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"What is Metaphysics?"

At the risk of bringing us back to Heidegger, I have to point out that although the Ancient Greeks did "start" metaphysics, their precursors had already killed metaphysics before they started it. At least according to Heidegger, both Heraclitus and Parmenides showed the inherent errors of metaphysical thinking prior to its coming into being in formal practice.

Continental philosophy, especially French, over the last 50 odd years has been keenly interested in dismantling the whole 2,500 year old edifice of metaphysical thought.

by Upstate NY on Wed Jan 2nd, 2008 at 01:59:25 PM EST
Upstate NY:
At least according to Heidegger, both Heraclitus and Parmenides showed the inherent errors of metaphysical thinking prior to its coming into being in formal practice.
One of the annoying things about philosophy is that whatever you say there's always a presocratic who said it first.

That doesn't mean that, for instance, Democritus was right about atoms for the right reasons. All this getting stuff right about the world on the basis of pure thought is a dangerous conceit.

We have met the enemy, and he is us — Pogo

by Migeru (migeru at eurotrib dot com) on Wed Jan 2nd, 2008 at 02:02:31 PM EST
[ Parent ]
But then, Gödel's theorem is just applying the presocratic paradox of "this statement is false" to formal logic. I'm not sure how it makes formal logic so unstable...

Un roi sans divertissement est un homme plein de misères
by linca (antonin POINT lucas AROBASE gmail.com) on Wed Jan 2nd, 2008 at 02:32:59 PM EST
[ Parent ]
It doesn't make it unstable, it just proves that truth functions are incomputable.

We have met the enemy, and he is us — Pogo
by Migeru (migeru at eurotrib dot com) on Wed Jan 2nd, 2008 at 03:11:55 PM EST
[ Parent ]
It's possible that first learning about the undecidability aspects of computer theory made the Gödel theorem lose its surprise factor...


Un roi sans divertissement est un homme plein de misères
by linca (antonin POINT lucas AROBASE gmail.com) on Wed Jan 2nd, 2008 at 03:28:09 PM EST
[ Parent ]
Gödel proved the incompleteness of Arithmetic.  Specifically, he demonstrated that in any axiomatic system capable of Arithmetic there are statements that can neither be proved or disproved within the axioms.

To fully understand what that meant and means requires an understanding of what Logic and Mathematics were 'on about' from around 1870 to l933.  To (greatly) simplify, Frege, Hilbert, Russell, Whitehead, & All That Crew were attempting to construct an intellectual tool that would always, when correctly used, derive a True and Valid answer.  

Gödel's Proof = You Can't.

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Wed Jan 2nd, 2008 at 10:56:09 PM EST
[ Parent ]
Yes, and it failed on "this statement is false". That's the basic point of Gödel's proof. I don't know how they expected to attribute a truth value to that statement, those formal logicians ; but that you can't attribute a truth value to it sounds even a bit reconforting... Logic doesn't get out of the realm of human experience about truth values.


Un roi sans divertissement est un homme plein de misères
by linca (antonin POINT lucas AROBASE gmail.com) on Thu Jan 3rd, 2008 at 04:13:57 AM EST
[ Parent ]
Many antinomies (paradoxes,) such as that one - a variation on wossname's 'All Cretans are liars ...' - have an oscillating first order Truth Value with the TV changing depending on the step: On True Then False Then True & etc XOR On False Then True Then False & etc.  Since they are infinitely oscillating there is no resolution possible.  

By moving to the Second Order, on the other hand, the True/False OR False/True oscillation is, sometimes, capable of resolution.

But that, very often, takes you outside the original axiomatic system.

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Thu Jan 3rd, 2008 at 05:27:32 AM EST
[ Parent ]
"Arithmetic is consistent"

That was the sailing-over-the-edge moment.  

Now it may be that arithmetic really is consistent, but that is another truth function that is "uncomputable."  

The Fates are kind.

by Gaianne on Thu Jan 3rd, 2008 at 04:48:01 PM EST
[ Parent ]
It depends on what you mean by "right."

Heidegger understands Parmenides to be saying something quite the opposite of those who came after. So, there is no agreement there.

And genealogy is important. If we are to credit certain Ancient Greeks with the very foundation of thinking about subject-object relations, then we can't ignore those who came before and troubled that very relationship. We'd be privileging the form of thought which dominated the next few millenia as somehow an originary idea.

by Upstate NY on Wed Jan 2nd, 2008 at 02:41:02 PM EST
[ Parent ]
One of the annoying things about philosophy is that whatever you say there's always a presocratic who said it first.

Is that a quote from Hesiod?

;-)

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Wed Jan 2nd, 2008 at 10:38:34 PM EST
[ Parent ]

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