On 18 Sep 2013, at 11:43, Telmo Menezes wrote:
On Tue, Sep 17, 2013 at 7:11 PM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 17 Sep 2013, at 11:49, Telmo Menezes wrote:
On Mon, Sep 16, 2013 at 2:35 PM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 15 Sep 2013, at 10:37, Telmo Menezes wrote:
On Sun, Sep 15, 2013 at 9:54 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 14 Sep 2013, at 04:25, Craig Weinberg wrote:
<snip>
With computationalism, it is more easy and clear. What exists, at
the
ontological level, is what make true a sentence like "ExP(x)". So
number
exists, once we assume arithmetic or combinators ..., because
they make
true
Ex(x = x). And then (and only then), we can define different
notions of
epistemological existence, and they will be as many notion of
existence
as
we have modalities (notably those coming from incompleteness, as
they are
unavoidable. They will make true proposition with the shape []
Ex []
P(x),
or []<> Ex [] <> P(x), etc...
Ok, nice. I'm slowly getting used to modal logic. It's a weird thing
to learn because it seems to require removing things from your
thought
process rather than adding them (at least for me). It's hard because
it's simple.
That's the idea of math and logic. It is abstraction. it
simplifies, indeed.
So we will get notions of psychological
existence, physical existence, etc.
Ok, but what is the computational substrate?
*any* first order logical specification of *any* turing universal
system
will do.
I suggest a very tiny part of arithmetic, but the S and K
combinators will
do as well, or the Unitary group, etc.
There is still a
dissatisfaction in having to just accept it. I guess one can go back
to the idea of God, in a way.
God created 0, and its successors, and then said to them add, and
multiply.
Ok. I'm agnostic, so I don't cringe at this sort of statement. I guess
I'm also an atheist, because I reject the idea of anthropomorphised
gods, but that's irrelevant here. My dissatisfaction with this is
empirical: god has been used so many times to cover up for our lack of
knowledge that, when confronted with current lack of knowledge and one
hears the word "god" one tends to become suspicious. On the other
hand, if there is something fundamental we provably can't know, I
guess it's fair enough to call that thing "god". But I think we should
be extra-extra-careful before making that move.
I am agnostic too. But, like for consciousness, we can agree on some
proposition about those notion, and reason from there.
As you know I use "god" in a very large sense, and then, with comp and
the classical theory of knowledge, "god" or "divine" means mainly
"true", or related to true, with in mind the idea that "truth" is not
something definable, although we can agree on many truth.
All the rest is what emerge from a universal matrix of cohering
Computations/dreams (1-computations, 3-computation) provably
existing as a
consequence of the addition and multiplication laws.
If you can believe that 17 is prime, independently of you, then you
can
understand, that, if you assume computationalism, arithmetic, as
seen from
different internal self-referential view, contains such "universal
matrix",
or the universal dovetailing or any sigma_1 complete set of number,
or a
Post creative set, a universal purpose computer, reflecting itself.
Arithmetic provides the block-mindscape. The existence and unicity
of a
block multiverse emerging from it is basically unsolved, nor even
yet made
enough precise.
It's just what is. But then this is an
ontological statement. Does this substrate exist? You can not use
the
previous reasoning to support its existence, or can you?
I can't. I only justify why machines develop such beliefs, even
for "good"
(relatively correct for they local purpose in their probable history)
reason. Just that the physical reality is not the fundamental
reality. The
physical reality is a complex self-referential sum made by a
universal
machine/number, and selected or varied through first person
(sometimes
plural) experiences.
There is no substrate (in that picture). Just dreams, or limit on
computations, probably related to (Turing) Universal group, braids,
as the
empirical evidences suggest, but that is what we must recover from
the
machine looking inside (in different ways corresponding to the
intensional
variants, the arithmetical hypostases).
Even events seen in dreams get some
notion of existence, for example.
That's nice. I even have problems with statements like "batman
doesn't
exist".
Really?
I will send you a video!
Doesn't he, in some sense?
Certainly, in many sense. He has "real" cousins, like jetman:
http://www.youtube.com/watch?gl=BE&v=x2sT9KoII_M
A batman with a french accent! Coincidence?
Europa is full of thinks. Dracula has also many cousins ...
Are there any coincidence? Well, they are all relative too.
And certainly not, in some common sense.
Here, with comp, it is easy at the start, only 0, s(0), s(s(0), ...
exist.
The rest will come from the many relationships the number inherits
from the
+ and * laws. (+ the comp invariance of consciousness manifestation
and
experience for the digital substitution at some level). That gives
the
relative perceptions, the dreams, the beliefs, and (but only God
knows), the
truth.
If we don't recover common sense existence, we fail. But unless
comp is
false, why should it contradicts common sense? Thanks to Everett we
do have
evidence of sharable histories and stable first person scenarios.
Comp get
close to solipsism, but should avoid it.
But maybe it doesn't. At least some week form of solipsism, where
there is in fact only me, but the notion of "I" is extended. No?
I would say that there are as many notion of "I", that there are
intensional nuances.
The most basic is the 3-I, like when the machine says I have two arms,
(Bp), then there is the 1-I, when the machine says that she has two
arms, and it is the case that she has two arms (Bp & p), then there is
the observer I, when the machine says that she has two arms, and it is
possible, not contradictory, for that machine that she has two arms,
or equivalently that 0=0 is not a contradiction, Bp & Dp, equivalent
with Bp & Dt. Then the "feeler" whioch combines both Dt and "& p".
They all see arithmetic very differently.
The modalities Bp & p, and Bp & Dt & p, are solipsistic, by their non
communicable/justifiable relation with truth. But the others are not.
Comp will doubtfully change most of
physics, no more than evolution can changed actual biology.
Right. Or even evolution itself can be seen in a new light under the
MWI, but there's no reason to reject it. It might just not be the
ultimate approximation to truth (like classical vs. modern physics).
OK.
Bruno
We cannot invite him for coffee but
we can talk about him and we all know what we're talking about.
No doubt.
I think that with comp you don't have to believe in anything more
than the
independence of the numbers' properties and relationships.
Plato's God is truth, and with comp, if sigma_1 truth is enough for
the
ontology, you need much more than the arithmetical truth, to get
the inside
view(s) and their mathematics.
Fortunately, this is reflected only on the first order extensions
of the
arithmetic hypostases. That has been worked out for G and G* by the
Russian
and Georgian logicians. See Boolos 1993 for this.
http://iridia.ulb.ac.be/~marchal/
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