John,
Le 03-févr.-06, à 23:45, John M a écrit :
--- Bruno Marchal <[EMAIL PROTECTED]> wrote: Just compare past systems of 'logic' - say back to 3000 years, about "the same nature (world)" and you can agree that ALL OF THEM cannot be true.
I agree. I would say HALF of them are true. My point is that we can test it.
The 'artifact' did not change. I do not believe that we reached the "ultimate" level in logic and mental capabilites as of Febr. 2006
I agree. I guess in our local and sharable past, humans reached loebianity 200,000 years ago. Here and there, but also beyond time in Platonia, loebian machines introspect herselves and discover "sort of theory of everything", let us say. My point is that we can get that theory of everything by interviewing a universal( turing) machine introspecting herself (that's what leads to G, G*, ...) The machine's theory of everything is testable because it includes physics. Now I have discovered that Plotinus (200-300 after JC) is, accepting one correction, 100% loebian, and that its theory of matter (70% Plato, 30% Aristotle) is, relatively to the arithmetical interpretation, equivalent with mine (which is the loebian one, strictly speaking).
If we can identify our ignorance. It is like agnosticism:
Indeed. Although the modest machine is mute there. (sometimes I forget that!)
ignorance about what?
about ourselves and the rest. Already about numbers.
We have to know "about it" to structure it.
And it is very hard to do so, but in our west, there was an Old School discussing the point from Pythagoras to the late neoplatonist. I think the peak is Plotinus. But in the east: same discussions with different words. Today, we have the math for listening to machines and angels, belonging to vast lattices of angels (non-machines).
Solipsism can be humiliating: "I cannot be right".<G> #rd person is not denied in my position: it is just represented by MY 1st person interpretation of it, so while "there is" a 3rd person "truth" it emerges in us as our 1st person understanding.
No problem with that. We can start from the first person as well. In some of its presentation Plotinus follows that path. Technically it is less simple. Albert Visser got the logic of intutionistic provability, and its corresponding version of the Loeb truth. But you know I am a Platonist , and then classical logic is more easy to handle. Anyway, we get all "hypostases". Incompleteness leads naturally to many different points of view, even with "Truth" limited to the truth of proposition about numbers.
Bruno http://iridia.ulb.ac.be/~marchal/
