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| Author |
Message |
orinoco
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Eat your heart out, spock!
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Dec 5 21:56 UTC 1994 |
Heh! Just read about Goedel's theorem--here's a goodie!
Goedel, after much work, proved that our system of logical reasoning is
inconsistant using--here's the catch--our system of logical reasoning. So
if this system of logic is wrong, then Goedel's proof is wrong, so our system
is right after all.
That's kinda like the one where the professor tells the class about a system
of time travel that he developed, so they plot to go back in time to kill the
professor. This means that the professor couldn't have invented time travel,
being dead, so the students couldn't have killed him, so he would have lived
after all. The point of that paradox is to prove that time travel is
impossibel, so does that mean that the first one proves that logic is
impossible?
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| 24 responses total. |
sidhe
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response 1 of 24:
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Dec 7 03:44 UTC 1994 |
A quick scan of how the world runs itself will tell you that logic is a
manufactured concept!
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peacefrg
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response 2 of 24:
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Dec 8 02:41 UTC 1994 |
AAAAAAAAAAaaaaaaaa.......!!!!!!
I'm confused.
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jkrauss
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response 3 of 24:
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Dec 9 00:51 UTC 1994 |
Dammit, pseudos aren't allowed to be smarter than their creators, orin!
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orinoco
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response 4 of 24:
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Dec 13 01:33 UTC 1994 |
yes they are!
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selena
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response 5 of 24:
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Dec 28 21:43 UTC 1994 |
Dammit orin, I'm a model, not a vulcan!
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ashdown
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response 6 of 24:
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Jan 3 22:53 UTC 1995 |
Would'nt time travel take you back to a point intime where as
all outcomes from this moment in time are different from the reality
you left in the future. Time is a tree with many branches.
As you climb up you have many choices which branch to take.
Time traveling in the past would give you the opportunity
to take different paths as you head to the top branches where you
die. And stop thinking time is linear!
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sidhe
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response 7 of 24:
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Jan 9 02:42 UTC 1995 |
Indeed, time is not linear, so much as it is a vibrational frequency.
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ashdown
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response 8 of 24:
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Jan 9 23:29 UTC 1995 |
How true
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nephi
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response 9 of 24:
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Jan 21 07:08 UTC 1995 |
Orinoco, please tell us more about Goedel's theorem. I'm really interested.
Could you state his proof?
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sidhe
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response 10 of 24:
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Jan 23 05:26 UTC 1995 |
yes, please?
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selena
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response 11 of 24:
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Mar 24 16:31 UTC 1995 |
ooorin...
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nephi
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response 12 of 24:
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Mar 25 08:12 UTC 1995 |
I just mailed him the entire item to try to get him to come back
here and enlighten us.
Hope it works.
8*)
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orinoco
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response 13 of 24:
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Mar 25 22:53 UTC 1995 |
Alright, here's what Goedel did.
<orinoco thumbs through a generic dusty tome>
To do this, i must first define two terms. First, the term "proof pair".
the two statements A and B are a proof-pair if you can proove B by starting
with A as an axiom. Suppose that statement A is "x=1" and statement B is
"x+1=2" Then, the two statements would form a proof-pair. You can prove B,
using algebra, from statement A. Is everybody still with me? Any questions?
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selena
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response 14 of 24:
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Mar 26 06:42 UTC 1995 |
go on..
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nephi
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response 15 of 24:
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Mar 26 10:03 UTC 1995 |
..ditto..
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orinoco
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response 16 of 24:
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Apr 1 02:33 UTC 1995 |
Ok, now for the next step.
Suppose that any logical statement could be transformed into
a number, three digits for each symbol. Thus, if x was 111
in this code, 1 was 222, and = was 333, the statement
x=1 (our friend statement A) would become 111333222.
We can then say that two *numbers* form a proof-pair
if the two *statements* that they translate into form
a proof-pair.
Now, suppose that there is another function, call it
arithmoquine, that acts on two numbers to produce a
one-number result. (I am not exactly clear on *how*
the arithmoquine function works, more on that later)
Then, make a statement (call it G) in the logical symbols
of your choice that says the following:
Rthere arenUt two numbers, x and y, such that they form a
proof-pair, *and* x is the arithmoquine of a number called
uS
now, as it turns out, Goedel figured out what number u is,
and (this is the sneaky part) *when you arithmoquine u, you
get the statement G!* So what Goedel is saying in statement
G is that
Rthere arenUt two numbers, x and y, such that they form a
proof-pair, and x is statement GS
cleaning it up a little more you get
Rthere is no number, y, such that G and y form a proof-pairS
or, better yet,
Rthere is no statement that you can prove *this statement*
fromS
Eat your heart out, Spock
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orinoco
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response 17 of 24:
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Apr 1 15:41 UTC 1995 |
those R's and S's should be "'s
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nephi
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response 18 of 24:
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Apr 2 07:53 UTC 1995 |
I'm still confused.
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orinoco
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response 19 of 24:
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Apr 6 23:15 UTC 1995 |
what part don't you get....i realize that it can be confusing, but i can't help
unless i know what you need help on....
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selena
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response 20 of 24:
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Apr 7 14:42 UTC 1995 |
The MAJORITY of it.
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orinoco
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response 21 of 24:
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Apr 9 20:48 UTC 1995 |
Pretty much, he just made a statement that says "YOU CAN'T PROVE ME!"
if it's a true statement, then you can't prove it, and if there's a true
statement you can't prove then logic must be flawed...
if it's false, you CAN prove it, and if you can prove something false then
logic must be flawed....
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selena
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response 22 of 24:
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Apr 10 05:28 UTC 1995 |
Logic IS flawed. That should be a given.
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orinoco
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response 23 of 24:
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Apr 13 18:49 UTC 1995 |
you can't even avoid the problem by inserting the idea of unprovable
statements...."you can prove that this is false" should work....
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jhudson
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response 24 of 24:
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Nov 21 01:06 UTC 2002 |
P -> -P "You can prove this is false" in predicate notation
-P v -P Equiv
-P Equiv
"You can prove this is false" is therefore a false statement.
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