Re: Artificial Philosophizing
Le 15-févr.-06, à 17:30, [EMAIL PROTECTED] a écrit : As Bruno said, now we really don't know what a machine is. Actually I was just saying that no machine can *fully* grasp *all aspect* of machine. But machines can know what machines are. Only, if a machine M1 is more complex than M2, M2 will not been able to prove the consistency of M1, for example. And then if we are machine (comp) such limitations apply to us, and this provides lot of informations, including negative one which we can not prove except that we can derive them from the initial comp act of faith (yes doctor). cf: Bruno: ... and note that the coherence of taking simultaneously both a and b above is provided by the incompleteness results (Godel, ...) which can be summarized by ... no machine can grasp all aspect of machine. Tom: So in the absense of a precise definition, perhaps we end up running away from ill-defined words like machine, reason, soul, faith, etc., for who knows what personal reasons. That is why I propose simple definitions. Reasoning = provability = Bp = Beweisbar(p) cf Godel 1931. Soul = first person = provability-and-truth = Bp p = third Plotinus' hypostase. This can look as an oversimplification but the gap between truth and provability (incarnated in the corona G* minus G) detrivialises (if I can say) all this. My fault. I will come back on this. Bruno http://iridia.ulb.ac.be/~marchal/
Re: Artificial Philosophizing
--- Bruno Marchal [EMAIL PROTECTED] wrote: Le 15-févr.-06, à 17:30, [EMAIL PROTECTED] a écrit : As Bruno said, now we really don't know what a machine is. Actually I was just saying that no machine can *fully* grasp *all aspect* of machine. But machines can know what machines are. Only, if a machine M1 is more complex than M2, M2 will not been able to prove the consistency of M1, for example. And then if we are machine (comp) such limitations apply to us, and this provides lot of informations, including negative one which we can not prove except that we can derive them from the initial comp act of faith (yes doctor). cf: Bruno: ... and note that the coherence of taking simultaneously both a and b above is provided by the incompleteness results (Godel, ...) which can be summarized by ... no machine can grasp all aspect of machine. Tom: So in the absense of a precise definition, perhaps we end up running away from ill-defined words like machine, reason, soul, faith, etc., for who knows what personal reasons. That is why I propose simple definitions. Reasoning = provability = Bp = Beweisbar(p) cf Godel 1931. Soul = first person = provability-and-truth = Bp p = third Plotinus' hypostase. This can look as an oversimplification but the gap between truth and provability (incarnated in the corona G* minus G) detrivialises (if I can say) all this. My fault. I will come back on this. Bruno Bruno: since when do we think 'beweisbar' (provable) anything within the domain of our knowledge-base which may have connotations beyond it (into the unlimited)? Since when do we want to speak about Truth in a general sense? Our 'truth'? Our percept of reality? I think simple definitions are limiting the validity of the 'definition' into a narrower model. John M
Re: Artificial Philosophizing
Hi John, Le 16-févr.-06, à 16:21, John M wrote: since when do we think 'beweisbar' (provable) anything within the domain of our knowledge-base which may have connotations beyond it (into the unlimited)? Since when do we want to speak about Truth in a general sense? Our 'truth'? Our percept of reality? I think simple definitions are limiting the validity of the 'definition' into a narrower model. My reasoning will work already with arithmetical truth. This is non trivial. Leibnitz, Hilbert, and many mathematicians before Godel would have believed that arithmetical truth gives a narrower model, but after Godel we know that we cannot formalized that notion in any effective way. The fashion today consists even in considering it to be a too large concept. But I will make clear (well I will try, or refer to some literature) that what I say can be extended on much more large notion of truth. I assure you John that the approach is everything but reductionnist. Even just about numbers there is no effective TOE (by Godel). Now, there are angel like Anomega (Analysis + Omega rule) which can grasp the whole arithmetical truth, thanks to their infinite power, but then they cannot grasp the whole analytical truth, and will suffer similar limitation as the more terrestrial machines. Here truth has nothing to do with any form of perception. We are in Platonia, by hypothesis. We keep our eyes closed, if you want. Note also that without simple definition we would not progress, and would not been able to find our errors, or our limitations. Bruno PS a) I answer Tom, and Ben tomorrow. b) For those who read Plotinus, what I call Angels, is what Plotinus call Gods. It corresponds just to loebian entities which cannot been simulated by a computer. There is a chapter in Boolos 1993 describing Anomega, and showing it obeys to G and G*. http://iridia.ulb.ac.be/~marchal/
Re: Artificial Philosophizing
Responses interspersed below. Le 15-févr.-06, à 17:30, [EMAIL PROTECTED] a écrit : As Bruno said, now we really don't know what a machine is. Bruno: Actually I was just saying that no machine can *fully* grasp *all aspect* of machine. But machines can know what machines are. Only, if a machine M1 is more complex than M2, M2 will not been able to prove the consistency of M1, for example. And then if we are machine (comp) such limitations apply to us, and this provides lot of informations, including negative one which we can not prove except that we can derive them from the initial comp act of faith (yes doctor). Actually I was referring to what you said in the belief... thread http://www.mail-archive.com/everything-list@eskimo.com/msg08680.html where you respond to my statement This runs counter to the whole PHILOSOPHY (mind you) of modern science, that we are simply machines, and that there is no WHY. with: This is due to the materialist who like to use the idea that we are simply machine just to put under the rug all the interesting open problem of (platonician) theology. Since Godel's discovery this position is untenable. Now we know that we don't know really what machines are. With the comp-or-weaker hyp, we already know that if we are machine then the physical laws emerges from in a totally precise and testable way. Tom: So in the absense of a precise definition, perhaps we end up running away from ill-defined words like machine, reason, soul, faith, etc., for who knows what personal reasons. Bruno: That is why I propose simple definitions. Reasoning = provability = Bp = Beweisbar(p) cf Godel 1931. Soul = first person = provability-and-truth = Bp p = third Plotinus' hypostase. This can look as an oversimplification but the gap between truth and provability (incarnated in the corona G* minus G) detrivialises (if I can say) all this. My fault. I will come back on this. Bruno Actually, when I was talking about a lack of precise definition, I wasn't referring to you, Bruno. I was talking about what happens in the general conversation when we don't define our terms, or when we are assuming different definitions based on different philosophies consciously or unconsciously held. On the contrary, I would echo John Mikes' sentiment that some of your definitions seem too simple for my taste. I think I would agree with your definition of reasoning though, but I take issue with your definition of Soul = first person = provability-and-truth = Bp p. I think elsewhere you also define Knowledge as Belief Truth, and I have the same problem with that. These definitions seem too simple. These seem equivalent to accidental true belief and accidental true proof. They lack the justification factor. (I feel a reference to G*/G coming. ;) ) Anyway, perhaps we can start a new thread if we want to talk about this part some more, or this is probably what you've been trying to explain to us all along in previous threads. Tom
Re: Artificial Philosophizing
Bruno: That is why I propose simple definitions. Reasoning = provability = Bp = Beweisbar(p) cf Godel 1931. Soul = first person = provability-and-truth = Bp p = third Plotinus' hypostase. This can look as an oversimplification but the gap between truth and provability (incarnated in the corona G* minus G) detrivialises (if I can say) all this. Tom: ... On the contrary, I would echo John Mikes' sentiment that some of your definitions seem too simple for my taste. I think I would agree with your definition of reasoning though, but I take issue with your definition of Soul = first person = provability-and-truth = Bp p. I think elsewhere you also define Knowledge as Belief Truth, and I have the same problem with that. These definitions seem too simple. These seem equivalent to accidental true belief and accidental true proof. They lack the justification factor. (I feel a reference to G*/G coming. ;) ) Anyway, perhaps we can start a new thread if we want to talk about this part some more, or this is probably what you've been trying to explain to us all along in previous threads. Bruno: Bp p seems too simple. Actually, given that I limit myself in the interview of sound machines, we know that they obey to Bp - p, by definition (a sound machine proves only true statements: so Bp - p). So we know Bp and Bp p are equivalent, so you could at I should have said that Bp p seems wrong, not that it's too simple. I was trying to say that it seems wrong to say that Bp p gets us further than Bp, i.e. provability + truth is more than provability. In order for Bp p Bp, it seems to me that we would have to have access to truth (p) directly, we would have to *know* that we've proved something to be true, not just that we've been consistent. In order to be *sound* we have to be given true truth for our reasoning to start with (and then of course be then be consistent with it). This is similar to why I don't think that knowledge is simply true belief. Bruno: first believe that the soul = the intellect. Exercise: what is wrong? Answer tomorrow :-) (+ answers to Danny and Ben). Bruno I don't know what you're trying to get at with soul = intellect. To me the intellect is simply at the same par with provability and reason. The intellect has to be given true truth in order for it to come up with true truth (if it reasons consistently). More than that, the intellect has to be given true truth and know that it was given true truth, in order to reason its way to more true truth and know that it has done so. Tom
