On 17 Sep 2013, at 11:49, Telmo Menezes wrote:
On Mon, Sep 16, 2013 at 2:35 PM, Bruno Marchal <[email protected]>
wrote:
On 15 Sep 2013, at 10:37, Telmo Menezes wrote:
On Sun, Sep 15, 2013 at 9:54 AM, Bruno Marchal <[email protected]>
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.
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
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. Comp will
doubtfully change most of physics, no more than evolution can changed
actual biology.
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.
Best,
Bruno
http://iridia.ulb.ac.be/~marchal/
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