PROOF INFINITY DOES NOT EXIST! Not even ONE type
in [Math]
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From: Wolf K on 8 Jul 2010 15:03 On 08/07/2010 13:52, MoeBlee wrote: [...] > I strongly recommend Torkel Franzen's book, written for the layman, > about incompleteness. > > MoeBlee And anyone else who thinks they understand it. I recall deriving the proof, oh, almost 50 years ago now, and thinking I got it. Well, just because you can replicate a proof doesn't mean you understand the theorem. Franzen is especially good at teaching you what GT does _not_ mean. cheers, wolf k.
From: |-|ercules on 8 Jul 2010 16:50 "MoeBlee" <jazzmobe(a)hotmail.com> wrote > On Jul 7, 10:07 pm, c...(a)kcwc.com (Curt Welch) wrote: > >> I've not studied Godel's proof enough to feel like I really understand it's >> ramifications. But my best guess > > Your best guess is not a good one: > >> is that it's not really very significant >> at all. I think it just shows us an interesting fact of what can be done >> with language. When we make language self referential with a negative, we >> can create a form of logical "negative feed-back" that prevents the >> statement form being true or false. If we say "this statement is not >> true", we have created a negative self reference in our language. And once >> we do that, we have created a statement that can't be true, or false. The >> language is logically inconsistent with itself. > > No, that's not it at all. > >> I might be wrong, > > You are. > >> but I don't believe Godel's proof shows us anything more >> than the simple power of language to be self inconsistent when we write >> negative self referential statements. > > You belief is incorrect. > >> When we include language about whether something in the language is >> "provable" we make the problem more complex by looping the negative self >> reference through the external human (or machine) that is "doing the >> proof". But I believe the end result is no different than what happens >> when we write "this statement is not true". We are just using the same >> basic power of negative self reference in language to "mess up" the truth >> of any set of language statements. >> >> I think the only thing Godel shows us is that negative self reference is >> the poison apple of all formal language. > > As you started out saying, you don't know enough about the > incompleteness theorems. > > I strongly recommend Torkel Franzen's book, written for the layman, > about incompleteness. > > MoeBlee Actually Curt is spot on. Godel's proof is a farce. Come back when you can tell me the truth value of the following proposition: This statement cannot be proven by MoeBlee True or false Moeblee? Don't forget to give your reasoning! Herc
From: |-|ercules on 8 Jul 2010 16:53 "|-|ercules" <radgray123(a)yahoo.com> wrote > This statement cannot be proven by MoeBlee Oh dear. According to 'the incompleteness theorem' I just placed a bound on the comprehension ability of MoeBlee!! We all know the statement is true, but MoeBlee cannot prove it!!! WHAT A CROCK OF SH1T Herc
From: MoeBlee on 8 Jul 2010 17:41 On Jul 8, 3:50 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > This statement cannot be proven by MoeBlee "Herc cannot understand that Herc is an ineducable loon." Paradox free! MoeBlee
From: Curt Welch on 8 Jul 2010 17:55
"K_h" <KHolmes(a)SX729.com> wrote: > "Curt Welch" <curt(a)kcwc.com> wrote in message > news:20100708093928.442$LY(a)newsreader.com... > > "|-|ercules" <radgray123(a)yahoo.com> wrote: > >> "Curt Welch" <curt(a)kcwc.com> wrote... > > > >> I realize the difficulty in confirming a rock exists. But all you > >> have to do is confirm *something* exists. Even if you're in error the > >> conclusion is still true. E x > >> > >> Herc > > > > That's an interesting point. I don't see any argument against the idea > > that something exists is an absolute truth. I think therefore I am. > > That might be the one and only absolute truth. > > Mathematical truth exists. To my recollection, I have never seen anybody > claim that 2x7=14 is false or fails to be true after somebody dies. That's generally true. The question is not normally thought about. Humans tend to think and talk as if there are always humans around. But what happens if _everyone_ that understands the language died? What does it mean to suggest the "truth of the statement lives on" at that point? All that is left is ink marks in books at that point. Since when did an ink mark represent some form of absoluter truth? Why is one ink mark an absolute truth and another is not? If the truth doesn't live on in the ink mark, where does it exist? I claim that once all the humans (or other advanced machines that can use the language like we can - which generally don't exist yet) are gone, then the truth of the statement is gone as well. > The > equation 10+20=30 is an absolute truth and that truth does exist. But what do you think you are making reference to when you say it exists? Where exactly does it exist? What form does it exist in? How do truths (absolute or otherwise) even exist at all? > It is > obvious that there are an infinite number of such truths so infinity, as > a platonic truth, must exist. :) > > But sadly, our ability to express the idea with language still runs > > into the problem of potential failure to correctly communicate with > > some small probability of error, and likewise, our ability to even > > think the idea comes with the same error. So even if the idea is > > itself, when expressed correctly, an absolute truth, it's not an > > absolute truth that our brain can ever correctly express or understand > > the idea. > > Humans do have limitations but those limitations are not limitations on > existence. Yes, the rest of the universe continues to exist whether we are here or not. Sometimes people use the word "exist" to mean "can be perceived by a human" (or exists in the mind) and in that case, that type of existence is dependent on the human, but that's a special case, and the general rule. > > We currently have no way of knowing if our understanding of E x might > > suffer such a condition. As such, we have no way of proving that E x > > is an absolute truth for any given understanding of "existence" or > > "absolute". We can only define it to be an absolute truth we we limit > > our scope to within the framework of the language itself (which is > > saying we are limiting it to the times where the langauge processing > > hardware (our brains) are functioning correctly. > > So you have existential doubts about the truth of 4+5=9? No, I have no doubt. I simply understand that truth is never absolute. We just pretend it is. To have doubt about the truth is to fail to pretend that truth is absolute. I don't fail to do the same pretending we all do on these issues. I accept (and well know) that humans make mistakes for example. I've looked at what you wrote above and checked the math about 5 times now to make sure you didn't try to trick me by listing a non-truth (or didn't accidentally make a typo in creating your example). Even with all that extra checking, my belief that you created a true statement in the language could still be in error with some small probability. But this question is even more fundamental than that, getting down to the Heisenberg uncertainty principle at the lower levels of our physical world. This all gets down to the fact that you can't separate the intent of the language (or the intent of the ideas), from the actual physical implementation of it. We can for example try to say "it is possible to write an absolute truth using the language of math", in reference to the type of example you wrote. So even if you made a typo, we can increase the odds that my statement is an absolute truth because surely, there are so many true statements in math, that we can't be wrong in saying that there exists at least one statement in math that is an absolute truth? But the problem is that it's impossible (or at least seems to be) to build language processing hardware that is guaranteed to correctly interpret, and produce, this language 100% of the time. A simple mechanical example for example would be a computer that allowed you to type in a statement and it would report if the statement was true. I can easily write a simple version of such a program: if input = "4+5=9" then output "true" else output "false" That is a language processor that "understands" the "truth" of "4+5=9". It doesn't understand anything else about math, so its understanding and language powers are highly limited, but other than that, it understands in the same mechanical way do (at least I claim it does). As long as that computer works correctly, then the "truth" of that statement exists. But it's impossible to build a computer that will follow the intent of that code example above with 100% accuracy. Given enough time, you can guarantee the machine will fail to act correct. And because it fail at some point, there is no "absolute truth" in the statement, or in the hardware implementation that defines the "meaning" of the language. However, when doing math, we ignore all this, and pretend that it's reasonable to assume we have machines (or humans) (or at least _one_ machine) that never makes mistakes (the God machine??). So as long as we can pretend this God machine exists, we can also pretend the truth continues to "exist" as an absolute truth. But there is no God machine, and there is no absolute truth. Just truths that are so close to absolute, that there is no point, except in these esoteric debates, to even bother with the thought that truth is never absolute. -- Curt Welch http://CurtWelch.Com/ curt(a)kcwc.com http://NewsReader.Com/ |