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).
> 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.
> 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/
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