Hi Günther,
On 30 Nov 2008, at 18:53, Günther Greindl wrote:
>
> Hi all,
>
> Bruno, do you still keep a notion of causality and the likes in
> platonia? I have collected these snips from some recent posts:
OK, I will comment, and perhaps say more for the benefit of the
others. But in a nutshell, the simplest notion of "causality" in
Platonia is the implication. A "causes" B, if and only A is false or B
is true. I recall that "the Platonia" of Peano Arithmetic is just
arithmetical truth or the "standard model of Elementary Arithmetic,
like the Platonia of Zermelo Fraenkel set theory is (the more dubious)
Set Theoretical truth. In some context I can use deduction as a form
of Platonist causality, which, for first order Lobian Machine.
As expected it is a mathematical causality, and has a priori no
relation with physical causality ...
Then, you can consider key subset of the implication/deduction
causalities: the computational causality, for example A "causes" B if
all computations (executed by the UD) going through A are going
through B. Or things like that (they will be many variants). All
notions should be translatable in formal arithmetic (or combinators,
fortran programs, etc.) when we interview the machines in Platonia,
notably to retrieve the physical laws (or the believe in the physical
laws). When this is done we should have the comp physical notions
capable of explaining or intuitive notion of physical causality.
>
>
> Brent Meeker wrote:
>
>> But is causality an implementation detail? There seems to be an
>> implicit
>> assumption that digitally represented states form a sequence just
>> because there
>> is a rule that defines that sequence, but in fact all digital (and
>> other)
>> sequences depend on causal chains.
>
> Kory wrote:
>
>> I have an intuition that causality
>> (or its logical equivalent in Platonia) is somehow important for
>> consciousness. You argue that the the slide from Fully-Functional
>> Alice to Lucky Alice (or Fully-Functional Firefox to Lucky Firefox)
>> indicates that there's something wrong with this idea. However, you
>> have an intuition that order is somehow important for consciousness.
>
> But we must realise that causality is a concept that is deeply related
> (cognitively, in humans) to time and physical change.
I agree. Especially physical causality. But even the notion of
"responsibility" is deeply related to time (and causality).
>
>
> But both time and space _emerge_ only from the inside view (1st person
> or 1st person shareable) in the sum over all computations.
Assuming comp, and that we are correct, ok.
>
>
> In Platonia (viewed, for the time being, ludicrously and impossibly,
> from the outside)
A powerfull lobian machine like ZF can do this, looking at some
Platonia, in a precise way when reasoning on the "Platonia" of a
simpler sound Lobian Machine. (Even for the 1-Platonias, the first
person pov in Platonia (this gives the hypostases)).
> - there is no notion of time, space, sequentiality,
> before and after.
Right. But don't overlook that the number zero is before the number
one, which is itself before the number two, which is before the number
three, etc. (With "before" interpreted by minus one). The UD itself
has a first computation step, then a second, then a third, etc. But
like "a movie", you can look at all of them, well if you are
infinitely patient of course, and immortal. It is in that sense
(before making things more technical) that the UD computes in Platonia.
>
>
> The very notion of causation must be one that arises only in the
> inside
> view, as a "succession" of consistent patterns.
OK.
>
>
> In a sense, order (shareable histories) must arise from the Platonic
> Eternal Mess (chaos) -> somehow along the lines of self-organization
> maybe:
> http://en.wikipedia.org/wiki/Self-organization#Self-organization_in_mathematics_and_computer_science
>
> In this sense, the computations would "assemble themselves" to
> "consistent histories".
>
> Bruno said:
>> Even
>> in Platonia consciousness does not supervene on description of the
>> computation, even if those description are 100% precise and correct
>
> Hmm, I understand the difference between description and computation
> in
> maths and logic, and also in real world, but I do not know if this
> still
> makes sense in Platonia -> viewed from the acausal perspective
> outlined
> above. Well maybe in the sense that in some histories there will be
> platonic descriptions that are not conscious.
>
> But in other histories those descriptions will be computations and
> conscious.
A "movie" *in* Platonia, would be a description of a computation
encoded in some static way by some occasional program or entity. Even
in Platonia, such a description is not a computation, but only a
description (without any causality, even in the simple imlication/
deduction sense). It is the difference between the fact that three
added to two gives five, and the writting or the Gödel number of the
sentence "3+2=5".
It is really the difference between a reality (be it mathematical),
and a picture (be it dynamic) of that reality.
Consciousness will be related to "true mathematical facts", not on
description of those facts. The difficulty here is that consciousness
is also related to description in the memory of a machine.
Comp implies the "unification" in the sense of Bostrom. Conscious
experiences are unique, they cannot be replicated, and they supervene
on all the computations, and thus all implementations going through
their corresponding 3 comp states, or below.
Best,
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Mon Dec 01 2008 - 10:39:10 PST