far as I know, there’s reason to think the universe is or isn’t complete.
TVAA, nothing you will ever post will change the fact that there are a very precise set of conditions necessary for GIT to apply. You have not only failed to show that anything satisfies these conditions, but you have also failed to show that you understand them, or even that you know they exist, or that you can accurately understand anyone else’s arguments. All you’ve ever done amounts to posting “I’m right; why can’t you see that?” over and over again. It was never interesting then, and it sure as hell isn’t now.
Yes, ultrafilter. Whatever you say. I’m sure that if you keep repeating your claim that I don’t understand what I’m talking about, people will start to believe you.
Or, of course, you could point out contradictions between the things I say and the explanations of mathematicians that I’ve provided links to. You could actually demonstrate that I don’t understand instead of asserting it.
But I’m sure your current strategy will work out just fine.
It seems to me that my statements have always been consistent with the explanations of GIT given by actual mathematicians. The only people whose statements are demonstrably inconsistent have been Spiritus Mundi and his SuperFriends.
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?
And before I forget: you’re an impotent stooge, ultrafilter. You enjoy licking stages after performances by Gallagher. You’re a lawyer-loving codpiece-sniffer.
(I wouldn’t want the tone of the thread to fall, after all. :D)
If your analogy between reality, the universe, and axiomatic mathematical systems is the reason you say this, then I fear this is incorrect as Spiritus has already mentioned.
Speaking of record players, don’t you hate it when one just skips and skips and skips and skips and … do you see that as demonstrating consistency or incompleteness?
Hey, Spiritus, considering how this thing is a-draggin’ on, do you mind if I start calling you Saint George?
We know already that the behavior of the universe is described by a set of statements at least as powerful as those required for arithmetic.
Godel’s Second Incompleteness Theorem provides a rigorous proof that the system of the universe cannot generate a proof of its own consistency.
An inconsistent system can generate a proof of any statement (and a counterproof for every statement). Nothing can be said to be true or false in such a system. Nothing can be said to possess any property (because it must also lack the property).
In order to argue that GIT-2 applies, we need to presume that the universe is consistent. In order to make any argument, we need to presume that the universe is consistent. Taking the opposite assumption negates all arguments, conclusions, and statements that can be made.
First, it’s not an analogy. Analogies are comparisons made between systems that manifest similar principles. The things I’m discussing are fundamentally the same.
You may disagree if you like, and we could have an interesting discussion of the reasons why I’m holding this position, but if you can’t honestly say you understand it you can’t reasonably claim it’s false, either.
Secondly, that isn’t the reason I say this. I’ve already told you why the assumption that the universe is consistent is the only possible one. We already know that the universe is sufficiently powerful (if you dispute this, please make an argument against it). GIT-2 shows that it’s the case that the proof of the consistency of a sufficiently powerful system cannot be constructed within that system.
Oh, Fatwater Fewl: if the record player’s behavior was inconsistent, it would engage in all possible interactions with the records. There would be no way we could even conceptualize that case, even in theory.
Feel free to criticize what you have grounds to question, but it’s unwise to mock that which you don’t understand.
Such a realist! I don’t know that we know that… I do know we use such a set of statements to describe the behavior of the universe with varying degrees of accuracy.
I am unaware of what it means for a universe to be consistent. I am aware of what it means for a axiomatic mathematical system to be consistent, but you haven’t linked the two in my mind well enough yet. Sorry.