Bruno Marchal wrote: > Hi David, > > > Le 18-août-06, à 02:16, David Nyman wrote (answering John): > > > > > [EMAIL PROTECTED] wrote: > > > > John > > > > Thanks for taking the trouble to express your thoughts at such length. > > I won't say too much now, as I have to leave shortly to meet a long > > lost relative - from Hungary! However, I just want to make sure it's > > clear, both for you and the list, that: > > > >>> "Comp is false". Let's see where *that* leads..... > > > > isn't intended as a definitive claim that comp *is* false. > > To be honest I have not yet seen where you postulates comp wrong in > your long anti-roadmap post. > Recall that I take comp as YD + CT + AR (Yes Doctor + Church Thesis + > Arithmetical Realism). > So, strictly speaking comp can be false in seven ways: > > YD CT AR > 1 1 1 comp is true > 1 1 0 comp is false 1 > 1 0 1 " " 2 > 1 0 0 " " 3 > 0 1 1 " " 4 > 0 1 0 " " 5 > 0 0 1 " " 6 > 0 0 0 " " 7 > > 1. AR is false, but CT is true, and YD is true. This would mean there > is a program which stops or does not stop according to my knowledge of > it. It is beyond my imagination, even if, as a logician I know that I > have to postulate AR. Of course the UD would loose all its purpose. > 2. CT is false. This would mean there exist a way to explain in a > finite time how to compute a function from N to N, such that no > computer can be programmed to compute it. Possible but unlikely. > 3) YD is true, but CT is false and AR is false. This means the doctor > is helped by Gods or Goddesses. > 4) YD is false (and CT and AR are true). This means I am an actual > infinite object. > 5) 6) 7): combination of above. > > > > Rather, *if* > > it is false, in what ways specifically, and what are the alternatives? > > Can they be stated as clearly and explicitly as Bruno is trying to do > > for his approach ('to see where it leads')? Hence the 'anti-roadmap', > > or perhaps better - 'another roadmap', or some ideas for one. > > It is certainly interesting. But comp is a very weak statement, so > non-comp is very strong. It needs some actual infinite to be > "implemented". Judson Webb range "comp" in the "finitist doctrines" > (but not in the ultra-finitist doctrine). >

I believe that we are finite, but as I said in the "computationalsim and supervenience" thread, it doesn't seem that this is a strong enough statement to be useful in a TOE. It seems that you cannot have YD without CT, but if true I would leave Bruno to explain exactly why. The substitution level being a finite level is not strong enough to conclude that there is a non-zero probability that the doctor will get it right. That would be a bad bet/faith. > > > Most of > > the thoughts in it were originally expressed in some earlier postings > > on 'The Fabric of Reality' list, which Bruno was kind enough to copy to > > this list. Anyway, it's intended as a point of departure (for me > > certainly) and I look forward to some strenuous critiques. > > > > One misgiving I have, now that I've finally grasped (I think) that the > > comp 'theology' entails 'faith' in the number realm, ... > > > I prefer to reserve "faith" for the resurection "promised but not > guarantied" by the (honest) doctor. > I need infinitely less faith to believe that each number has a > successor than to believe the sun will rise tomorrow. AR is very weak. > Sometimes I regret to have been explicit on AR, because it looks like > everyone believe in it, except when we write it explicitly. People put > many things in it, which are not there. Not believing in AR also > entails that there is a finite polynomial (on the integers) such that > two different people can find different integer values when applying > the polynomial on the same number, and despite those people agree on > the meaning of + and * and zero and "+1". > > > > ... is that by this > > token it seeks to provide a TOE (Bruno, am I wrong about this?) > > You are right. By the UDA it is not a matter of choice. > > > > > That > > is, beginning with an assertion of 'faith' in UDA + the number realm, > > we seek to axiomatise and 'prove' a complete theory of our origins. > > Bruno is a very modest person, but I worry about the 'modesty' of the > > goal. > > Modesty is not incompatible with ambitious goal. You can decide to > climb the everest Mountain, and recognize you have climb only two > meters high :) > > > > > Of course, it's highly probable that I just misunderstand this > > point. However, I'm having trouble with my faith in numbers, > > monseigneur. > > We cannot build a theory without accepting some intuitive truth, and > some third person presentation of those truth. AR false means that the > simple y = sin(x) real function could intersect the real axes on some > non integer abscisse. Do you really believe that? Quantum mechanics > relies completely on AR. If AR is false, QM is inconsistent (and almost > all math). > So, either you put in AR something which is not there (like peter D > Jones who want me doing "Aristotle error" on the numbers (like if I was > reifying some concreteness about them), or you should have a powerful > argument against AR, but then you should elaborate. > > I'd say a candidate for making AR false is the behavior of the prime numbers, as has been discussed regarding your Riemann zeta function TOE. As I suggested on that thread, it could be that the behavior of the Riemann zeta function follows a collapse that is dependent on the observer. This would seem to agree with my view that the search for invariance, "grouping things", which is an observer-dependent action, is even more fundamental than prime numbers. And of course the primes lie at the heart of arithmetic. > > > My own intuition begins from my own indexical > > self-assertion, my necessity, generalised to an inclusive > > self-asserting necessity extending outwards indefinitely. > > > Here I have a pedagogical, if not diplomatical, problem. What you say > is exactly what the lobian *first person* will feel. I hope you will > see this eventually. > > > > > > I don't look > > for a way to 'get behind' this, and to this extent I don't seek a TOE, > > because I can't believe that 'everything' (despite the name of this > > list) is theoretically assimilable. > > > It is not. Here is the funny thing: the third person "ultimate reality" > with comp seems to be not so great: it is just the natural numbers, > including their relations in term of addition and multiplication. > This is enough to give rise to first person plenitude(s) which are way > bigger than "just the numbers". Indeed the first person plenitude > escapes *all* theories. (Even provably so, and that is why comp gives a > sort of vaccine against almost all "normative" psychology or theology. > Accepting comp is like accepting we cannot control everything. Comp, > well understanded, should be appreciate by those who likes freedom, and > be feared by those willing to control too much. > It looks paradoxical, but it is only "counter-intuitive. It is akin to > "Skolem paradox" in "model theory". Some little structure can have > giant substructures. > > > > This may well be blindness more > > than modesty, however. > > > > Having said this, of course in a spirit of learning I'm trying to > > understand and adopt *as if* true the comp assumptions, and continue to > > put my best efforts into getting my head around Bruno's roadmap as it > > emerges. I have a lot of experience of changing my mind (and maybe I'll > > get a better one!) > > > I certainly appreciate your good will, > > Bruno > > http://iridia.ulb.ac.be/~marchal/ --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---