On 03 Nov 2015, at 21:17, John Mikes wrote:
I read it all, did not find what PA and RA are standing for.
Can you explain in brief?
PA is Peano Arithmetic. RA is Robinson Arithmetic(*).
RA can be proved to be "sigma_1 complete" or "Turing universal": it
imitates all digital process, and thus all brains if we assume
computationalism. But RA is poor in its cognitive ability: it can be
said already being a little bit self-aware, because it obeys to the
self-awareness axiom ([]p -> [][]p), but it is not aware of its self-
awareness ([]p -> [][]p is true for RA, but RA cannot prove it).
PA is basically RA + the induction axioms (F(0) & for all x F(x) -> F(x
+1)) -> for all x F(x). This makes PA enough introspective so that it
got the G/G* theology and the ability to "know" (guess) it under the
meta-assumption of self-correctness and mechanism.
Bruno
(*) RA is logic + the non logical axioms:
0 ≠ (x + 1)
((x + 1) = (y + 1)) -> x = y
x = 0 v Ey(x = y + 1)
x + 0 = x
x + (y + 1) = (x + y) + 1
x * 0 = 0
x * (y + 1) = (x * y) + x
PA is RA + the infinitely many axioms (for each F being a formula in
arithmetic):
(F(0) & for all x F(x) -> F(x+1)) -> for all x F(x).
RA might be conscious, but is not aware that it is conscious (like, I
think, worms)
PA is conscious, and is aware of the fact, and its non-communicability
or ineffability (like most animals with a brain big enough, like I
think, already an octopus).
Note that RA is very often called Q in the literature.
Some nuances exist, like using or not the third "predecessor axiom":
x = 0 v Ey(x = y + 1).
Thanks
John M
On Tue, Nov 3, 2015 at 4:06 AM, Bruno Marchal <[email protected]>
wrote:
On 02 Nov 2015, at 18:30, Brent Meeker wrote:
On 11/1/2015 11:09 PM, Pierz wrote:
On Sunday, November 1, 2015 at 6:25:57 PM UTC+11, Brent wrote:
On 10/31/2015 11:47 PM, Pierz wrote:
On Sunday, November 1, 2015 at 4:18:05 PM UTC+11, Brent wrote:
On 10/31/2015 8:55 PM, Pierz wrote:
OK, a subject title designed to provoke, but here's a thought
that has intrigued me. Computationalism (and let's not worry for
the time being about whether one buys Bruno's UDA) states that
consciousness supervenes on computation. This necesssarily
implies (by Church thesis) that the hardware doesn't matter.
This commits us to some unintuitive scenarios in which thought
is instantiated by means of carrier pigeons delivering letters
with symbols written on them, or dominoes falling or whatever.
It's assumed that such a computation must reach a certain level
of complexity in order to become conscious, though what level of
complexity is not specified. According to some views (Brent has
expressed this position), it is necessary that the computations
reference a "world", though I'll admit I
don"t understand the rationale for that exactly. Important
though is that it is neither necessary that the computations are
carried out in some localised "device"/brain nor that they are
carried out by "wetware".
So my thinking is this: isn't evolution precisely such a
computation?
I take it you mean life is doing a computation which consists of
finding ways to live and reproduce. Life on Earth is executing
THE paradigmatic genetic algorithm.
Exactly.
It is undoubtedly an extremely complex calculation (more so than
any human thought has ever been), and it
undoubtedly "references a world". Bruno mentions "Loebianity" in
this context as well, or the capacity for self-reference. I'm
not so sure about this in relation to an evolutionary
computation. Certainly it is a highly recursive procedure with a
continual self-environment feedback loop. I don't understand
Loebianity sufficiently to say whether genes , or the gene-
environment system, might possess it. However I'm also not sure
if it's required for consciousness, or
merely self- consciousness. I don't see that the possession of
qualia demands the possession of self-awareness, though I can
also see that it is at least conceivable that an evolutionary
feedback system might possess a kind of self-reference.
Anyway it seems that if we're committed to computationalism plus
Church thesis, then we have to consider the possibility that
evolution may be a conscious process - indeed the onus should be
on us to say why it wouldn't be conscious. Which does not mean I
am suggesting some mystical additional ingredient. Evolution
would still be described objectively in terms of random mutation
plus environmental selection, but this process may have an
interior component, its own "1P".
Yes, I think that's right in a sense. Life in a sense forms a
representation of the world. If a alien scientist were told
just about the living organisms on Earth he could infer a great
deal about the inorganic aspects of the planet. I don't know if
you could say it's self-aware, except by inclusion of ourselves.
The problem is that it may be conscious in such a different way
from humans or animals that it doesn't really add anything to our
understanding of it to say it is conscious. I've sometimes had a
similar idea about the atmosphere and weather. Isn't weather a
kind of computation performed by the atmosphere and isn't it
aware of things in its environment like solar heating, ocean
currents and temperatures, human activities like jet liners and
burning fossil fuel,...
Yes. But then isn't an orbiting planet carrying out a
computation? Isn't a river? Isn't an atom doing quantum
computing? It almost becomes a matter of perspective whether any
given physical process is a computation or not, e.g., if someone
wanted to compute the route that water would take down a given
slope, they could "compute" it analogically with actual water on
an actual slope. Which, combined with computationalism, seems
like the (ahem) slippery slope to panpsychism, which I am happy
enough with, but which I suspect to be too mystical for your
metabolism...
I don't see anything mystical about saying all those physical
processes are computations, i.e. they are also information
processes. Have you slipped over from computation to assuming
they are conscious?
Computationalism is precisely that assumption (that computation
equates to consciousness).
No, it's the assumption that some particular computation
instantiates consciousness.
OK.
Computation is a pure 3p notion.
Consciousness is a pure 1p notion.
Nothing can be more different.
A computation just can makes it possible for a person to manifest
its consciousness relatively to a universal number/environment.
However, usually the assumption is also that a certain level of
computational complexity must be reached before consciousness
"kicks in". If as Bruno suggests, it's "all or nothing", then it's
hard to see why the light should suddenly be switched on when a
computation reaches some magical complexity threshold.
It's my view that consciousness is realized by certain kinds of
computation in interaction with an environment (which we call "the
physical world"). It's not just a matter of complexity (the
internet's plenty complex) or even "integrated information" (c.f.
Scott Aaronson's blog on Tononi). I don't think we know exactly
what it is, but I suspect it has to do with language and other
representations of the world. I think that there are
qualitatively different kinds of consciousness, not a continuum and
not all-or-nothing.
I agree, except that "all or nothing" is for the presence or absence
of consciousness, a bit like a point of the complex plane is, or is
not, in the Mandelbrot set, even if we can never be sure for a point
which is very near the boundary (we zoom, and still don't know after
1 billions years, and have no idea how long it could take for the
zoom to decide this).
Of course one can argue that the internet is conscious or the
weather is conscious or arithmetic is conscious -
Only if we can name the entity, but "weather" or even "arithmetic"
is fuzzy notion. To say that arithmetic is conscious is different
than to say that RA is conscious, or PA is conscious, etc.
but these depend adding the qualification "but not like my
consciousness".
RA is conscious like my consciousness after salvia (say)
PA is conscious like you and me. Indeed, we are both PA, but
reconstituted in different bodies with different memories.
I think this is a cheap argument. We only know what consciousness
is from introspective experience; so at least until we know how to
produce and manipulate that we have no basis for extrapolating to
other forms with which we have no experience. The kinds of
consciousness I refer to are ones that we do experience at
different times, e.g. awareness of without self-awareness.
If it's more of a continuum then that does suggest panpsychism,
though what the consciousness of simple processes is like is
pretty hard to imagine. Panpsychism does still sound to me like a
pretty big jump from the materialism we know and (some of us)
love. A world of conscious information processes is not quite a
world with soul, but perhaps also not so far from it.
Now you not only project consciousness onto the world, but hope for
immortality.
Well, in machine's theology, the proof of the immortality of the
soul by Socrates is valid, but is not constructive, and its
practical aspect is dependent of you degree of appreciation of not
knowing who you (first person are).
Then, a priori computationalist immortality seems to be something
more to fear than to hope, but both computer science and salvia can
be reassuring by allowing possibilities of jumps between type of
consciousness state (but *that* is still wishful thinking, as such
jump are hard to relate with some type of death.
Once a machine is above the Gödel-Löbian treshold, it has at each
instant an infinite of futures, and near death or near catastrophes,
it continues in the closer world consistent with its memory. If the
subject identifies too much with its memory, the experience can be
unpleasant. Some training in "let it go" can help, perhaps.
Bruno
Brent
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