John, Le 04-févr.-06, à 17:20, John M a écrit :
Bruno, You missed my point: whatever you want to test is still WITHIN the - I condone - HALF which you deem true. But it is perfectly circular: you test our human logic/understanding within human logic/understanding.
I don't think so. I test human introspection and theorizing, with physical apparatus, or just by comparing with today's physics. I already got that the loebian physics cannot be boolean, and that it looks like a quantum logic (details need more advanced stuff, but that appears through the genuine "hypostasis" ("person point of view" in Plotinus).
I say "loebian physics" instead of my usual "machine physics" because I take more and more into account that G and G* are correct for much more than machine, it concerns many angels too.
The caveman 200,000 years ago used the same (?) for establishing our mental ways with a lot less empirical cognitive inventory for use. And we still don't know all (understatement). Ignorance without knowing what we don't know - unstructurably.
It is here that the theorem of Godel, Lob and Solovay put a big light on the roots of the difficulties so that I invite people to take a look at it. Thanks to Solovay we can use simple modal logic to express the main point. I will say more when we go back to the hypostases ...
At some point I should present some "concrete" lobian machine like Peano Arithmetic, Zermelo-Fraenkel theory, and some concrete angels like Anomega (Analysis + the divine (even Boolos uses the term page xxxiii) omega rule which permit you to infer universals from an infinity of proofs). Like Boolos and the logician I use "Analysis" for axiomatic second order arithmetic.
All obeys G and G*. G and G*. Here the "schrodinger equation" of self-reference, if you want.
Best, Bruno http://iridia.ulb.ac.be/~marchal/