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Science Forum Index » Logic Forum » What should I say to the post-grads about Godel?...
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| John Jones |
Posted: Fri Jun 13, 2008 2:04 pm |
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Joined: 26 Oct 2004
Posts: 4263
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The Prof has asked me to briefly introduce to the post-grads the
significance of Godel's incompleteness theorem to logic, notions of
determinism and free-will, and to other pertinent issues in philosophy.
This might include a discussion on the significance of proof itself.
What would you say to them on this topic? A few are analytic
philosophers, but most are, I think, continentalists, though this
shouldn't matter as Godel seems to be branching everywhere. These guys
aren't stupid though .. |
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| MoeBlee... |
Posted: Fri Jun 13, 2008 2:04 pm |
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Guest
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On Jun 13, 12:04 pm, John Jones <jonescard... at (no spam) aol.com> wrote:
Quote: The Prof has asked me to briefly introduce to the post-grads the
significance of Godel's incompleteness theorem to logic, notions of
determinism and free-will, and to other pertinent issues in philosophy.
This might include a discussion on the significance of proof itself.
What would you say to them on this topic? A few are analytic
philosophers, but most are, I think, continentalists, though this
shouldn't matter as Godel seems to be branching everywhere. These guys
aren't stupid though ..
Why in the world would you presume (other than your prof's clearly
deranged recommendation) to discuss Godel's incompleteness theorem at
a post-graduate level when you know virtually zilch about basic logic
at a freshman level?
MoeBlee |
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| Chris Menzel... |
Posted: Fri Jun 13, 2008 2:04 pm |
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On Fri, 13 Jun 2008 12:18:14 -0700 (PDT), MoeBlee <jazzmobe at (no spam) hotmail.com>
said:
Quote: On Jun 13, 12:04 pm, John Jones <jonescard... at (no spam) aol.com> wrote:
The Prof has asked me to briefly introduce to the post-grads the
significance of Godel's incompleteness theorem to logic, notions of
determinism and free-will, and to other pertinent issues in
philosophy. This might include a discussion on the significance of
proof itself.
What would you say to them on this topic? A few are analytic
philosophers, but most are, I think, continentalists, though this
shouldn't matter as Godel seems to be branching everywhere. These
guys aren't stupid though ..
Why in the world would you presume (other than your prof's clearly
deranged recommendation) to discuss Godel's incompleteness theorem at
a post-graduate level when you know virtually zilch about basic logic
at a freshman level?
Wait, now, there's plenty of great stuff he can find about Gödel's
theorem on the internet that he can share with his fellow Seekers:
* Minds are not machines
* Determinism is false (follows from previous)
* There are unprovable truths
* Gödel's theorem is actually unknowable because it involves self-reference
* All knowledge is self-referential
* The universe is ultimately unknowable (follows from previous)
* Morality is relative.
That'll get him started. Knock 'em dead, JJ!
ps: Oh, wait, that last one follows from Einstein, sorry. |
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| MoeBlee... |
Posted: Fri Jun 13, 2008 2:04 pm |
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On Jun 13, 1:29 pm, Chris Menzel <cmen... at (no spam) remove-this.tamu.edu> wrote:
Quote: On Fri, 13 Jun 2008 12:18:14 -0700 (PDT), MoeBlee <jazzm... at (no spam) hotmail.com
said:
On Jun 13, 12:04 pm, John Jones <jonescard... at (no spam) aol.com> wrote:
The Prof has asked me to briefly introduce to the post-grads the
significance of Godel's incompleteness theorem to logic, notions of
determinism and free-will, and to other pertinent issues in
philosophy. This might include a discussion on the significance of
proof itself.
What would you say to them on this topic? A few are analytic
philosophers, but most are, I think, continentalists, though this
shouldn't matter as Godel seems to be branching everywhere. These
guys aren't stupid though ..
Why in the world would you presume (other than your prof's clearly
deranged recommendation) to discuss Godel's incompleteness theorem at
a post-graduate level when you know virtually zilch about basic logic
at a freshman level?
Wait, now, there's plenty of great stuff he can find about Gödel's
theorem on the internet that he can share with his fellow Seekers:
* Minds are not machines
* Determinism is false (follows from previous)
* There are unprovable truths
* Gödel's theorem is actually unknowable because it involves self-reference
* All knowledge is self-referential
* The universe is ultimately unknowable (follows from previous)
* Morality is relative.
That'll get him started. Knock 'em dead, JJ!
ps: Oh, wait, that last one follows from Einstein, sorry.
From Skolem too, because, any theory of moral behavior is utlimately
only relative to different non-standard models!
MoeBlee |
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| Newberry... |
Posted: Fri Jun 13, 2008 5:31 pm |
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On Jun 13, 12:04 pm, John Jones <jonescard... at (no spam) aol.com> wrote:
Quote: The Prof has asked me to briefly introduce to the post-grads the
significance of Godel's incompleteness theorem to logic, notions of
determinism and free-will, and to other pertinent issues in philosophy.
This might include a discussion on the significance of proof itself.
What would you say to them on this topic? A few are analytic
philosophers, but most are, I think, continentalists, though this
shouldn't matter as Godel seems to be branching everywhere. These guys
aren't stupid though ..
You should stress that Goedel's incompleteness theorem has nothing to
do with determinism and free will. |
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| Jesse F. Hughes... |
Posted: Fri Jun 13, 2008 8:19 pm |
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John Jones <jonescardiff at (no spam) aol.com> writes:
Quote: The Prof has asked me to briefly introduce to the post-grads the
significance of Godel's incompleteness theorem to logic, notions of
determinism and free-will, and to other pertinent issues in philosophy.
This might include a discussion on the significance of proof itself.
What would you say to them on this topic?
My condolences on the occasion of learning about Godel from John
Jones.
Quote: A few are analytic philosophers, but most are, I think,
continentalists, though this shouldn't matter as Godel seems to be
branching everywhere. These guys aren't stupid though ..
Well, then maybe the damage will be minimal.
--
"I'd step through arguments in such detail that it was like I was
teaching basic arithmetic and some poster would come back and act like
I hadn't said anything that made sense. For a while I almost started
to doubt myself." -- James S. Harris, so close and yet.... |
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| herbzet... |
Posted: Fri Jun 13, 2008 10:05 pm |
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John Jones wrote:
Quote:
The Prof has asked me to briefly introduce to the post-grads the
significance of Godel's incompleteness theorem to logic, notions of
determinism and free-will, and to other pertinent issues in philosophy.
This might include a discussion on the significance of proof itself.
What would you say to them on this topic? A few are analytic
philosophers, but most are, I think, continentalists, though this
shouldn't matter as Godel seems to be branching everywhere. These guys
aren't stupid though ..
I think you should take some pains to correctly _state_ the two
incompleteness theorems before attempting to discuss the nature
of the proofs or the philosophical significance of the theorems.
The _statement_ of the theorems is not that hard, and leads naturally
to the other topics.
[You might also want first to distinguish the incompleteness theorems
from Godel's completeness theorem (his Phd thesis) -- or maybe not.]
Well-begun is half-done.
--
hz |
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| Marshall... |
Posted: Sat Jun 14, 2008 8:07 am |
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On Jun 14, 7:54 am, Jan Burse <janbu... at (no spam) fastmail.fm> wrote:
Quote: John Jones schrieb:
Godel and Turin were both troubled with their theories. Both authors
were more concerned about the status of human thought or the mind which
their theories or ideas offered, ather than the theories themselves. I'm
surprised you didn't know that.
And turing was homosexual and troubled,
thats why he lost his g, and became turin.
That was a sad time; let us put over it a veil,
a shroud of turin, if you will.
Marshall |
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| translogi... |
Posted: Sat Jun 14, 2008 8:13 am |
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On Jun 13, 8:04 pm, John Jones <jonescard... at (no spam) aol.com> wrote:
Quote: The Prof has asked me to briefly introduce to the post-grads the
significance of Godel's incompleteness theorem to logic, notions of
determinism and free-will, and to other pertinent issues in philosophy.
This might include a discussion on the significance of proof itself.
What would you say to them on this topic? A few are analytic
philosophers, but most are, I think, continentalists, though this
shouldn't matter as Godel seems to be branching everywhere. These guys
aren't stupid though ..
Maybe he wants you to sing Boolos article of godels theorem in words
of one syllable.
It doesn't rhyme but you can do it in stacatto.
with many preformers in harmony and every next preformer starting
after the previous preformer says "proved" or "prove" it will make a
nice preformance. (but you do need a lot of preformers, (38)
(It is in Boolos Logic logic logic, Have also a look at the other
articles maybe you can learn something from it)
But probably it is better to start with Pospesels "propositional
logic"
Or if your harmony isn't all to good you can rap it.
It is all short words so it is likely that it is posible.
(I am not a rap fan)
But please don't try to explain it if you don't understand it
yourself. or disagree with it.
Greetings |
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| Nam D. Nguyen... |
Posted: Sat Jun 14, 2008 11:03 am |
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Neil W Rickert wrote:
Quote: John Jones <jonescardiff at (no spam) aol.com> writes:
The Prof has asked me to briefly introduce to the post-grads the
significance of Godel's incompleteness theorem to logic, notions of
determinism and free-will, and to other pertinent issues in philosophy.
This might include a discussion on the significance of proof itself.
What would you say to them on this topic?
Goedel's theorem is a technical result within mathematical logic,
with no significance elsewhere.
Perhaps so. But it's interesting to note that a mathematical logic
technical result would have "no significance elsewhere", given the
importance of mathematics elsewhere!
Quote: In particular, it has zero significance with respect to notions of
determinism and free will.
That of course isn't true. The notion of "determinism" is vested in
syntactical provability, and "free will" in the concept of the natural
numbers! |
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| Nam D. Nguyen... |
Posted: Sat Jun 14, 2008 11:48 am |
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Nam D. Nguyen wrote:
Quote: Neil W Rickert wrote:
John Jones <jonescardiff at (no spam) aol.com> writes:
The Prof has asked me to briefly introduce to the post-grads the
significance of Godel's incompleteness theorem to logic, notions of
determinism and free-will, and to other pertinent issues in
philosophy. This might include a discussion on the significance of
proof itself.
What would you say to them on this topic?
Goedel's theorem is a technical result within mathematical logic,
with no significance elsewhere.
Perhaps so. But it's interesting to note that a mathematical logic
technical result would have "no significance elsewhere", given the
importance of mathematics elsewhere!
In particular, it has zero significance with respect to notions of
determinism and free will.
That of course isn't true. The notion of "determinism" is vested in
syntactical provability, and "free will" in the concept of the natural
numbers!
One could then see why, as a "technical" result, GIT bears no importance
of the kind of mathematics we use to *prove* in practical applications.
One can't in general use free will to prove determinism. Similarly, neither
can one use the *assumed* arithmetic truths (which is a weaker notion)
to prove the syntactical consistency (which is a stronger notion) of, say, PA. |
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| Neil W Rickert... |
Posted: Sat Jun 14, 2008 3:10 pm |
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"Nam D. Nguyen" <namducnguyen at (no spam) shaw.ca> writes:
Quote: Neil W Rickert wrote:
Goedel's theorem is a technical result within mathematical logic,
with no significance elsewhere.
Perhaps so. But it's interesting to note that a mathematical logic
technical result would have "no significance elsewhere", given the
importance of mathematics elsewhere!
You are making a generalizationn to all technical results within
mathematical logic. However there is nothing in what I said that
would license such a generalization.
Quote: In particular, it has zero significance with respect to notions of
determinism and free will.
That of course isn't true. The notion of "determinism" is vested in
syntactical provability, and "free will" in the concept of the natural
numbers!
I believe the original author was referring to the philosophical
concepts of "free will" and "determinism", and not to determinism
within formal systems. |
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| John Jones |
Posted: Sat Jun 14, 2008 4:17 pm |
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Joined: 26 Oct 2004
Posts: 4263
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Nam D. Nguyen wrote:
Quote: Neil W Rickert wrote:
That of course isn't true. The notion of "determinism" is vested in
syntactical provability, and "free will" in the concept of the natural
numbers!
Say more please. Why does the concept of natural numbers imply
free-will? The only reason I can come up with is that, against Godel,
these numbers must be made, and are not given. And so, if we are
creative agents, then we have free-will.
Is this what you meant? |
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| John Jones |
Posted: Sat Jun 14, 2008 4:20 pm |
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Joined: 26 Oct 2004
Posts: 4263
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Neil W Rickert wrote:
Quote: "Nam D. Nguyen" <namducnguyen at (no spam) shaw.ca> writes:
Neil W Rickert wrote:
Goedel's theorem is a technical result within mathematical logic,
with no significance elsewhere.
Perhaps so. But it's interesting to note that a mathematical logic
technical result would have "no significance elsewhere", given the
importance of mathematics elsewhere!
You are making a generalizationn to all technical results within
mathematical logic. However there is nothing in what I said that
would license such a generalization.
In particular, it has zero significance with respect to notions of
determinism and free will.
That of course isn't true. The notion of "determinism" is vested in
syntactical provability, and "free will" in the concept of the natural
numbers!
I believe the original author was referring to the philosophical
concepts of "free will" and "determinism", and not to determinism
within formal systems.
More exactly, employing 'technical' mathematics to pass judgemnent on
the way of the world, rather than vice versa. Are we machines for example. |
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| John Jones |
Posted: Sat Jun 14, 2008 4:27 pm |
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Joined: 26 Oct 2004
Posts: 4263
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translogi wrote:
Quote: On Jun 13, 8:04 pm, John Jones <jonescard... at (no spam) aol.com> wrote:
The Prof has asked me to briefly introduce to the post-grads the
significance of Godel's incompleteness theorem to logic, notions of
determinism and free-will, and to other pertinent issues in philosophy.
This might include a discussion on the significance of proof itself.
What would you say to them on this topic? A few are analytic
philosophers, but most are, I think, continentalists, though this
shouldn't matter as Godel seems to be branching everywhere. These guys
aren't stupid though ..
Maybe he wants you to sing Boolos article of godels theorem in words
of one syllable.
It doesn't rhyme but you can do it in stacatto.
with many preformers in harmony and every next preformer starting
after the previous preformer says "proved" or "prove" it will make a
nice preformance. (but you do need a lot of preformers, (38)
(It is in Boolos Logic logic logic, Have also a look at the other
articles maybe you can learn something from it)
But probably it is better to start with Pospesels "propositional
logic"
Or if your harmony isn't all to good you can rap it.
It is all short words so it is likely that it is posible.
(I am not a rap fan)
But please don't try to explain it if you don't understand it
yourself. or disagree with it.
Greetings
It was in the woods of course that Godel first worked on the Interim
Hypothesis before accidentally straying from the leafy path until,
wandering into the abandoned woodchoppers hut, he at last found his way
back with the help of all his forest friends. |
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