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Kenneth Haugland wrote: I thought Godel proved that a system can't prove its own consistency unless it is inconsistent.
Not even close.
Consistency: X is provable, therefore X is true.
Completeness: X is true, therefore X is provable.
The most important of the two aspects is consistency, because if you're able to prove something that's actually false, there's no point to proving anything.
The layman's version of Godel's Incompleteness Theorem claims that in any closed system there are statements that are true and unprovable, because proving them would violate consistency.
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Argue with this[^] guy instead:
Stated more colloquially, any formal system that is interesting enough to formulate its own consistency can prove its own consistency iff it is inconsistent.¨
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Therefore, proving that the formal system isn't consistent in the first place, despite it being able to prove that it is.
But the real problem is that neither "Google" nor "evil" have been formally defined. So there's no formal system where Google can claim /or/ prove to be either not-"evil" or "evil".
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It wasn't meant to be taken literally in the first place, but saying that Google is good or evil, is all in the matter of the beholder. What cost benefit should you lay as evidence of it?
My general perception is that Godel's theorems is valid for systems with a finite axiom, or a system you try to define by some limited number of axioms. This has all to do with the historical development in mathematics, going back to Euclid's axioms of lines etc. Many people before Godel suspected it was not possible to do this, among others Gauss, Riemann etc. They early found the parallel postulate difficult to deal with, or should I say completely wrong for 3D.
So to use Godel's proof of anything in this world, you first have to establish the formal system, axioms, which can me enumerated, and then come to a conclusion. I'm not so sure it isn't true what I said about the inconsistency of the statement, because I don't think you can prove that it cant be formulated into a mathematical system of axioms, can you?
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Not even close."
Bzzt! Wrong! Gödel's second incompleteness theorem states that a consistent system cannot prove its own consistency. And of course inconsistent systems can prove anything, true or false, including their consistency.
Consistency: X is provable, therefore X is true.
Completeness: X is true, therefore X is provable.
This is an odd and confusing way to state these, as it isn't clear that they are universally qualified.
Better is:
Consistency: For all X, if X is provable then X is true.
Completeness: For all X, if X is true then X is provable.
The layman's version of Godel's Incompleteness Theorem claims that in any closed system there are statements that are true and unprovable, because proving them would violate consistency.
That "because" omits a lot. Gödel's proof of his (first) Incompleteness Theorem shows that, given a consistent formal axiomatic system (capable of expressing elementary arithmetic), it is possible to construct a true statement (the "Gödel sentence" for that system) that cannot be proved. The Gödel sentence G is an encoding of the statement "G cannot be proved within the theory T". If G could be proved, that would be a contradiction, making the system inconsistent. And since it cannot be proved, it's true.
modified 20-Apr-15 22:47pm.
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jibalt wrote: Gödel's second incompleteness theorem states that a consistent system cannot prove its own consistency. And of course inconsistent systems can prove anything, true or false, including their consistency.
It's better said that if a system S includes a statement about its own consistency, then by definition S is inconsistent. To demonstrate its consistency, you have to include statements that are outside of S.
jibalt wrote: This is an odd and confusing way to state these, as it isn't clear that they are universally qualified.
Granted, that's the way I learned it, but we could nitpick all day, since it should say:
Consistency: For all X \in S, ...
because there are statements outside of S that can "declare" the completeness of S. Of course, that would create a new system S_0, which has its own "Godel sentence". And so on.
jibalt wrote: If G could be proved, that would be a contradiction, making the system inconsistent. And since it cannot be proved, it's true.
It's not that "since it cannot be proved, it's true"; every false statement in S could be considered true by that phrase, which would break consistency.
My understanding of Godel's ITs (once again, as someone who's still grasping wisps of understanding about it): If a system has to discard either consistency or completeness, consistency is more important, so completeness goes out the window. G has to be true and unproven, violating completeness, since proving G would violate consistency, which defeats the purpose of having the system in the first place.
(Apologies for leaving out the o with the dieresis atop; Godel deserves to have his name written correctly, but I'm at a loss on how to type it with my current keyboard settings.)
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"It's better said that if a system S includes a statement about its own consistency, then by definition S is inconsistent."
No it isn't. You don't even seem to what a definition is.
I didn't bother to read further.
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jibalt wrote: You don't even seem to KNOW what a definition is.
FTFY
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Marc Clifton wrote: Without evil, we wouldn't know what good is. Thus, evil is simply a "lesser good".
That smacks of Manicheanism...
If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack.
--Winston Churchill
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No, no, it doesn't. Really, it doesn't!
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I actually didn't know they had this motto. I googled it (cough), found a Wikipedia page about it and on there this note:
Google now appears to have dropped the original motto altogether (a carefully reworded version remains on the aforementioned Google Code of Conduct as of 10 April 2015, "You can make money without doing evil" [..])
If the brain were so simple we could understand it, we would be so simple we couldn't. — Lyall Watson
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Sascha Lefévre wrote: You can make money without doing evil
Can they?  Why is Google obsessed with the word "evil" anyways?
“Everything is simple when you take your time to analyze it.”
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Because they're 'projecting'...they blame everyone else for their own shortcomings ie: they're evil.
You see this a lot...for example, people who 'promote awareness' seem to have a severe lack of it themselves.
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My favourites are the conspiracy theorists who say that we should have secret meetings to discuss how to deal with all the conspiracies.
I wanna be a eunuchs developer! Pass me a bread knife!
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Didn't you get the email invite to the one on Tuesday?
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
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What?!
No, I didn't!
It's a plot, isn't it?!
Someone in the group is trying to get one over on me!
We need to discuss this. Choose a date -- and don't tell the others!
I wanna be a eunuchs developer! Pass me a bread knife!
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It's more of a guideline.
I wanna be a eunuchs developer! Pass me a bread knife!
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I rather read it as an acknowledgement.. yes, it's possible; you are free to choose so, but why would we?
If the brain were so simple we could understand it, we would be so simple we couldn't. — Lyall Watson
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In the future, when we are all using driver-less Google cars and you make a statement like that, you'll die in a freak car 'accident'.
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Hehehe 
“Everything is simple when you take your time to analyze it.”
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It's an anagram of "Embody Evil".
(Hey, that's about as accurate as half the statements made in meetings, and there's a chance he's dylsexic, and I'll get away with it)
I wanna be a eunuchs developer! Pass me a bread knife!
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It's an anagram of "Violent Bed" if that helps?
Bad command or file name. Bad, bad command! Sit! Stay! Staaaay...
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I'm sure it would help someone; just not sure whom.
I wanna be a eunuchs developer! Pass me a bread knife!
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