need help :-)
dushya
theorem ? am i right in thinking that this theorem guarantees
existence of at least one formula G within any logical system ( "good"
enough that it can "explain" natural numbers ) such that G can not be
proved within that system itself. i have read the proof but couldn't
understand it very clearly. in it Godel assumes that all formulas of
the system can be arranged in a sequence and hence are countable. is
that a legitimate assumption?
John Jones
Yes, it was the idea that a system is both an object and an organising
principle of objects.
Jesse F. Hughes
You know, it's one thing to be stupid in your own threads. Then
you're harming no one. But when a poster asks a legitimate question,
common decency suggests that you keep your ignorance to yourself.
By the way, I see that Cardiff lists current PhD topics in philosophy
at
<http://www.cardiff.ac.uk/encap/degreeprogrammes/postgraduateresearch/currentphdtopics/index.html>.
You claimed once to be pursuing a PhD at Cardiff. How is it that
you're not listed there? Back in March 2008, you claimed to submit a
thesis proposal titled "the manifesting conditions of objects". How's
that coming along?
(At the time, I thought that John Jones was likely a put-on. That
still seems a pretty good guess, but it's a very long put-on, if so.
He has a fairly long history on other fora as well. Still, he was
either lying about the PhD program at Cardiff or his thesis proposal
was rejected, and yet he's still going on... or?)
--
Jesse F. Hughes
"Please. I was a philosophy major. Nobody can 'know' anything. And
I DO know." -- George Greene embarrasses philosophy majors everywhere.
Frederick Williams
>
> hi everyone .. can anyone help me understand Godel's incompleteness
> theorem ? am i right in thinking that this theorem guarantees
> existence of at least one formula G within any logical system ( "good"
> enough that it can "explain" natural numbers ) such that G can not be
> proved within that system itself.
Neither G nor not-G is provable. "Outside" the system G can be seen to
be true. These results depend on assumptions about the system's
consistency.
> i have read the proof but couldn't
> understand it very clearly. in it Godel assumes that all formulas of
> the system can be arranged in a sequence and hence are countable. is
> that a legitimate assumption?
If the number of symbols is countable and the formulae are of finite
length then there are countably many formulae.
What are you reading?
--
Which of the seven heavens / Was responsible her smile /
Wouldn't be sure but attested / That, whoever it was, a god /
Worth kneeling-to for a while / Had tabernacled and rested.
Bill Taylor
> existence of at least one formula G within any logical system ( "good"
> enough that it can "explain" natural numbers ) such that G can not be
> proved within that system itself. i have read the proof but couldn't
> understand it very clearly. in it Godel assumes that all formulas of
> the system can be arranged in a sequence and hence are countable. is
> that a legitimateassumption?
It's not an assumption, it's a trivial consequence of the definition
of a "logical system".
b
John Jones
Ah you see, just as the "Peristalltic Set of Unforseen movemments" is
often misspelt, so the "Set of Unintended Circumstances" is often sporadic.
But if you check with a G�del scholar, you feeble-minded old goat, you
should get a confirmation of the sense of my response. Treating a system
as both object and organizing principle of objects is KEY to G�del's
whole enterprise.
It might also bring you up to date with this topic for you to know that
the whole point of G�del's project was to serve his own take on
Naturalism, for which a rejection of the metaphysics of his mathematical
procedure was necessary. Alright?