Godel's Incompleteness Theorem

blackzeus

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Godel was also a paranoid schizophrenic so I can't take his views on religion seriously

http://en.wikipedia.org/wiki/Ad_hominem

An ad hominem (Latin for "to the man" or "to the person"[1]), short for argumentum ad hominem, is a general category of fallacies in which a claim or argument is rejected on the basis of some irrelevant fact about the author of or the person presenting the claim or argument.

Mathematicians invoking logical fallacies to prove a point? Say it ain't so
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Remember, it's Godell laughing at you, not me.
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I would pay good money to be able to take a time machine back to when Godell did his best Martin Luther impression and dropped this bomb on the Math Priests :lolbron:
 

blackzeus

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Really is amazing how much boils down to "trust what you repeatedly observe." even in modern science and mathematics :wow:

It's amazing how much theory and phenomena exists that we can't prove but know to be true :wow: Greeks and Egyptians had it right when they called their universities temples of learning. I'll never forget when I was using Fourier diff equations for digital signal processing in my comp-e days, we were learning how to design filters for converting analog signals to digital signals (butterworth, hi pass, lo pass, etc). I'm lookin' at some of the sh*t like :why:, how did y'all prove this, the professor straight up told me "Don't think, just believe". :lawd: I never forgot because that's the EXACT same thing the pastor at the church I used to go to as a kid used to say.
 
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Y'all need to get to the background of what is going on here, for a deeper understanding, y'all missin' the point like the Miami Heat. Here is a wiki link on Godel:

http://en.wikipedia.org/wiki/Kurt_Gödel#Religious_views



Y'all not realizing that Godel just shat on modern math with his theory. All the major scientists of his era (and let's be real, the 30-50s was the last TRUE era of advancement in scientific theory)

Not true. There have been huge leaps in scientific discoveries and formulations since the fifties.


were saying evolution this and God doesn't exist that, and faith is b.s. bla bla bla. Godel was like, "O rly? :mjpls: let's have a look see at the basis of your great math, natural numbers. Well I can't believe it, these numbers ain't loyal!
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Can I join your religion of math?"
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Not quite right, either. The setting was less auspicious than all that. Hilbert set up a challenge for mathematicians to settle the big questions (as he perceived them) in maths. One of them was showing conclusively how a mathematical theorem can be complete and consistent. Goedel showed that it was impossible. That's not to say that mathematical theorems themselves become nullified or reduced to statements of faith, just that they can't be proven to be consistent nor complete.

Incidentally, barely anyone noticed what Goedel did when he first presented his first paper on incompleteness. The positivist interpreters of Wittgenstein held sway. Took quite a while for it to make a ripple, then an effect.

Edit: I should add that Goedel didn't understand the theory of evolution, and that might have led him to dismiss it. Not that it really has anything to do with the Incompleteness theorems.
 

blackzeus

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Not true. There have been huge leaps in scientific discoveries and formulations since the fifties.

How much have we advanced since the days of Einstein and E=MC^2 in regards to theoretical physics? We took a quantum leap (:lolbron:) from the '00s to the '50s. People were talking about electric cars since the 20s breh. Most of the new recent advancements have been in data storage, data monitoring, and communications (and the associated monitoring thereof). I wonder why that is? :mjpls:



Not quite right, either. The setting was less auspicious than all that. Hilbert set up a challenge for mathematicians to settle the big questions (as he perceived them) in maths. One of them was showing conclusively how a mathematical theorem can be complete and consistent. Goedel showed that it was impossible. That's not to say that mathematical theorems themselves become nullified or reduced to statements of faith, just that they can't be proven to be consistent nor complete.

While I do agree with the bolded, it wasn't as much a challenge as it was a think tank of sorts, on the desire to collaborate with other mathematicians/scientists to formalize and prove all math can follows from a finite set of rules/axioms, the mathematical tower of Babel if you will. Then Godel came and .....

nuclear-explosion-o.gif


Incidentally, barely anyone noticed what Goedel did when he first presented his first paper on incompleteness. The positivist interpreters of Wittgenstein held sway. Took quite a while for it to make a ripple, then an effect.

You mean to say disciples, no?
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( btw, the harmonic resonance in their dancing is otherworldly :to:). It is what it is breh, yo, let me know if you computer has defined pi yet
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How much have we advanced since the days of Einstein and E=MC^2 in regards to theoretical physics? We took a quantum leap (:lolbron:) from the '00s to the '50s. People were talking about electric cars since the 20s breh. Most of the new recent advancements have been in data storage, data monitoring, and communications (and the associated monitoring thereof). I wonder why that is? :mjpls:

Well since Einstein and his ilk, scientific theories have advanced considerably. The path, actually, is flowing in much of the same way that eventually presented the world with the theory of relativity, etc. Quantum mechanics and the theory attempting to describe the quantum world are blossoming. The presence of the Higgs boson has been verified, which in turn, is another step towards narrowing down the makings of our universe. That's just one example in physics. In biochemistry, cloning is yet another example of progress. Many more abound.

While I do agree with the bolded, it wasn't as much a challenge as it was a think tank of sorts, on the desire to collaborate with other mathematicians/scientists to formalize and prove all math can follows from a finite set of rules/axioms, the mathematical tower of Babel if you will. Then Godel came and .....

nuclear-explosion-o.gif

Yes, but, in retrospect, I think that was the only logical conclusion.


You mean to say disciples, no?
praise-at-church-o.gif
( btw, the harmonic resonance in their dancing is otherworldly :to:). It is what it is breh, yo, let me know if you computer has defined pi yet
tumblr_n4cpiliw9K1rz36j2o1_100.png

Some were disciples, others merely convinced Wittgenstein's arguments had merits. Young Goedel was probably the latter, as he was, for a good while, a member of a positivist group.

By the way, why would I expect my (or any) computer to define pi?
 

blackzeus

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Edit: I should add that Goedel didn't understand the theory of evolution, and that might have led him to dismiss it. Not that it really has anything to do with the Incompleteness theorems.

So Goedel destroys the whole idea of lack of intelligent design aka all encompassing axiom based math via mathspeak aka logic, which possibly makes him the greatest philosopher/logician of all time, and you claim to say this same man didn't understand the theory of evolution from Darwin the Incestuous Quack?

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Now I understand why Jesus whipped you moneychangers, desecrating the temple of learning with your petty exchanges of worthless logic

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blackzeus

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Well since Einstein and his ilk, scientific theories have advanced considerably. The path, actually, is flowing in much of the same way that eventually presented the world with the theory of relativity, etc. Quantum mechanics and the theory attempting to describe the quantum world are blossoming. The presence of the Higgs boson has been verified, which in turn, is another step towards narrowing down the makings of our universe. That's just one example in physics. In biochemistry, cloning is yet another example of progress. Many more abound.

So confirming a 50 year old theory is advancement?
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What quantum leap have we taken breh? Where is the Unified Field Theory breh? There is no comparison between the 1850s and 1950s, and 1960s and now. Most of the modern advancement in physical technology is based on ideas from damn near 100 years ago breh. The integrated circuit was invented in 1949, and we're still using it almost 70 years later.



Yes, but, in retrospect, I think that was the only logical conclusion.

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Some were disciples, others merely convinced Wittgenstein's arguments had merits. Young Goedel was probably the latter, as he was, for a good while, a member of a positivist group.

By the way, why would I expect my (or any) computer to define pi?

Inherent limitations breh, inherent limitations.
 
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So Goedel destroys the whole idea of lack of intelligent design via mathspeak aka logic,

Um, no he didn't. I invite you to re-read Goedel's ontological proof once again.

which possibly makes him the greatest philosopher/logician of all time, and you claim to say this same man didn't understand the theory of evolution from Darwin the Incestuous Quack?

3727390-1171196867-23243.gif

Um, no again. I'm saying he didn't understand the theory of evolution based on the comments he made on the theory. Statements that show a gap in knowledge on the subject. The theory of evolution isn't intrinsically linked to theology: both atheists and theists accept it, so it has nothing to do with any of the gods existing.

Now I understand why Jesus whipped you moneychangers, desecrating the temple of learning with your petty exchanges of worthless logic

jesusmoneychangers.jpg
tumblr_n4cpiliw9K1rz36j2o2_250.png

In the quiet words of the Virgin Mary, "Come again?"
 
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So confirming a 50 year old theory is advancement?
tumblr_n4cpiliw9K1rz36j2o2_250.png

Yup. Do you think Einstein won his prizes for inventing science? His first was for formulating and confirming effects on and related to the photoelectric effect: a phenomena that had been worked on for many decades before he arrived on the scene. The same goes for his theories on relativity. Built on formulations and findings by contemporaries and scientists from many centuries before his time. That's what science is: "standing on the shoulders of giants".

What quantum leap have we taken breh? Where is the Unified Field Theory breh? There is no comparison between the 1850s and 1950s, and 1960s and now. Most of the modern advancement in physical technology is based on ideas from damn near 100 years ago breh. The integrated circuit was invented in 1949, and we're still using it almost 70 years later.

...and Brownian motion was first discovered in the early 19th century. Einstein was one of the scientists that finally made a breakthrough on it, (what, a century later?). That's science. We still use Newton's laws. I gave a couple of examples of advancements. You glossed over them.





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Inherent limitations breh, inherent limitations.
Yes, so neither of us are expecting miracles from computers.
 

blackzeus

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Um, no he didn't. I invite you to re-read Goedel's ontological proof once again.

http://en.wikipedia.org/wiki/Gödel's_ontological_proof

Cliff Notes:

It is in a line of development that goes back to Anselm of Canterbury (1033–1109). St. Anselm's ontological argument, in its most succinct form, is as follows: "God, by definition, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist."

When can no greater be conceived? Can we conceive infinity+1 ? If we can't, but we BELIEVE it exists, then God exists in our understanding. If God exists in OUR understanding (which is pathetic since we can't even sum divergent series), how can he not exist in ALL reality?

^^^^^How is this not a proof of intelligent design? If you can't conceive something you believe to exists, then something greater than you must have designed it! You nikkaz man. :mindblown:


Um, no again. I'm saying he didn't understand the theory of evolution based on the comments he made on the theory. Statements that show a gap in knowledge on the subject. The theory of evolution isn't intrinsically linked to theology: both atheists and theists accept it, so it has nothing to do with any of the gods existing.

1shty4xn.wizardchan.this-cannot-be-real.gif
I have no words for your breh.




In the quiet words of the Virgin Mary, "Come again?"

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Go exchange your philosophies elsewhere breh, you desecrating our temple of learning :blessed:
 

blackzeus

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Yup. Do you think Einstein won his prizes for inventing science? His first was for formulating and confirming effects on and related to the photoelectric effect: a phenomena that had been worked on for many decades before he arrived on the scene. The same goes for his theories on relativity. Built on formulations and findings by contemporaries and scientists from many centuries before his time. That's what science is: "standing on the shoulders of giants".



...and Brownian motion was first discovered in the early 19th century. Einstein was one of the scientists that finally made a breakthrough on it, (what, a century later?). That's science. We still use Newton's laws. I gave a couple of examples of advancements. You glossed over them.



Breh we used Newtonian physics for almost 250 years before Einstein, Planck, Bohr, etc came along. What they did was groundbreaking, what we have done is not, we have merely just applied their breakthroughs to real life situations. DNA cloning is based on isolating endonucleases, and inserting them into bactera that replicate DNA, but isolation of nuclei and molecular biology theory has been here since the 1870s. Applying theories is not the same as creating new ones. Please also note this is a total deviation from the original thread topic.


Yes, so neither of us are expecting miracles from computers.

Yes, and neither was Godel, finally something we can agree on :myman:
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http://en.wikipedia.org/wiki/Gödel's_ontological_proof

Cliff Notes:



When can no greater be conceived? Can we conceive infinity+1 ? If we can't, but we BELIEVE it exists, then God exists in our understanding. If God exists in OUR understanding (which is pathetic since we can't even sum divergent series), how can he not exist in ALL reality?

^^^^^How is this not a proof of intelligent design? If you can't conceive something you believe to exists, then something greater than you must have designed it! You nikkaz man. :mindblown:

You don't see anything wrong with your assumption? The assumption is taking Goedel's proof to leading logically to God (with a capital "g"), rather than to something greater than which a logician can conceive - i.e. supernatural being(s) or the universe/universes. Both have their logical and non-logical merits. Again,. I invite you to actually look at Goedel's proof and see what it actually shows.

Second, we can conceive of sets of infinity, so, to some extent we can describe a set describing infinite numbers and add one to it. Not sure why you think that argument adds anything constructive to Goedel's ontological proof.

Third, it might be that we are using different terminologies, but again, acceptance of the theory of evolution does not preclude theism. One can (and many do) accept the theory of evolution and be a theist. Now, with that out of the way, conceiving of deities really isn't evidence for intelligent design. Logically speaking, the conception is merely evidence of said deity potentially existing.

Finally, the inability to conceive of something is either evidence of the thing being a logical impossibility (Invisible Pink Unicorn, for instance. Or, for another, an immanent yet transcendent god), or the limited scope of the mind. It isn't proof of any gods.



1shty4xn.wizardchan.this-cannot-be-real.gif
I have no words for your breh.

Wait, you didn't actually think atheists had the exclusive rights to the theory of evolution, did you? Most of the people that accept evolution are theists. Some of the best biologists that study and teach the theory are Christians, etc.


stock-vector-jesus-overturns-the-money-changer-s-tables-68908939.jpg
Go exchange your philosophies elsewhere breh, you desecrating our temple of learning :blessed:

I see you've appointed yourself guard of the "temple of learning". Cool.

Breh we used Newtonian physics for almost 250 years before Einstein, Planck, Bohr, etc came along.

Not quite. The flaws in Newtonian physics had been apparent many decades before any of them appeared on the scene. Many scientists had been working on the problems inherent in Newtonian physics (particularly the gravity problem) before Einstein, building on their works, finally nailed it in an ingenious manner. Einstein's theories will be superseded some day, and the groundwork is being laid in much the same way it was laid before Einstein.

what we have done is not, we have merely just applied their breakthroughs to real life situations. DNA cloning is based on isolating endonucleases, and inserting them into bactera that replicate DNA, but isolation of nuclei and molecular biology theory has been here since the 1870s. Applying theories is not the same as creating new ones. Please also note this is a total deviation from the original thread topic.

Yes, and it's a huge deal to make that grand step from spotting and splicing DNA to cloning a mammal. It's a huge fukking deal. A monumental breakthrough. That's the same thing with science while Einstein, Bohr, Planck et al. were practising it. Don't over-glamourise it. From the improvements made by - encapsulated in the main figureheads of - Einstein, Bohr, Heisenberg, Pauli ... quantum theory has galvanised the world of physics. That's just to expand on my earlier example. These too are exciting days in science. You, perhaps, aren't following any of sciences too closely.

And I know we've diverged from the original topic, but you brought it up and I responded accordingly.

Yes, and neither was Godel, finally something we can agree on :myman:
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Oh, I suspect we agree on more things. Then again, I never made an assertion about the goings of computers, so:manny:
 

blackzeus

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You don't see anything wrong with your assumption? The assumption is taking Goedel's proof to leading logically to God (with a capital "g"), rather than to something greater than which a logician can conceive - i.e. supernatural being(s) or the universe/universes. Both have their logical and non-logical merits. Again,. I invite you to actually look at Goedel's proof and see what it actually shows.

Second, we can conceive of sets of infinity, so, to some extent we can describe a set describing infinite numbers and add one to it. Not sure why you think that argument adds anything constructive to Goedel's ontological proof.

Third, it might be that we are using different terminologies, but again, acceptance of the theory of evolution does not preclude theism. One can (and many do) accept the theory of evolution and be a theist. Now, with that out of the way, conceiving of deities really isn't evidence for intelligent design. Logically speaking, the conception is merely evidence of said deity potentially existing.

Finally, the inability to conceive of something is either evidence of the thing being a logical impossibility (Invisible Pink Unicorn, for instance. Or, for another, an immanent yet transcendent god), or the limited scope of the mind. It isn't proof of any gods.

You're right, I should fall back. Intelligent design /= Christian God. I concede to that.



Wait, you didn't actually think atheists had the exclusive rights to the theory of evolution, did you? Most of the people that accept evolution are theists. Some of the best biologists that study and teach the theory are Christians, etc.

This is a qualitative not quantitative statement. I expect better from you breh, and based on all the commotion in the Bible Belt rural South about teaching evolution in schools, it's hard to agree. And don't confuse teaching natural selection with belief in the evolutionary theory.



I see you've appointed yourself guard of the "temple of learning". Cool.

Not me, breh, Godel. And a nikka was just havin' fun, that's all :russ:

Not quite. The flaws in Newtonian physics had been apparent many decades before any of them appeared on the scene. Many scientists had been working on the problems inherent in Newtonian physics (particularly the gravity problem) before Einstein, building on their works, finally nailed it in an ingenious manner. Einstein's theories will be superseded some day, and the groundwork is being laid in much the same way it was laid before Einstein.

Breh the Industrial Revolution in the 1800s was built on Newtonian physics, and that same technology was used right up until the early 1900s with the lightyear (:lolbron:) advancements in theoretical physics. We went from cannons and gunships to satellites and atom bombs in less than 50 years :wow:



Yes, and it's a huge deal to make that grand step from spotting and splicing DNA to cloning a mammal. It's a huge fukking deal. A monumental breakthrough. That's the same thing with science while Einstein, Bohr, Planck et al. were practising it. Don't over-glamourise it. From the improvements made by - encapsulated in the main figureheads of - Einstein, Bohr, Heisenberg, Pauli ... quantum theory has galvanised the world of physics. That's just to expand on my earlier example. These too are exciting days in science. You, perhaps, aren't following any of sciences too closely.

And I know we've diverged from the original topic, but you brought it up and I responded accordingly.

It's a huge f*ckin' deal in practical application. Not so much in theoretical advancement. The modern travel industry would be impossible without the invention of the jet, doesn't mean there's been a great advancement in theoretical aerodynamics :manny: I will admit I haven't been following the sciences too closely since college, but trust me if they came out with a UFT I would have heard :russ:



Oh, I suspect we agree on more things. Then again, I never made an assertion about the goings of computers, so:manny:

True, we were responding back and forth. Just to finish in reference to the main topic, Godel was right, and the underlying theme behind his work was his intent to prove a higher power existed, whether it's the Christian God or the unicorn as you say is still up for debate :russ:
 
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