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The Eternal Return

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'punk' On Dec 5 2006 Wrote:

> One might look at an action as worth doing

> on a lark, but if one reconsiders along Nietzsche's

> lines and say "is this action worth doing over

> and over again forever through eternity"

There is no way I can ever know if I’m repeating the same thing over and over again, not while I’m in the same brain state, thus there is no reason I should give a bucket of warm spit over the matter one way or the other. And that is why Nietzsche’s metaphor is so brain dead dumb.

John K Clark

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Bold Standard on Dec 6 2006 Wrote:

> Um, how about the law of causality?

If there really is a “law of causality” then we are undergoing a huge crime wave because violations are happening constantly. But hey, cheer up, I expect to be kicked of the list again very soon, then you can go back to your comfortable 19’th century world view.

John K Clark

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But hey, cheer up, I expect to be kicked of the list again very soon, then you can go back to your comfortable 19’th century world view.

Does that chip on your shoulder make it hard to type? : P

And do you grant that there is, at least, a law of identity and law of non-contradiction in logic? That is: A is A and cannot be non-A at the same time and in the same respect? If not, what laws of logic do you accept?

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Bold Standard on Dec 6 2006 wrote:

> Does that chip on your shoulder make it hard to type?

No not at all, and considering the 19’th century mentality I see around here I think I’ve earned that chip. I’m right and you are not, it’s as simple as that.

> And do you grant that there is, at least, a law of identity

> and law of non-contradiction in logic?

Well, I grant that there is The Identity Of Indiscernibles. The philosopher who discovered it was Leibniz about 1690. He said that things that you can measure are what's important, and if there is no way to find a difference between two things then they are identical and switching the position of the objects does not change the physical state of the system.

Leibniz's idea turned out to be very practical, although until the 20th century nobody realized it, before that his idea had no observable consequences because nobody could find two things that were exactly alike. Things changed dramatically when it was discovered that atoms have no scratches on them to tell them apart. By using The Identity Of Indiscernibles you can deduce one of the foundations of modern physics the fact that there must be two classes of particles, bosons like photons and fermions like electrons, and from there you can deduce The Pauli Exclusion Principle, and that is the basis of the periodic table of elements, and that is the basis of chemistry, and that is the basis of life. If The Identity Of Indiscernibles is wrong then this entire chain breaks down and you can throw Science into the trash can.

The Schrodinger Wave Equation proved to be enormously useful in accurately predicting the results of experiments, and as the name implies it's an equation describing the movement of a wave, but embarrassingly it was not at all clear what it was talking about. Exactly what was waving? Schrodinger thought it was a matter wave, but that didn't seem right to Max Born. Born reasoned that matter is not smeared around, only the probability of finding it is. Born was correct, whenever an electron is detected it always acts like a particle, it makes a dot when it hit's a phosphorus screen not a smudge, however the probability of finding that electron does act like a wave so you can't be certain exactly where that dot will be. Born showed that it's the square of the wave equation that describes the probability, the wave

equation itself is sort of a useful mathematical fiction, like lines of longitude and latitude, because experimentally we can't measure the quantum wave function F(x) of a particle, we can only measure the intensity (square) of the wave function [F(x)]^2 because that's a probability and probability we can measure.

Let's consider a very simple system with lots of space but only 2 particles in it. P(x) is the probability of finding two particles x distance apart, and we know that probability is the square of the wave function, so P(x) =[F(x)]^2. Now let's exchange the position of the particles in the system, the distance between them was x1 - x2 = x but is now x2 - x1 = -x.

The Identity Of Indiscernibles tells us that because the two particles are the same, no measurable change has been made, no change in probability, so P(x) = P(-x). Probability is just the square of the wave function so [ F(x) ]^2 = [F(-x)]^2 . From this we can tell that the Quantum wave function can be either an even function, F(x) = +F(-x), or an odd function, F(x) = -F(-x). Either type of function would work in our probability equation because the square of minus 1 is equal to the square of plus 1. It turns out both solutions have physical significance, particles with integer spin, bosons, have even wave functions, particles with half integer spin, fermions, have odd wave functions.

John K Clark

Edited by johnclark
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There is no way I can ever know if I’m repeating the same thing over and over again, not while I’m in the same brain state, thus there is no reason I should give a bucket of warm spit over the matter one way or the other. And that is why Nietzsche’s metaphor is so brain dead dumb.

We once thought that the law of physics you are now so proudly touting to be utterly unanswerable. Think Bohr-Einstein, quantum agnosticism, and the very proof that you alluded to, Bell's inequality. I wouldn't be so sure about this, either. But personally, I find the metaphysical discussion largely uninteresting--it is any impact on decision-making that I find significant. For looking at things from different perspectives can be very helpful. Though symbolizing logic is a pain in the ass and essentially tells you nothing you cannot express in plain English, imagine trying to prove Godel's Incompleteness Theorem without it.

Is it necessary to have a doctorate in physics before one can evaluate a given philosophy?

It sure don't hurt.

[Edit for typo]

Edited by aleph_0
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I had always heard that Gödel's incompleteness theorem was nonsense, though I actually have no first hand knowledge of it. Doesn't Leonard Peikoff attack it in The Ominous Parallels?

Dismissing the work of Gödel, the greatest logician since Aristotle, with a vague wave of you hand is just the sort of thing that gives Objectivists a bad name. I start to associate them with hillbilly TV preachers and their opposition to Evolution.

John K Clark

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I had always heard that Gödel's incompleteness theorem was nonsense, though I actually have no first hand knowledge of it. Doesn't Leonard Peikoff attack it in The Ominous Parallels?

The main problem with Gödel's incompleteness theorem is that very few people know what it is Gödel was saying. A lot of people get this idea that the theorem says that actual knowledge is impossible or limited; he is in fact saying the exact opposite. He is saying that even though there are statements which cannot be proven deductively, i.e. through the repeated application of rules of inference to a finite set of axioms, they can be shown to be true. The thorem is an attack on "pure" deduction and contextless, completely formalized logic, not on actual knowledge.

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So do you think I'm accurate in comparing him to Augustine on this point?

Having only read Augustine's "Confessions", I see no reason not to compare the two.

In any event, despite his testosterone filled bluster and bravado, Nietzsche was always something of a Victorian prude at heart. He just wanted to find a way to be a Victorian prude without Christianity.

His early education was essentially training for becoming a pastor and that really continued to shape him to the end.

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If one disregards rationalism (the incompleteness theorem is possible only under rationalism) and actually looks to reality as the basic means of knowledge, then there is no such question.

I would be [morbidly] entertained to hear an attempt at a semi-cogent argument for this. Given the previous discussion on the objectivity of logic, I can see how this would run--but granted the theorem in question makes a statement about syntactic systems, it would be, if possible, an even more comedic running-jump into a brick wall to deny the theorem.

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'Cogito' on Dec 6 2006 Wrote:

> A lot of people get this idea that the theorem

> says that actual knowledge is impossible or

> limited; he [Gödel] is in fact saying the exact opposite.

Well you’re half right; Gödel doesn't say we can't know anything, he says you can't know everything.

> He is saying that even though there are statements

> which cannot be proven deductively, i.e. through the

> repeated application of rules of inference to a finite

> set of axioms, they can be shown to be true.

Quite untrue, he says some things are true but CANNOT be SHOWN to be true.

For example take the Goldbach Conjecture, it

states that every even number greater that 4 is the sum of two primes greater than 2. Let's try it for some numbers:

6=3+3

8=5+5

10=3+7

12=5+7

14=3+11

16=3+13

18=7+11

20=3+17

22=5+17

24=7+17

26=7+19

28=11+17

30=11+19

This all looks very promising, but is it true for all even numbers? Checking all even numbers one by one would take an infinite number of steps, to test it in finite number of steps I need a proof, but I don't have one, nobody does. The Goldbach Conjecture was first proposed almost 300 years ago and since that time the top minds in mathematics have looked for a proof but have come up empty. Perhaps nobody has found a proof because it's not true. Could be, but modern computers have looked for a counterexample, they've gone up to a trillion or so and it works every time. Now a trillion is a big number but it's no closer to being infinite than the number 1 is, so perhaps The Goldbach Conjecture will fail at a trillion + 2 or a trillion to the trillionth power. It's also possible that some brilliant mathematician will come up with a proof tomorrow, as happened with Fermat's last theorem, but there is yet another possibility, it could be un-provable.

The Goldbach Conjecture is either true or it's not, Godel never denied that, the question is, will we ever know if it's true or not? According to Gödel some statements are un-provable, if The Goldbach Conjecture is one of these it means that it's true so we'll never find a counterexample to prove it wrong, and it means we'll never find a proof to show it's correct. For a few years after Gödel made his discovery it was hoped that we could at least identify statements that were either false or true but had no proof. If we could do that then we would know we were wasting our time looking for a proof and we could move on to other things, but in 1935 Turing proved that sometimes even that was impossible.

If Goldbach is un-provable we will never know it's un-provable, Gödel told us that such statements exist but he didn't tell us what they were. A billion years from now, whatever hyper intelligent entities we will have evolved into will still be deep in thought looking, unsuccessfully, for a proof and still grinding away at numbers looking, unsuccessfully, for a counterexample.

John K Clark

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Well you’re half right; Gödel doesn't say we can't know anything, he says you can't know everything.

Are you trying to distinguish between consistency and omega-consistency? If so, 1) only two years after Godel, there was a proof which dropped the "omega" and 2), that's not the clearest way of saying it.

Quite untrue, he says some things are true but CANNOT be SHOWN to be true.
Quite untrue, he says that some things are true but cannot be derived from a purely syntactic system of operations. If one claims that something is true in the first place, one damn well better be able to show that it's true.

For example take the Goldbach Conjecture...

What does this have to do with Godel's proof? Godel showed that some things are true but cannot be proved by a complete, consistent, axiomatizable theory of arithmetic. We have no idea whether Goldbach's Conjecture is true. It may be unprovable and it may be un-disprovable--but that is all together a distinct concept from Godel's Incompleteness, which is about formal theories.

[Edit for grammar.]

Edited by aleph_0
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Gödel doesn't say we can't know anything, he says you can't know everything

Godel's work has a limited applicability in certain mathematical contexts and it is a mistake to try to apply his theory outside of its range of applicability - to areas which have no relation to mathematics.

Godel himself said that he "had not established any boundaries for the powers of human reason, but rather for the possibilities of pure formalism in mathematics".

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I have to second the above in a slightly different way:

Goedel's work is of little or no interest to anyone who is not a mathematician.

Any attempt to get something out of Goedel that is not purely mathematical in nature results only in nonsense.

Or more technically:

Goedel is only considered with certain kinds of mathematical theorems in certain kinds of formal systems. If you aren't talking mathematics expressed in a formal system Goedel isn't relevant.

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'aleph_0' On 'Dec 7 2006 Wrote:

> Are you trying to distinguish between consistency and omega-consistency?

No. All true formal theories of arithmetic are omega-consistent and thus obey Gödel. Systems that are consistent but not omega consistent are too too simple and weak to do anything very interesting so are little studied even by experts. Boring.

Me: “he [Gödel] says some things are true but CANNOT be SHOWN to be true”.

You: “Quite untrue, he says that some things are true but cannot be derived from a purely syntactic system.”

It absolutely mystifies me what was “quite untrue” about what I said.

> If one claims that something is true in the first place, one damn well better be able to show that it's true.

Exactly, that what so puzzles me about your response. You admit there are some true things you can not prove to be true, so how did you know it is true? How did you “show that it is true” to other people? If you say “I saw it in a dream” am I supposed to accept that?

> [Goldbach's Conjecture] may be unprovable and it may be un-disprovable --but that is all together a distinct concept from Godel's Incompleteness, which is about formal theories.

Godel is about what formal systems, like mathematics, can show to be true. Mathematics is the foundation of Physics and Physics is the foundation of Chemistry and Chemistry is the foundation of Biology and Biology is the foundation of Psychology.

> What does this [Goldbach Conjecture] have to do with Godel's proof?

As I said before if you had been paying attention, since 1930 even conjecture in mathematics is now living under a shadow, it may be true so you’ll never find a counterexample to prove it false but it may also be un provable so you’ll never know its true because you’ll never find a proof. To claim this doesn’t have enormous implications for philosophy is to stick ones head in the sand; and that is what disturbs me about Objectivists. It’s not like the discovery was made last week, it’s more than 75 years old and Quantum Physics is even older, yet the followers of Ayn Rand continue exactly as before as if nothing had happened. I mean, I like her novels a lot too but for goodness sake!

John K Clark

Edited by johnclark
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'~Sophia~' on 'Dec 7 2006

> Godel's work has a limited applicability in certain mathematical contexts

Godel's work has a huge applicability in many mathematical contexts, and in philosophy he can not be overstated.

> it is a mistake to try to apply his theory outside of its range of applicability

Like Logic?

>Godel himself said that he "had not established any

> boundaries for the powers of human reason,

> but rather for the possibilities of pure formalism in mathematics".

I don’t know if you made that quote up but it wouldn’t greatly surprise me if he had actually said it; as an old man he also said he had just written a mathematical proof of the existence of God. You see, 45 years after he did his great work his wife died and the poor man went completely insane. It’s ironic that the greatest logician since Aristotle starved himself to death. He refused to eat because he thought unnamed sinister forces in Princeton New Jersey were trying to poison him. Genius and madness, two sides of the same coin.

John K Clark

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Godel is about what formal systems, like mathematics, can show to be true.

Drawing conclusions about what is possible from applying Godel's Theorem outside of its range of applicability (which Godel himself warn against) is pure rationalism. Reality isn't based upon a set number of axioms. Truth and falsehood has meaning outside of what can be explained by mathematical system. His work does not establish any boundaries for the powers of human reason and knowledge.

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Objectivists do not carry on as though nothing has happened. If you'll notice, there are a fair number voicing ardent philosophical disagreement with the equation of all mankind's knowledge to a pure mathematical formalism while throwing observation and induction out the window, as well as the idea of quantum nonidentities acting noncausally in infinitely many nonexistent planes of existence, or rather that their existence and identities are determined by the act of thinking about them.

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> And do you grant that there is, at least, a law of identity

> and law of non-contradiction in logic?

Well, I grant that there is The Identity Of Indiscernibles. The philosopher who discovered it was Leibniz about 1690. He said that things that you can measure are what's important, and if there is no way to find a difference between two things then they are identical and switching the position of the objects does not change the physical state of the system.

Leibniz's idea turned out to be very practical, although until the 20th century nobody realized it, before that his idea had no observable consequences because nobody could find two things that were exactly alike. Things changed dramatically when it was discovered that atoms have no scratches on them to tell them apart. By using The Identity Of Indiscernibles you can deduce one of the foundations of modern physics the fact that there must be two classes of particles, bosons like photons and fermions like electrons, and from there you can deduce The Pauli Exclusion Principle, and that is the basis of the periodic table of elements, and that is the basis of chemistry, and that is the basis of life. If The Identity Of Indiscernibles is wrong then this entire chain breaks down and you can throw Science into the trash can.

So, you grant only that there is an Identity of Indiscernibles, but not that there is a Law of Identity? Doesn't the Identity of Indiscernibles depend on the Law of Identity? It would be absurd to claim that A=B unless A=A and B=B, wouldn't it?

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So, you grant only that there is an Identity of Indiscernibles, but not that there is a Law of Identity? Doesn't the Identity of Indiscernibles depend on the Law of Identity?

It’s just that I don’t find A=A to be terribly interesting; but the Identity of Indiscernibles, the fact that if you switch two objects and there is no change to the system then they are identical, well, that can lead to far more remarkable things.

Thought Experiment:

You step into my matter duplicating chamber. The chamber is symmetrical. You stand 5 feet from the center. I turn on the machine. A person who looks just like you seems to appear 10 feet away. He's staring at you.

Questions:

1)Are you the original or the copy?

2)What experiment did you perform to make that determination?

3)Does that other fellow agree with you?

4) If it turns out you're the copy would there be any reason to be upset?

The Identity of Indiscernibles tells us these are the answers:

1) It doesn’t matter.

2) There is none.

3) Probably not but I don’t care.

4)No.

John K Clark [email protected]

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