On Fri, 22 Sep 2000 16:43:53 +0200 (SAST) Peter van Heusden <pvh at egenetics.com> wrote:
> Yeah, but we're all pretty much agreed that Hegel was talking bollocks
> here, right?
Nope. I'm a flake, I believe this stuff.
> Anyway, I'm no authority on Hegel, but it seems to me that this 'solution'
> requires a constant state of not examining itself. Which doesn't get you
> much further than a state of paranoid indecision.
Actually, the reverse. The 'truth' of the problem would entail Understanding the constitutive nature of the paradox through constant reflection.
If H is applies to itself, this creates a paradox, that is clear enough. This sounds like a modification of Zeno's paradox about the logical impossibility of motion.
In effect: H will never reach its goal (like Zeno's arrow) because it is impossible for H to execute a self-contradicting program (it is impossible for Zeno's arrow to move). This isn't dissimilar to Habermas's notion of a performative contradiction: one cannot use an argument to invalidate the value of arguments.
The 'true infinity' of H is this performative contradiction, H is nothing more and nothing less than H - its own logical impossibility. The interesting point here would be this: if one executes the problem and a result occurs, then H would cease to be H - something new would have been created. The key here is the consistency of H 'in-itself' as H. H, however, is only a contradiction insofar as the terms of its deployment are static. So your point about the cessation of examination is the condition upon which H can be said to be a paradox. H is only a contradiction if one does not think! Upon thinking, H can only be understood to be what it is, a contradiction (a negation of a negation).
To put this in terms of Habermas, a performative contradiction only holds true for those who already believe in performative contradictions (ie. the constitution of the problem requires a necessary stasis). The point, however, would be that the metastasis of the problem entails understanding that performative contradictions can only exist as identical with non-contradictory propositions, which is the basis of a negative dialectic, which is probably *the* paradigm of ideology critique.
Ok, this is all very much beyond me. This says nothing.
ken