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piffle
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PostPosted: Wed Sep 01, 2004 10:19 am    Post subject: Reply with quote

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From my limited understanding of the incompleteness theorem, it requires your logical system to operate on the representations of its own statements, sort of like Lisp. If you forbid such a thing, I think you are good to go.

Goedel's Theorem contained 2 main important results:

  1. Every (omega-consistent) system of recursive relations (roughly, every "formal, axiomatic system of sufficient strength") contains a specific proposition such that neither it, nor its contradiction is derivable from the the axioms of the system (it is undecidable) [Proposition VI]. Furthermore, every recursive relation is arithmetical [Proposition VII]. It follows from these two theorems that any system at least stong enough to represent arithmetic contains an undecidable proposition. That's bad enough, but as it turns out, given the nature by which Goedel "arithemetized" propositions, the given undecidable proposition takes the form of a mere statement about whole numbers. As such, it can simply be verified, and indeed it was. That is to say, there is at least one true (in the logical sense) statement about whole numbers that is not derivable from the axioms of arithematic. Quite a schocking conclusion for the mathematicians and logicians of the early 20th century.
  2. The consistency of a system is unprovable in the system itself. [Proposition XI] This is the part that dealt a death blow to Hilbert's programme for axiomatizing the foundations of mathematics: there is no way to prove that a logical antimony is not present in the natural number system, and thus, by extension, in all of analysis. Given the acceptance of material implication (the usual notion of "if-then") as a valid rule of logical inference, the discovery of a logical antimony would mean that any and all propostions ("1=2") could be proven immediately. This leaves only two justifications for mathematics: faith (Platonic mysticism), and pragmatic sanction (it's really damned useful, even if it turns out to be broken).

Back to your regularly scheduled thread. . .


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hellbringer
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PostPosted: Wed Sep 01, 2004 10:36 am    Post subject: Re: Truth, justice and something something Reply with quote

jetblack wrote:

Sure, but I have to work with what I've got. Frankly, without an objective reality, there is no true system of knowledge. There is no truth at all. I do contend that there is a fairly large body of evidence (mostly from science) to support the assumption that there is an objective reality.


Excuse my intrusion in the discussion, but since we once had a similar discussion (can't bother to search now, but i remember it being here) I would just like to give my 2 cents.
While I would agree with you that there is plenty of evidence for an objective reality, I think your claim that any true system of knowledge needs such a reality is imposing a much more stricter condition than is really needed. For example, I would contend that science only needs a reality that behaves objectively, not an objective reality.
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piffle
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PostPosted: Wed Sep 01, 2004 10:41 am    Post subject: Reply with quote

Quote:
I do contend that there is a fairly large body of evidence (mostly from science) to support the assumption that there is an objective reality.

In fact this is utterly and completely not the case, at all. In fact, the conclusions of standard quantum mechanics make the existence of an objective reality an impossibilty. This is the very situation that Einstein wrestled with at the end of his career. Einstein failed in his search for a theory that could preserve objective reality, and at the same time be consistent with the predictions of quantum mechanics (the most accurate predictions yet made by any physical theory). In hindsight, this is not surprising. Bell's inequality made it an experimental question as to whether such a theory was possible. And now, the physical observed results of Aspect's experiments over the last decade evidently answer the question, and close the book on objective reality. Your contention here is wholly unsupported.

As an aside, this would be yet another reason (albeit an obtuse one) that it is difficult to accept the notion of absolute human rights.
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PostPosted: Wed Sep 01, 2004 2:10 pm    Post subject: Reply with quote

piffle wrote:
Quote:
I do contend that there is a fairly large body of evidence (mostly from science) to support the assumption that there is an objective reality.

In fact this is utterly and completely not the case, at all. In fact, the conclusions of standard quantum mechanics make the existence of an objective reality an impossibilty. This is the very situation that Einstein wrestled with at the end of his career. Einstein failed in his search for a theory that could preserve objective reality, and at the same time be consistent with the predictions of quantum mechanics (the most accurate predictions yet made by any physical theory). In hindsight, this is not surprising. Bell's inequality made it an experimental question as to whether such a theory was possible. And now, the physical observed results of Aspect's experiments over the last decade evidently answer the question, and close the book on objective reality. Your contention here is wholly unsupported.

As an aside, this would be yet another reason (albeit an obtuse one) that it is difficult to accept the notion of absolute human rights.


From my (admitedly limitted) knowledge of quantum mechanics, it doesn't neccesarily kill an objective reality, but rather a deterministic one, i.e. while reality may be indeterministic, it is not arbitrary since we are able to make predictions.
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PostPosted: Wed Sep 01, 2004 2:37 pm    Post subject: Reply with quote

piffle wrote:
Quote:
I do contend that there is a fairly large body of evidence (mostly from science) to support the assumption that there is an objective reality.

In fact this is utterly and completely not the case, at all. In fact, the conclusions of standard quantum mechanics make the existence of an objective reality an impossibilty.

....


Forgive me, for my knowledge of theoretical physics is apparently lacking. How, precisely, does quantum mechanics disprove the proposition that existence exists? :?:
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PostPosted: Wed Sep 01, 2004 2:38 pm    Post subject: Reply with quote

utabintarbo wrote:
piffle wrote:
Quote:
I do contend that there is a fairly large body of evidence (mostly from science) to support the assumption that there is an objective reality.

In fact this is utterly and completely not the case, at all. In fact, the conclusions of standard quantum mechanics make the existence of an objective reality an impossibilty.

....


Forgive me, for my knowledge of theoretical physics is apparently lacking. How, precisely, does quantum mechanics disprove the proposition that existence exists? :?:


He is not saying that...
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PostPosted: Wed Sep 01, 2004 3:00 pm    Post subject: Reply with quote

jetblack wrote:
I'm not so sure that I'm begging the question, though.

Err, well, I'm mostly sure that you are ... :?

jetblack wrote:
Sure, but I have to work with what I've got. Frankly, without an objective reality, there is no true system of knowledge. There is no truth at all. I do contend that there is a fairly large body of evidence (mostly from science) to support the assumption that there is an objective reality.

This seems to agree with the pragmatic alternative that I offered you. You choose the realist model simply because it gives you something to work with.

Quote:
True, I understand the "is/ought" problem. However, my concern with objective good derives from a concern about how I should live my life. There's no way to phrase the question without some sort of "ought". I know that I am always vulnerable to the claim that there is no way in which I ought to live, but such a life to me seems empty and meaningless. I choose not to live that way. If I have to back into a justification, well, I guess I have to.

Well, you can always go the presupposition route. In the system of ethics I developed (that I think you are aware of), I did an end-run around the is-ought problem by making it a "practical" ethics instead of a "moral" ethics.

Quote:
Perhaps. She has become quite the bugaboo. All I know of Rand is from The Fountainhead, which I loathe. I don't agree that her conclusions inevitably flow from this line of reasoning, for a lot of the reasons that piffle stated about quantifying harm.

Yeah, my smear campaign against her was quite effective, wasn't it? The Swift Boat Veterans for Truth would be proud. It is interesting that people much more easily accepted my 3-4 posts of personal attacks than they did my usual posts of reasoned argument, don't you think?
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PostPosted: Wed Sep 01, 2004 3:10 pm    Post subject: Reply with quote

I must applaud jetblack for his validation of the concept of rights.

I did not have the ambition to try to convince the 3-5 people on this forum of what essentially the world accepts as axiomatic: the existence of human rights. Though I recognize that this is a proposition that *does* require a formal proof, I thought it redundant to effectively re-hash the proofs of others that have come before me. These people can read after all.

However, I am happy you made the effort! :D
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piffle
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PostPosted: Wed Sep 01, 2004 3:25 pm    Post subject: Reply with quote

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I did not have the ambition

Don't be so hard on yourself. It's not that you did not have the ambition; rather, you did not have the means, as such a thing is not provable.
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PostPosted: Wed Sep 01, 2004 3:27 pm    Post subject: Reply with quote

piffle wrote:
Don't be so hard on yourself. It's not that you did not have the ambition; rather, you did not have the means, as such a thing is not provable.

Well-played, good sir.
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piffle
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PostPosted: Wed Sep 01, 2004 3:40 pm    Post subject: Reply with quote

Quote:
From my (admitedly limitted) knowledge of quantum mechanics, it doesn't neccesarily kill an objective reality, but rather a deterministic one, i.e. while reality may be indeterministic, it is not arbitrary since we are able to make predictions.

The orthodox (Copenhagen) interpretation of quantum mechanics states that on the microscopic level, before making a measurement of a particle, say, that particle has no definite existence. I promise you, the only way to say "the particle really was somewhere before we measured it, we just did not know where" is to introduce hidden variables. That would be fine, except that Bell's inequality and Aspect's subsequent results have experimentally ruled this possibility out. The only way to salvage things would be through nonlocal hidden variables. So there you have it: either there is no objective reality, or if there is, there is no causality and the present depends on the future. These are the only options we have left that are consistent with actual observations of the world. Take your pick.

If you are truly interested you can get Einstein and Bohr's opposing 1935 Physical Review papers, Bell's 1964 paper, and Aspect's papers starting in 1981 (in particular "Experimental tests of realistic local theories via Bell's theorem"). David Mermin from Cornell also wrote lucidly on this subject. Some of them are reasonably accessible even with a modest background.
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piffle
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PostPosted: Wed Sep 01, 2004 3:52 pm    Post subject: Reply with quote

Here is an interesting question. Would absolute human rights "exist" even if there were no human beings in the universe?
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PostPosted: Wed Sep 01, 2004 4:07 pm    Post subject: Reply with quote

Piffle, if you'll excuse my undefined use of the word "good" you are too smart for your own good! :D but to answer your question, no I don't think human rights exist when there are no humans.. they only exist in our minds a'la Robert Pirsig's "Quality"
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PostPosted: Wed Sep 01, 2004 4:21 pm    Post subject: Reply with quote

GOBY wrote:
Piffle, if you'll excuse my undefined use of the word "good" you are too smart for your own good! :D but to answer your question, no I don't think human rights exist when there are no humans.. they only exist in our minds a'la Robert Pirsig's "Quality"

Uhoh, did you just say that rights are subjective? Well, at least you're honest :)

Or maybe I don't understand your position correctly. Do you take the hard-line Objectivist stance, or do you think rights are merely useful as social conventions?
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PostPosted: Wed Sep 01, 2004 4:30 pm    Post subject: Reply with quote

piffle wrote:
Here is an interesting question. Would absolute human rights "exist" even if there were no human beings in the universe?

Nicely put. While I am a mathematical platonist as I believe it does solve more philosophical problems then it creates, I see no such use for adopting a platonist position on the concept of rights. With mathematics you have something on which everyone agrees and arguably would exist even with no people. I have heard no convincing arguments to show that rights are this way. Only utabintarbo seems to think this though and he has no fashion sense :twisted:
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piffle
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PostPosted: Wed Sep 01, 2004 4:34 pm    Post subject: Reply with quote

Quote:
It is interesting that people much more easily accepted my 3-4 posts of personal attacks than they did my usual posts of reasoned argument, don't you think?

Best to artfully combine the two; that way, people accept your position, and you can claim they did so because of your superior argument, to boot!.
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PostPosted: Wed Sep 01, 2004 4:34 pm    Post subject: Reply with quote

papal_authority wrote:
... Only utabintarbo seems to think this though and he has no fashion sense :twisted:


Hey! I am a fine looking dude!
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PostPosted: Wed Sep 01, 2004 4:43 pm    Post subject: Reply with quote

piffle wrote:
Here is an interesting question. Would absolute human rights "exist" even if there were no human beings in the universe?


Obviously not. The concept of "human rights" presupposes the existence of humans.

Neither would epistemology, so why continue the discussion?
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PostPosted: Wed Sep 01, 2004 4:44 pm    Post subject: Reply with quote

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While I am a mathematical platonist as I believe it does solve more philosophical problems then it creates

What about Wigner's question? Or the Banach-Tarksi "Paradox?"
Quote:
With mathematics you have something on which everyone agrees

But you don't have such -- the answer to "what is mathematics" depends on who you ask! There are set-theorists nee Hlibert-style formalists. There are contructivists, and intuitionists. Do you accept material implication? Do you accept the uncountable Axiom of Choice? What about the Continuum Hypothesis? People don't agree on these most fundamental things.
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PostPosted: Wed Sep 01, 2004 4:44 pm    Post subject: Reply with quote

Baron, the second one.. rights are useful social conventions, and only to the extent that we can approximate what is "just." Until we start living at a quantum scale or traveling near the speed of light, newtonian physics do just fine for making those approximations. For all practical purposes, we can ignore the rest. That's why I say piffle is too smart.

IMO rights are like physical laws-- they only exist to the extent that we can define them, but everything in nature (the approximate nature that we live in) says they're "self evident."
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PostPosted: Wed Sep 01, 2004 4:45 pm    Post subject: Reply with quote

piffle wrote:
Best to artfully combine the two; that way, people accept your position, and you can claim they did so because of your superior argument, to boot!.

You truly are a modernday Solomon, piffle.

Except without the 500 concubines.
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PostPosted: Wed Sep 01, 2004 4:54 pm    Post subject: Reply with quote

piffle wrote:
Quote:
From my (admitedly limitted) knowledge of quantum mechanics, it doesn't neccesarily kill an objective reality, but rather a deterministic one, i.e. while reality may be indeterministic, it is not arbitrary since we are able to make predictions.

The orthodox (Copenhagen) interpretation of quantum mechanics states that on the microscopic level, before making a measurement of a particle, say, that particle has no definite existence. I promise you, the only way to say "the particle really was somewhere before we measured it, we just did not know where" is to introduce hidden variables. That would be fine, except that Bell's inequality and Aspect's subsequent results have experimentally ruled this possibility out. The only way to salvage things would be through nonlocal hidden variables. So there you have it: either there is no objective reality, or if there is, there is no causality and the present depends on the future. These are the only options we have left that are consistent with actual observations of the world. Take your pick.

If you are truly interested you can get Einstein and Bohr's opposing 1935 Physical Review papers, Bell's 1964 paper, and Aspect's papers starting in 1981 (in particular "Experimental tests of realistic local theories via Bell's theorem"). David Mermin from Cornell also wrote lucidly on this subject. Some of them are reasonably accessible even with a modest background.

OK, I've only had 1 year of college-level quantum mechanics, so I an not an expert in the field, but this is my understanding of the matter. Yes, Bell did show that local hidden variables do not exist. But there still exists the wave function associated with the object, that collapses into an eigenstate associated with a quantity when you make an appropriate measurement. The whole point of quantum mechanics is that the wave function is there, but we can't see it directly - we must make repeated measurements, and from the distribution of the results (eigenvalues) we get, figure out what the wave function was before its collapse.

Philosophically, this is no different from conventional theory of science. An objective reality is there, but we can never be certain we actually know it; however, repeated experiments grant us a reasonable probability of figuring out what the reality is.

EDIT : terminology error


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piffle
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PostPosted: Wed Sep 01, 2004 4:55 pm    Post subject: Reply with quote

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Except without the 500 concubines.

Well, I'm gay, you know -- what would I do with 500 concubines anyway!
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PostPosted: Wed Sep 01, 2004 4:59 pm    Post subject: Reply with quote

piffle wrote:
But you don't have such -- the answer to "what is mathematics" depends on who you ask! There are set-theorists nee Hlibert-style formalists. There are contructivists, and intuitionists. Do you accept material implication? Do you accept the uncountable Axiom of Choice? What about the Continuum Hypothesis? People don't agree on these most fundamental things.

Very good points and I don't want to get too off topic. I was just trying to say that if someone were to present a simple proof (irregardless of axioms used) that someone could check it and say "yes if we accept those axioms then your conclusion follows". That is what I meant when I said "everyone agrees." My main point however, was not defend mathematical platonism nor define what mathematics is, but rather that I cannot see any benefits to adopting a platonist position about rights...
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PostPosted: Wed Sep 01, 2004 5:04 pm    Post subject: Reply with quote

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But there still exists the wave function associated with the object

Really, exists where? Quantum mechanics is our convenient way of organizing our observations about the world. But the universe just does what it does, our models are dictated by it, not the other way around. So, where is the particle, since that's what we ultimately care about?

I promise you , the modern "conventional theory of science" does not suppose an objective reality. You can go read about as much even in your Griffith's Introduction to Quantum Mechanics.

As an aside, the "collapse of the wavefunction" is easy enough to describe mathematically -- you just zero off all the off-diagonal elements in some matrix -- but it is completely unmotivated. You can't derive it from anything, and it certainly does not follow from the normal unitary time evolution which holds immediately before, and after an observation.
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