On 14 May 2013, at 04:15, Pierz wrote:
On Tuesday, May 14, 2013 12:13:19 AM UTC+10, Bruno Marchal wrote:
On 13 May 2013, at 09:30, Pierz wrote:
> On Monday, May 13, 2013 2:49:32 AM UTC+10, Bruno Marchal wrote:
The inside view comes when we agree that knowledge obeys to S4, and we
recover S4 (S4Grz) by linking truth to belief.
In a sense, for a machine M1 much stronger than a machine M2, the
theology of M2 can be made mathematical. What M2 cannot do
"mathematically" is to lift that theology on herself, unless she bet
(cautiously) on some self-correctness principle, but that cannot be
done in any 3p method, and usually math is considered as 3p-science,
so that correctness is not a part of math, but on faith in some
reality made by the machine M2. Likewise, I decide to not look at such
machine as zombie, and that means I project a non mathematical thing
(my consciousness) on them. This too is not mathematical.
In fact some mathematicians understood already that the encompassing
notion of "mathematical truth", or even just "arithmetical truth" is
not accessible by mathematics. In practice, this is no problem because
we hardly need such an encompassing notion, but in "theology" we need
it for the inside views.
Well I'll need to read the magical island story to make any sense of
Computerland or Numberland are more magic than the Wonderland :)
A good book is Boolos 1979. A nice recreative introduction to G is
Smullyan's "Forever Undecided". In that last book it looks like it
concerns only people living in some fairy tale, with perfect liars and
truth-tellers inhabiting some magic island, but that fairy tale is
shown to be the case for ideally perfect machines thanks to the
"famous" diagonalization lemma of Gödel.
Cool. Thanks for those references. A fairy tale! I can cope with
Nice. I will come back on this, soon or later on Russell's FOAR list.
I think you did a pretty good summary of the UDA(*). I am not sure
what you are missing. Feel free to try to point on an assumption which
would have been made implicitly, or if a step is not valid. UDA1-7 is
enough I think, as step 8 is more subtle, and can certainly be
Ha! Nothing on the net is safe!
(I will reread it and answer some questions there asap)
I wrote that for my philosophy group quite some time ago (well, 2011
as you can see). Since then I have gotten my head around step 8. My
agnosticism about the argument stems not so much from having found a
concrete flaw as from a lack of confidence in our understanding of
the nature of consciousness (a question about the comp assumption
itself), as well as an uncertainty about your use of arithmetical
realism. I know you insist that your version of AR is "weak", but I
wonder if you're not conflating types of "being". To be sure, I can
accept "7 is prime" as an independently "existing" fact, but of all
the problems of philosophy, the nature of what being is is surely
one of the trickiest.
Our minds just don't seem to be well equipped to grasp something so
fundamental - perhaps even the whole notion of being and non-being
is unintelligible when enquired into deeply enough. There are
propositions about the states of being in the world ("the cat is
dead"), and there are propositions about propositions - purely
logical ones (forgive my lack of rigorous philosophical terms here.
I'm not an academic philosopher
That's why you are clear and talk in an intelligible way. I am not an
academic philosopher too. I am a biologist/psychologist/theologian who
understood early that with comp, biology/psychology/theology admits
mathematical (even arithmetical) foundations.
and I can't recall the technical way of defining this distinction).
You've merged the two, making statements about the world a special
kind of logical statement. You've argued in effect in the MGA that
this move is the only elegant solution to the paradoxes that become
apparent when the notion of physical supervenience is pushed far
enough. But it is a pretty massive leap. I see the appeal of the
solution - but I've also wondered if paradoxes like the one exposed
by the MGA aren't actually better seen as refutations of the comp
That remains logically possible.
The comp hypothesis is in a sense a naive one - one notices that
computers can perform 'thinking-like' operations, solving problems
that we use thought for, so one makes the leap that perhaps the mind
itself is a computer.
Well, the brain, or the body, or the environment, at some level. The
mind is a too fuzzy term, even with comp. It can be the software
(still machine or number like), or the consciousness, which is more in
the limit of the UD* than in any particular computations.
This began as a natural hypothesis, before anyone saw the abyss that
it inevitably and logically leads to. To my mind, the MGA is
unnecessary. One can arrive at much the same point by imagining
computations carried out with hoses and buckets ("Olympia") or
spread out over continents and centuries, with partial results
passed around from one weird hose and bucket computer to another by
letters, pigeons, arrangements of stones or whatever. How on earth
can such a computational system contain consciousness?
Leibniz asked the same question with a brain, when look in details, it
is not different from buckets and stone and pigeons, ... Consciousness
is "in platonia", even a bit above (truth). The computational system
just makes it possible for the "divine consciousness" to forget its
divine nature and to concentrate on the terrestrial duties.
You really are forced either to abandon comp or to embrace the idea
that it's the logical relations themselves that "create" the
OK. I find this nice, as I tend to consider matter and physics as
hiding problem, or even create it, due to the incorrect conception of
reality (WYSIWYG, instead of non-wysiwig).
It stretches comp to the breaking point and throws one back on the
whole problem of consciousness yet again. I see the appeal in your
mathematical formalism, but it still leaves many strange unanswered
questions, like where time comes from for instance.
Subjective time comes from the third hypostases (the first person,
S4Grz1). Physical time is more mysterious and difficult to derive. It
might be just a local indexical gauge of some sort. Physicist have not
solved that problem either.
Maybe computationalism is just wrong.
Absolutely. Even if true, it is unbelievable, from a purely rational
standpoint. But there are also strong evidences for it, and few
evidences for an alternative theory.
It seems a digital substitution *should* work, but do we know really
enough to make that claim - or bet?
The next generation will not wait to know, they will accept copies,
just to have a higher probability to see the next soccer cup or
Our understanding of the brain is still in its infancy and the
philosophy of mind still flounders about in a logical quagmire (I've
read the deeply unsatisfactory texts).
But we don't need to understand the brain to copy it. We can't really
understand completely our own brain, and that's why I insist on the
act of faith or theological aspect of comp.
There are data from studies of psychedelics that are still *way* too
confronting and radical for the mainstream to even dare to talk
about because of the fear of being labelled a mystic and having
one's reputation as a serious scientist trashed.
In my case some other people did a good job, without mentioning
psychedelic. In a sense it makes me free to aboard such talk. But
then, with salvia, I have got a better understanding that many people
are not ready, neither for salvia, nor comp, nor QM or GR actually ...
What's appealing about your theory Bruno is that it does provide
some kind of framework within which those data could make sense - I
know you've talked about Someone-Who-Isn't-You's salvia experiences
as fitting or supporting comp, and have argued for greater openness
to the phenomenological evidence of psychedelics.
Yes. It is of course quite double edged today. Then salvia go quite
farer than comp. I am overwhelmed by the data on consciousness and
But the weakness of the arithmetical ontology is its permissiveness.
I have grave doubts about your claims of testability. You've
admitted that the mathematical problems of deriving physics from
arithmetic are "hard".
We got already the quantum shape, but we have no hamiltonian, nor
anything looking like a physical constant. It is works for the
infinity of future generations.
I think that is surely an understatement! The maths involves far too
But that's not really a problem. On the contrary, those infinities are
needed for having reasonable measure, and the modal logics can cope
with the constraints for the certainty case, from which we can derive
the logic they obey. The self-referential logics does bring a lot of
information, and notably that justifiable/non-justifiable distinction,
and the negative (neo-platonist) aspect of the theology.
On the face of it, it seems to me that pure arithmetic would permit
all self-consistent physics and any specific set of physical laws
would be a local condition so to speak (mathematically, not
spatially "local" of course).
Not really. That's an advanatge of comp: the physics is unique and the
same for all machines, but it is complex and has possible cluster of
multiverse (multi-multi-verse, intermediate realities between heaven
and earth, etc.).
There's also the question of measuring infinite sets - a problem
raised by Deutsch in "The Beginning of Infinity" when critiquing
ideas similar to yours. I've asked about this before but you assured
me Deutsch was wrong and you were right - alas my maths was not up
to disputing the point. But I still wonder how it's possible to
measure the proportion of infinite sets of computations. If I have
some function f(), then I can also imagine some function f1() where
f1() = f() +1 -1. Then of course I get f2() = f1() +1 -1, f3() =...
etc up to f()inf, all equivalent to f(). So deriving a proportional
measure seems impossible, since every function can be calculated in
an infinite number of (admittedly more or less efficient or
But infinities makes measure theory more easy. And the self-
referential constraints put a lot of order there. But of course, this
leads to very hard mathematical questions (one of which has been
solved by Vandenbussche).
Phew. So, in a word I find appeal in your ideas, but despite
recognizing the force of the argument, I remain agnostic on the
initial assumption of comp
I am too. That's why I am not a philosopher, but a scientist. A
scientist does not defend that a theory is true. Only that it is
testable, and then he can love it for its elegance, but true? Nobody
knows, especially for comp, we just can't know (but we can be deluded
in believing we know, like after surviving, apparently, with a
and am as inclined to see the UDA as an argument *against* comp as
to see it as an inevitable conclusion.
Without QM Everett, I would have thought so. But the MW looks like a
confirmation of the most startling consequence of comp, that we are
multiple. It does not make comp true, but it makes it quite plausible
with the current knowledge.
Truth is bigger than us, (a proposition I know you agree with), and
Truth I suspect is bigger than mathematics, bigger even than
arithmetical truth which incompleteness shows is beyond the reach of
formulation. In these deep realms we are over our heads in mystery
and I'm suspicious of any reduction to rationality.
Well, here rationality forces us to see the limit of that reduction,
like if the left brain can see the grandeur and depth, and the
necessity, of the right brain. This really gives sense, informally and
formally, to Plato. Even if false, all this can help to open our mind,
and have fun. Then comp gives a sense of modesty, which I like very
much, notably it reminds us that we are linked to something that we
cannot reduce in any 3p manner, so it looks more like a vaccine
against reductionism (notably of numbers and machines) than a
I certainly love comp. But, like salvia, this does not mean I believe
they are true. Just very interesting, quite mind blowing, and, as far
as I can know, rather plausible.
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