Fondamentalement, un événement est ce qui décide sur une zone d’indécidabilité encyclopédique. Plus précisément, il y a une forme implicative de type : E -> d(epsilon), qui se lit : toute subjectivation réelle de l’événement tel qu’il disparaît dans son apparaître, implique que epsilon, qui est indécidable dans la situation, a été décidé.

“As the length of a thread involving the Troll of Sorrow extends, the probability that the Halting Problem will be mentioned approaches one.”

The fact that it wasn’t The Troll of Sorrow himself who brought up the Halting Problem in this case seems to strengthen this claim.

(Kotsko’s First Law is that bloggers don’t keep their promises.)

Now you’re just teasing! OK, despite things I’ve said above, I’ve read enough of Zizek to satisfy myself I don’t really want to read any more. But neither Google nor Technorati produces anything obviously useful on Badiou – how about a link?

Yes, sir, and since this is a political thread, the issue is why leftists don’t make use of well-defined, “constrained,” systems or models instead of, say, getting carried away with cantor or lacan or hegelian Reason or whatever. A progressive “entitlement model” based on primary needs and resources, housing, existing technology, employment, etc, could be constructed fairly easily it seems, but the leftist-marxist detestation of modeling, quantification, etc. prevents that from happening as much as finance capitalism or a sort of faux-liberal monarchism does. Which is to say, the progressive it seems should value mathematical/economic applications and technique more than he does platonic contemplations (ie set theory as ontology), which may be gratifying for oxfordians or ivy league types but not for citizens taken as, they say, an aggregate.

The problem is that their use of science concepts as metaphors is usually subtly wrong. Zizek’s use of parallax as a metaphor, for example (from the small bits and pieces I’ve read) breaks down if you know much about parallax. Parallax is the shift in the apparent position of an object against a background caused by a change in point of view (dictionary.com’s use of “direction” is not really inspired, I’d say) and it’s a very familiar process—whenever you look at something with two eyes, your brain uses parallax as one of the ways of judging its distance. Zizek’s emphasis on parallax as metaphor of separation just doesn’t work; the object seen looks the same in either case, and all you have to do to see if against its background differently is change your location a bit.

In Zizek’s case, though, I think that he’s doing this on purpose. He has previously made arguments that were intended to be seen through in order to mock his enthusiasts. I’d guess that he finds the idea of people earnestly looking up parallax and their inner worries about whether they’ve gotten him right pretty funny.

If a system is complete, then there is an algorithm to determine the truth or falsity of every statement in the system. Let A be a statement. Systematically generate every possible proof in the system. If you generate a proof of A first, then A is true. If not-A is true, then A is false. This algorithm is very, very slow, but in theory it will always terminate.

The halting problem is a bit different. There may be uncomputable arguments /conclusions within certain systems, but that doesn’t mean that systems cannot be complete, does it.

axiom system:

• @ &

if @, then *

if *, then &

if &, then *

thus,

if @ then &,

and if @ then *

where is the uncomputability ?

Well in that case, one need only look, and the world of blogs outside of Crooked Timber may provide.

All are applications of elementary arithmetic, even if varying in difficulty. Thanks to Godel’s theorem, I know that the self-consistency of elementary arithmetic can’t be proved within arithmetic, but this is no more relevant to GE than the other cases.

Not so fast John. All your examples involve presumably only bounded numbers. In that case, consistency can be proven.

I read most of Sartre 30+ years ago […]. I had a reasonable go at Althusser

Now you impress me.