"Don't be evil"
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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 thought Godel proved that a system can't prove its own consistency unless it is inconsistent. So, Google is bad :-D
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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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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Google is king when it comes to violating it's own motto "Don't be evil" :laugh:
“Everything is simple when you take your time to analyze it.”
Not that examples are so hard to come by, but doesn't an assertion like this deserve just a little support? What did google do that pushed you into the "evil" camp? It has to be more than just realizing that all ad brokers are evil by construction. I mean, I know why google seems evil to me... * Owning the internet verb for "to search", and adulterating search results with paid content is pretty evil. * Announcing an open source operating system for phones and then after it is accepted spending years replacing it bit-by-bit with proprietary content is pretty evil. * Conspiring with a cartel of Silicon Valley employers to tamp down wages for the geeky talent that makes it great is pretty evil. I just wondered what you woke up to.
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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.
> 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.
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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.
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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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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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".
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 that examples are so hard to come by, but doesn't an assertion like this deserve just a little support? What did google do that pushed you into the "evil" camp? It has to be more than just realizing that all ad brokers are evil by construction. I mean, I know why google seems evil to me... * Owning the internet verb for "to search", and adulterating search results with paid content is pretty evil. * Announcing an open source operating system for phones and then after it is accepted spending years replacing it bit-by-bit with proprietary content is pretty evil. * Conspiring with a cartel of Silicon Valley employers to tamp down wages for the geeky talent that makes it great is pretty evil. I just wondered what you woke up to.
I woke up to the fact that Google's Android developer program is not fair. Besides that I have nothing against Google. I'am not in the "evil" camp, that's sounds bad :laugh:
“Everything is simple when you take your time to analyze it.”
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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.
jibalt wrote:
You don't even seem to KNOW what a definition is.
FTFY
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Not that examples are so hard to come by, but doesn't an assertion like this deserve just a little support? What did google do that pushed you into the "evil" camp? It has to be more than just realizing that all ad brokers are evil by construction. I mean, I know why google seems evil to me... * Owning the internet verb for "to search", and adulterating search results with paid content is pretty evil. * Announcing an open source operating system for phones and then after it is accepted spending years replacing it bit-by-bit with proprietary content is pretty evil. * Conspiring with a cartel of Silicon Valley employers to tamp down wages for the geeky talent that makes it great is pretty evil. I just wondered what you woke up to.
heheheh Very well played sir... Kudos to your eloquence and truth friend!
"... having only that moment finished a vigorous game of Wiff-Waff and eaten a tartiflet." - Henry Minute "Let's face it, after Monday and Tuesday, even the calendar says WTF!" - gavindon Programming is a race between programmers trying to build bigger and better idiot proof programs, and the universe trying to build bigger and better idiots, so far... the universe is winning. - gavindon