Bruno Marchal wrote: > > At 10:14 13/01/04 +0100, Georges Quenot wrote: > > >Some people do argue that there is no arithmetical property > >independent of us because there is no thing on which they would > >apply independentkly of us. What we would call their arithmetical > >properties is simply a set of tautologies that do come with them > >when they are considered but exist no more than them when they > >are not considered. > > But then what would be an undecidable proposition? This is how > Russell's and Whitehead logicism has break down. There is a ladder > of arithmetical propositions which ask for more and more > ingenuity to be proved. Actually arithmetical truth extend far beyond > the reach of any consistent machine (and consistent human with > comp). There is an infinity of surprise in there. > I guess you know that there is no natural number p and q such that > (p/q)(p/q) is equal to 2. If mathematical truth were conventionnal, > why did the pythagoreans *hide* this fact for so long? > So those propositions are neither tautologies, nor conventions. > David Deutsch, following Johnson's criteria of reality, would say > that such propositions kick back. > > You know, about arithmetic, and about machines btw, a lot of > people defends idea which are just no more plausible since > Godel has proved its incompleteness theorems. > Arithmetical proposition are just not tautologies.
There are three classes of (arithmetical) propositions: those who are tautologies (no matter how clever one has to be to figure that, they say nothing which is not already in the axioms), those whose negation are tautologies, and those whose neither themselves nor their negation are tautologies. It might be that we don't know which is which but it should be so in principle. > >> > Giving that I hope getting some understanding of the complex human > >> > from something simpler (number property) the approach of those > >> > people will never work, for me. > >> > >>And certainly vice versa. Though it is difficult to have them saying > >>it explicitely I have the feeling that the reason why they do not > >>want the natural numbers to be out there and even as not possibly > >>being considered as out there is that they do not accept that the > >>complex human be understood from something simpler (number property). > >>They do not even accept the idea being considered, were it as a mere > >>conjecture or working hypothesis. Their more official argument is > >>that such a view would prevent the foundation of human dignity. > > Damned!!! If there is one thing which could prevent the foundation > of human dignity, it is certainly that totalitarian idea following which > some ideas can not even be considered as an hypothesis or conjecture. This is indeed a problem. There could be more than one conception of human dignity. > But that happens all the time. There has been days you could be burned > even just because you ask yourself if by chance it was not the sun but > the earth which was moving. Unfortunately (again), yes. > Are you defending those guys? No. I am just explaining (or trying to explain) their position. > Are you asking me how to reply to those guy? I am interested in anybody's opinion on that problem. > My suggestion: if many people > thinks like that around you, just leave them. Like Valery said, those who are > not willing to use logic with you (that is to argument) are in war with you. > Run or kill them! This is a safe way to have soon everybody killing everybody. > It is not enough they have good intention, if they do not > want arguments, they are dangerous for all humans. I like to insist, in Valery > spirit, that logic is not a question of truth, but of politeness. I like the analogy. The fact is that there might be several (and possibly incompatible) protocols of politeness. > >I have not met any of them physically but I had discussion with > >some of them via Internet. There might not be so many of them but > >there are. You will find, at least in the US, a lot of people > >considering the views of evolution and/or of the big-bang as evil. > > Then what? If they disagree with dialog and argumentation, *I* will > consider them as evil. Possibly making you not better than them. But this not that simple. They do not disagree with dialog and argumentation. Rather they argue in different ways and/or with different premises. > >If they finally have to abandon these positions due to the amount > >of evidence in favor of it, the last line of defence for their > >conception of a personal God and for a significant role for Him > >could be at the level of artihmetical realism. Artihmetical > >realism by itself (not from a distinct personal God) is therefore > >seen as evil by them. As I mentionned, they usually do not put it > >that way. Rather they argue that such a view would prevent the > >foundation of human dignity and the like. > > They make probably the same confusion of those who believe > that determinism is in contradiction with free will. I would say that one of the concern they have behind this is the question of free will versus determinism (and/or randomness). You and others might see this as making "the same confusion of those who believe that determinism is in contradiction with free will". But there might also be more than one conception of free will and we could also consider that what they are doing is trying to defend another conception of free will that the one which is not in contradiction with determinism (and/or randomness). Though we may or may not share this conception, I don't think that we can dismiss it. The only thing we can say is that they cannot convince us of it or possibly even of its meaningfulness but in the same way we have no ground to prove them they are wrong. Basically, they want to believe that we humans are not reducible to numbers and I think that such a reductibility cannot be proved either way. Also I understand that one could feel offended by the idea that he could be reduced to mere numbers (not more but not less he would feel offended by the idea it could be reduced to a set of interacting molecules) even if these ideas are considered as just hypotheses. They want to believe (and they want to be generally believed) that there is (much) more than this in human beings (and incidently in themselves). > Actually I tend to think that Godel's and other incompleteness > result makes comp a sort of vaccine against reductionist view of > self and reality (and arithmetic). This is not obvious to me. Maybe what "reductionist" actually means needs to be clarified. > You know "reason" works only through doubt, and through the ability > to listen to different opinions. I tend to agree but it does not seem enough just to say it. > Now with Godel we can say more, > which is that "good faith" never fears "reason" and rationality. > Sincere Faith can only extend Ratio, and is always open to dialog. It seems that there exists other conceptions of what "good faith" and/or "Sincere Faith" should be. Idem for "Ratio". Georges.