Re: belief, faith, truth
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/
Re: belief, faith, truth
--- Bruno Marchal [EMAIL PROTECTED] wrote: 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. 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. 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. SNIP ignorance about what? about ourselves and the rest. Already about numbers. We have to know about it to structure it. Could Columbus ever 'structure' the No-American West-Coast region when he thought he is in Asia? Bruno: 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). Beautiful. 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, I don't believe you are a Platonist. You may accept some (side?)lines of Platonistic ways, but you are ~3 millennia past Platonism, I think even past Loebianism. You are a BrunoMarchalist. Bruno http://iridia.ulb.ac.be/~marchal/ John M
Re: belief, faith, truth
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/
Re: Belief, faith, truth
Bruno, Thanks for your response. I don't understand why you say my argument is not valid. Granted,much of what you write is unintelligible to me because you are expert in fields of which I know little. Nevertheless, a cat can look at a king. Here is what we've said so far: (Norman ONE) My conjecture is that a perfect simulation by a limited-resource AI would not be possible. If this is correct, then self-aware simulations that are perpetually unaware that they are simulations would not be possible. (Bruno ONE) This could be a reasonable conjecture. I have explain on the list that if we are a simulation then indeed after a finite time we could have strong evidence that this is the case, for example by discoveries of discrepancies between the "comp-physics" and the "observed physics". (Norman TWO) Humans have not made the discovery that they are simulations, therefore the mostPROBABLE (emphasis added)situation is that we are not simulations.(Bruno TWO) This argument is not valid. The reason is that if we could be "correct" simulation (if that exists), then that would remain essentially undecidable. (Then I could argue the premise is false. Violation of bell's inequalities could be taken as an argument that we are in a simulation (indeed in the infinity of simulation already "present" in the "mathematical running" of a universal dovetailer, or arithmetical truth.) (Norman THREE) I don't understand the part of "Bruno TWO" in parentheses - I'm not asking you to explain it to me. Are you saying that a perfect simulation would not necessarily discover it was a simulation? If so, I agree. This is supported in"Bruno ONE" where you said it was reasonable that if we are a simulation we would, in finite time,discover that this is the case. Therefore it seems to me that mystatement in "NormanTWO" is correct - note my inclusion of the word "probable."Do you agree? Or am I missing your point? Norman
Re: belief, faith, truth
On Sat, Feb 04, 2006 at 04:30:11PM +0100, Bruno Marchal wrote: I agree. I guess in our local and sharable past, humans reached loebianity 200,000 years ago. I'm not sure why you say 200Kya, other than it being the origin of our species. There is a fair bit of evidence that something significant happened to human brain function around 40,000 years ago (see Steven Mithen's Prehistory of the Mind). There was an explosion of representational art that occurred around that time. On the other hand, there is also evidence that other apes (Chimpanzees, a Gorilla, the Gibbon and so on) are capable of self awareness so maybe Loebianity arose 7-8 Mya. Cheers -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgpELqZL0VjDt.pgp Description: PGP signature
