Re: Lobian Machine
At 10:33 PM 12/29/2005, George Levy wrote: Bruno Marchal wrote: Godel's result, known as Godel's second incompleteness theorem, is that no consistent machine can prove its own consistency: IF M is consistent then M cannot prove its consistency Bruno, After I read your email, we had a gathering of family and friends, and my head being full of the subject of this post. I wanted to test the idea of Godel's second incompleteness theorem on the average people just to see how they would respond. I found the right place in the discussion to insert the paraphrase: If I am sane, it is impossible to know for sure that I am sane. This povoked some hilarity, especially with my kids (young adults) who probably view me as some kind of nutty professor. While this statement is mathematically true, it was not considered serious by the people I was talking with. I guess that the average human has no doubt about his own sanity.(But my kids had some doubts about mine) One way to prove that you are crazy is to assert that you are sane. This means that the average human is crazy! :-) George Hm. . . Godel was discussing sharply defined mathematical constructs, specifically, proof of N requires knowledge of non-N. As I'm sure you know, sanity is a *legal*, rather than a mathematical term. While this sort of logical fuzziness is probably in keeping with these times, I doubt if it really applies to Godel's theorem. RMiller
Re: Lobian Machine
George, The average human IS crazy according to comp. The smiley at the end of your sentence is unwarranted! This is a fairly undeniable ramification of what Bruno is telling us. If we *are* machines, why do we go about the place denying it? Those who have understood that computation precedes the laws of physics are the only ones who are sane (but of course I cannot prove that, being a consistent machine!) In my view this is where ART has a role in what we are discussing here. Perhaps artists (composers, painters, poets etc.) are the ones who know intuitively that we are all mad (because we don't know what we are) and who then exploit our insanity in a creative manner to remind us of this unconsciously. As Salvador Dali once said "The only difference between me and a madman is that I am not mad". But he could not prove that either. cheers, Kim Jones On 30/12/2005, at 3:33 PM, George Levy wrote: Bruno Marchal wrote: Godel's result, known as Godel's second incompleteness theorem, is that no consistent machine can prove its own consistency: IF M is consistent then M cannot prove its consistency Bruno, After I read your email, we had a gathering of family and friends, and my head being full of the subject of this post. I wanted to test the idea of Godel's second incompleteness theorem on the average people just to see how they would respond. I found the right place in the discussion to insert the paraphrase: If I am sane, it is impossible to know for sure that I am sane. This povoked some hilarity, especially with my kids (young adults) who probably view me as some kind of nutty professor. While this statement is mathematically true, it was not considered serious by the people I was talking with. I guess that the average human has no doubt about his own sanity.(But my kids had some doubts about mine) One way to prove that you are crazy is to assert that you are sane. This means that the average human is crazy! :-) George
Re: Lobian Machine
Bruno Marchal wrote: Godel's result, known as Godel's second incompleteness theorem, is that no consistent machine can prove its own consistency: IF M is consistent then M cannot prove its consistency Bruno, After I read your email, we had a gathering of family and friends, and my head being full of the subject of this post. I wanted to test the idea of Godel's second incompleteness theorem on the average people just to see how they would respond. I found the right place in the discussion to insert the paraphrase: If I am sane, it is impossible to know for sure that I am sane. This povoked some hilarity, especially with my kids (young adults) who probably view me as some kind of nutty professor. While this statement is mathematically true, it was not considered serious by the people I was talking with. I guess that the average human has no doubt about his own sanity.(But my kids had some doubts about mine) One way to prove that you are crazy is to assert that you are sane. This means that the average human is crazy! :-) George
Re: Paper+Exercises+Naming Issue
Thanks, Bruno, your brief added last par is of great help. I would NEVER mix provability and probability, I am not Spanish (b=v?) and think in semantical rather than formal meanings. I wish I knew what is a "modal logic" (G and G*) and am a bit perplexed of your (??) logic defining G* as beeing 'something or not'. (Like: "F" is =,<, or >, of "B")- Then again "true" may not exist, indeed. (1st pers?) Similarly it does not help me, if I get a lot of other 'names' for something I don't know what it is to begin with. I like WORDS. (I also like word-puzzles, but only solvable ones in my domains). * I glanced over the Stanford blurb and found exciting titles. When clicked, they overpoured me with equational lettering and I had no idea about their meaning. Even if I had a vocabulary of those letters, it is practically (humanly) impossible to "read" a text and follow those equations by looking up every letter for the meaning and content (with, of course clicking after all the connotations galore). Besides it is full of signs I cannot even read out and have nothing similar on my keyboard (maybe they are in some hidden modes as are the French accents). *** As a comparison: here is a description of a statement from my old profession about something I did: "when mixing the DVB and St in a DBP catalysed 1:3 stoichiometry it exotherms and has to be temp-controled. At reaction-startup I added the DEB and then dispersed the mix in an aqueous medium with PVA stabilizer. The beads were then WV-boiled off and filtered. They showed a controllable macroporous structure with large sp. surface internally for adsorptive sites. Then came the transform by polymeranalogous reactions to introduce polar or ionic sites." And so on. It made perfect sense in my profession. (Never mind) No modal or out of modal logic, no 'ABC... with signs' equations. *** How does the "provability" (no b) jibe with Poppers scientific 'unprovability'? Is falsifiability = provability? Bruno, I like what you SAY, I like YOUR logic, not somebody else's. I don't want to 'give up' on you because of a system so strange to me. I am 'fishing' for word-hooks in your writings. In 1940 I took philosophy (to major chemistry) and sociology. I should have taken logic instead of the Br. of Brandenstein. Of course it would have been of little use now, 65 years later. With friendship John --- Bruno Marchal <[EMAIL PROTECTED]> wrote: > Hi John, > > To search informations on the net on G and G*, it is > easier to search > on "logic of provability". > > G is also called KW, KW4, L, GL, PRL in other papers > or book. > G* is also called G', PRL^omega, GLS > > The Stanford entry is rather good: > http://plato.stanford.edu/entries/logic-provability/ > > In brief words G is a modal logic which describes > what a classical > theory or machine can prove about its own > provability abilities. And G* > is a modal logic which describes what is true > (provable or not by the > machine) about its own provability abilities. > > Don't confuse "provability" with "probability". > Careful when typing > because the "b" and the "v" are close on the > keyboard! > > Bruno > > > Le 29-déc.-05, à 00:48, John M a écrit : > > > Bruno, could you include some BRIEF words for the > > profanum vulgus about that ominous "G - G*" magic > as > > well? I searched Google, Yahoo, Wikipedia, but > could > > not find any reasonable hint. > > You and other savants on the list apply this > magic > > many times always. Am I the only one who missed > that > > in grammar school? > > > > John > >> > > > > > http://iridia.ulb.ac.be/~marchal/ > > >
Re: Paper+Exercises+Naming Issue
Hi John, To search informations on the net on G and G*, it is easier to search on "logic of provability". G is also called KW, KW4, L, GL, PRL in other papers or book. G* is also called G', PRL^omega, GLS The Stanford entry is rather good: http://plato.stanford.edu/entries/logic-provability/ In brief words G is a modal logic which describes what a classical theory or machine can prove about its own provability abilities. And G* is a modal logic which describes what is true (provable or not by the machine) about its own provability abilities. Don't confuse "provability" with "probability". Careful when typing because the "b" and the "v" are close on the keyboard! Bruno Le 29-déc.-05, à 00:48, John M a écrit : Bruno, could you include some BRIEF words for the profanum vulgus about that ominous "G - G*" magic as well? I searched Google, Yahoo, Wikipedia, but could not find any reasonable hint. You and other savants on the list apply this magic many times always. Am I the only one who missed that in grammar school? John http://iridia.ulb.ac.be/~marchal/
Re: Paper+Exercises+Naming Issue
Le 27-déc.-05, à 05:43, George Levy a écrit : Naming this field is difficult. This is why I made several suggestions none of which I thought were excellent. I think it is difficult because there is a conflict between pedagogy and diplomacy there. Bruno Marchal wrote: I don't think it is a question of vocabulary, It is only a question of vocabulary if you intend to communicate with other people. And this is where the difficulty lies. If you make the name too esoteric they will not even understand what the field is about. OK. But is not "theology" less esoteric than psychomechanics. Everyone knows what theology is all about: immortalilty/mortality issues, soul's fate in possible consciousness states, where do we come from, cosmogony, etc. "Scientific" theology is of course 100% agnostic on all this; yet it can provide theories and with comp (or weaker) even testable or partially testable theories (indeed with comp, physics is an integral part of theology: physics is given somehow by the mathematical structure describing the border of the intrinsic ignorance of machines. and actually I am not sure we are not in, well *perfect* perhaps not, but at least in an a larger matching area than you think. Perhaps, like so many, you have not yet really understand the impact of the discovery by Turing and its relation with Godel's theorem. When I talk on Platonia, it is really "Platonia" updated by Godel's and Lob's theorem. I hope you are open to the idea I could perhaps progress in my way of communicating that. It really concerns machines and even many non-machines. I think about abandoning comp for ind, where ind is for indexical, given that G and G* applies to almost anything self-referentially correct. I knew this for long, the comp hyp just makes the reasoning and the verification easier. I can already say that I disagree the word "quantum" should be in it. The name should not issue what will or should be derived by the theory. I do not fully understand the full ramification of how indexical relates to this field. Indexical is used in philosophy to designate term like "now", "here", "modern", "I", "this" etc. Their meaning change with the situation of their uses. For example "I" means Bruno for me and George for you. "here and now" means Brussels and 10h54 am, here and now, but the time I finish the sentence it already means something else (Brussels and 10h55 am). The approach I follow is based on the logic of self-reference. "Bp" is really an indexical: it means "I prove p" where "I" is put for a third person self-reference by the machine M, and strictly speaking the meaning of "I" is different for each machine (but by Godel Lob, still obeys similar laws of the self-referentially correct machine). However, I think that to use Indexical now is like Heisenberg using Entanglement instead of Quantum. Nobody would have understood what he was talking about. It was hard enough already to understand Quantum. All right, but "quantum" still does not work for this field because it would give the wrong impression that the quantum hyp. is assumed, where the UDA shows it must be derived. the comp hyp is neutral about which type of machine we would be. It could be a quantum one or not. All what matters is that the machine should be Turing emulable (or weaker: some Turing oracle can be assumed without changing the self-reference logics G and G*). BTW, COMP is not very good, because you have to explain what it is. Well, that is the name of the hypothesis. The point is to have some short acronym to put results in short formula like: COMP -> REVERSAL. But we were discussing the name of the entire field. What *is* G* \ G from a machine point of view? It is the self-referential truth which we cannot prove, but which can be hope or fear or just bet upon, like Dt, DDt, ... At first glance it appears to be the Mechanist Philosophy and this is what I originally thought. Yes. Comp is the DIGITAL or numerical or computational mechanist hypothesis. The mechanist philosophy is logically weaker due to the (mathematical at least) existence of non Turing-emulable analogue machine. The UDA, as it is now, does not work on such analogue machine. Of course comp is a natural modern sister of the mechanist philosophy. I think the best approach is to use a compound expression to bridge the gap between different fields. (i.e., Quantum electro-chromo dynamics, electro-magnetism, physical chemistry) There is nothing surprising that quantum physics could be derived from quantum psycho mechanics. Of course it is surprising...not to you or me or others on the list because we have been talking about it for so long... but to the average scientist in the street... or the university. And these are the people you intend to communicate with. I don't follow what you say. Quantum mechanics assumes the quantum hyp , and som
