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:
> 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

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