PROOF INFINITY DOES NOT EXIST! Not even ONE type
in [Math]
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From: |-|ercules on 8 Jul 2010 10:04 "Curt Welch" <curt(a)kcwc.com> wrote... > "|-|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. > > 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. > > So maybe what we are left with, is that E x is only an absolute truth in > the same sense that x = x is an absolute truth. That is, it's an absolute > truth only by definition of how the language works. And since language, and > more precisely the machine that interprets the language, can never function > absolutely, the "idea" can't exist as an absolute truth. It only exists as > a truth to the level of probability that the language processing machine > can function correctly? > > I guess maybe in the end, what this means, is that relative to the language > machine (us) that is processing the idea (having the though) it must always > be an absolute truth because it can only have a truth value when the > machine is functioning correctly, and at that point, the value must be > true. But relative to a second party observing the first party, they will > see that at times, the first party will fail to correctly process the > language and result in the statement, and the idea being false. > > And then, what if there were points in time where the universe as we > understand it stops existing? This might happen 1000 times a second every > second with the universe we understand blinking in and out of existence > constantly. But when we don't exist, we have no awareness of what has > happened, and as such, our reality is just the reality of the times where > we do exist, stitched together to create our view of the fabric of time. > If our universe works that way, then what happens to the idea of E x? All > human concepts of existence would be blinking on and off making E x false > half the time. Clearly not an absolute truth in that sense. But to detect > the fact that the human version of E x was not an absolute truth, there > w2ould need to be a second (non human & non physical in our understanding > of physical) langauge processing machine to notice, and think about the > fact that the human understanding of E x was not an absolute truth. > > 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. Why would existence have to be continuous? E x would only be absolutely true during the existence of it's formalism or perception of such, so at least it's temporally consistent. Use little e for 'some kind of' existence. e x. But the only thing brain in a vat thought experiments proved was that brain in a vat thought experiments don't prove anything. Herc
From: Wolf K on 8 Jul 2010 10:08 On 08/07/2010 09:49, Curt Welch wrote: > "|-|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. The full argument is: 1. If there is thinking, there must be a thinker 2. I think 3. Therefore I am a thinker Descartes assumed 1, since it has the form "If there is some action, there is an actor". That is unfortunately nor necessarily true, despite Descartes inability to doubt it. There is another deep assumption: "if there is an event, then is a cause." Descrates seems to have ebived that these assumptions are equivelent. They're not. An event need not be an action, therefore the cause need not be an actor. If thinking is an event rather than an action, then Descartes argument is unsound. An alternate version of Descartes argument (compressed) is: 1) Something happens 2) I observe something happens 3) Therefore, I am an observer 4) Therefore I exist Same issues: this time 2 is the doubtful premise. Heisenberg's uncertainty principle explains why: there need not be a conscious "observer" for "observation" to occur. H's unfortunate choice of "observer" muddles things. A clearer (IMO) statement of his insight runs something like this: All interactions between entities destroy some information. Extracting information from is an interaction; therefore extracting information destroys some information about each entity. Hence "observation" is merely another type of interaction. Or more succinctly: knowledge about the past is always incomplete. this, IMO, is the reason for "time's arrow." > 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. That's because "communication" is a type of interaction, so H's principle applies. [snip] Since as you rightly note the only certainly true statements are tautologies, they are not much help in the real world. OTOH, if we can construct an axiomatic model of some process/interaction/event/etc, then within that _limited_ domain tautologies may be translated into statements about the real world: we call such tautologies "predictions." Because no model is exact (it can't be, Heisenberg's principle explains why, and QM shows how), predictions are always more or less inaccurate. Note that increasing the domain of application requires increasing abstraction. Or so it seems to me. For now. ;-) wolf k.
From: Curt Welch on 8 Jul 2010 12:43 "|-|ercules" <radgray123(a)yahoo.com> wrote: > "Curt Welch" <curt(a)kcwc.com> wrote... > Why would existence have to be continuous? E x would only be absolutely > true during the existence of it's formalism or perception of such, so at > least it's temporally consistent. Use little e for 'some kind of' > existence. e x. Well, I guess it all boils down to whether it's ever valid to say such things as "be absolutely true during the existence of it's formalism or perception of such". No matter how short of a period that is, it is always a finite time span, and in order to make reference to the creation of the formalism, we are in fact making reference to the operation of some type of thinking machine (which is how such formalizations are created). Once we do that, we are making some sort of assumption about whether the machine is operating correctly throughout that time period. In an absolute sense, we can never make that assumption. Because we (as a society) don't generally have a clue about how the brain works, and what "Thought" is, we take large liberties with our beliefs about such things. It's an extension of how it was once generally accepted in society that humans had souls that persisted beyond the body. Even with more modern beliefs about the material limitations of the body and brain, we often (especially in fields like Mathematics which is intentionally disconnected from reality) extend the magical powers of the soul to the ideas and concepts of our formalism. That is, we often assume it's valid to talk about ideas, like "numbers" existing separate from us. That they "live on" even after we die. But even though that's a common way of talking, it's just wrong - it's as wrong as believing we have a soul that lives on after we die (wrong in the sense it's not consistent with known data - don't want to make value judgments for people and their personal beliefs). So, what you say about e x only having to be try for a short people while it's being formalized, is even in question once we stop pretending that "ideas" have a form of existence separate from the physical operation of a machine like a brain. Once we drop the soul-like treatment of ideas in our belief system, then all concepts of absolute truth I believe vanish from the universe. That's not to say we can't use langauge to describe a place where absolute truth does exist, just that our universe doesn't seem to be that place. So we can certainly talk about absolute truths as if they existed, and talk about the logical ramifications of such implications (as we do ad infinitum in Mathematics). But to talk about the idea of an absolute truth doesn't mean it can actually exist in our universe. The words that describe the idea of an absolute truth exist in our universe, but the absolute truth may not exist in any form. > But the only thing brain in a vat thought experiments proved was that > brain in a vat thought experiments don't prove anything. Well, that's something! :) > Herc -- Curt Welch http://CurtWelch.Com/ curt(a)kcwc.com http://NewsReader.Com/
From: MoeBlee on 8 Jul 2010 13:52 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
From: K_h on 8 Jul 2010 14:22
"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. The equation 10+20=30 is an absolute truth and that truth does exist. 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. > 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? _ |