On 19 Oct 2015, at 03:22, Bruce Kellett wrote:
On 17/10/2015 3:59 am, Bruno Marchal wrote:
On 16 Oct 2015, at 02:36, Bruce Kellett wrote:
It is the failure to clearly distinguish between these different
senses of the word 'exists' that cause most of your confusion.
The mathematical theorem is that when a machine looks inward, in
the sense made precise by Gödel, Kleene and others, the machine is
forced to distinguish 8 main different sort of existence, and in
fact many more.
The problem here is that we are not restricted to introspection --
looking inward. We discover the physical by looking outward --
observing the world around us. Sure, we can never prove that this
world is not an illusion, but the important point is that even if
the external world is an illusion, it defines what is real,
?
I would say that we infer the physical by postulating there is an
outward we can looking for. And we cannot deduce from the observation,
neither that there is an outward, still less use it to define what is
real.
That requires a metaphysical act of faith, as the antic argument
explained already. I might make a dream in which I discover a new
planet with some telescope.
I just do not assume (thus primitive) a physical reality. I agree that
there is one, but assuming it leads to insuperable difficulty in the
cognitive science.
because it is what we see and interact with.
Assuming that exists.
But the theory which assumes that exists (Arstotelian metaphysics)
fails on the mind body problem, so maybe we can take a look at a
theory which does not assume a physical reality, but try to derive its
appearance from something else, like the computations which already
exists once we agree on the axioms of elementary arithmetic.
That is what defines physical existence.
For a Aristotelian believers. Not necessarily for a platonist.
The fact that you cannot dispense with this level of physical
existence,
You have not prove that, and indeed what computationalism provides a
counter-example.
but you can dispense with all of mathematics,
Even with aristotle metaphysics, I am not sure of that, and thus I am
even less sure without it.
is a telling argument for the fact that the externally existing
physical is more fundamental that arithmetic.
I don't see any argument. I see just an act of faith that there is an
outward reality and that the observation defines it, which is an axiom
of self-awakeness.
The universe existed long before there were any conscious beings,
and even longer before arithmetic was invented.
1+1=2 well before humans invented arithmetic too. Don't confuse the
arithmetical truth, and the language and theories developed by humans
to explore it.
This is intrinsically different from any sense of the word 'exist'
that you get below.
Indeed. if computationalism is true, that existence is fictional. It
is a myth, a fairy tale. It explains neither consciousness nor the
observation (it is not obvious, but your refutation of step 8 was not
valid, as it invokes the primary matter, and attribute it something
non Turing emulable having a role for consciousness, contradicting
computationalism).
And it is the failure to understand that physical existence -- as
defined by looking out --
Looking out can defined the physical existence, but does not prove
that physical existence is not a particular modal existence.
is more fundamental that any purely theoretical 'existence' defined
in terms of some internal system of thought, that is the main
problem with your system.
There is a problem indeed, but it is interesting as it solution solves
the three parts of the mind-body problem (the mind, the body and the
relation in between). With an assumed or primitive material universe,
we get that a mind problem, needs to add an identity thesis which
makes computationalism inconsistent.
Of course, if you abandon computationalism (and most of its weakened
version actually) then materialism might make sense. I find this
unsatisfying because this is like inventing something nobody can prove
the existence to make a simple theory false, before even studying it
or testing it. Then most people believe in computationalism, and by
keeping the materialist myth, they come up with the elimination of
person and consciousness, which is nonsense for many.
Bruno
Bruce
The ontic basic existence can be based on any first order logical
specification of a Turing universal language or system. Once
chosen, the ExP(x) means it exists a basic element which has the
property P.
To fix the thing I use as basic element the number+basic +/*laws,
but the theology of the machine, including physics, will not depend
on which universal basic system has been taken. The first basic
Turing universal system is like a sort of base in which we can
describe and study all the others.
I will also say that a relation R(x,y, ..) or a property P(x)
exists for a shorten of it is true that R(x, y, z) for some x, y, z.
Then we have the 8 nuances that no machine can miss when looking
inward deep enough, which is exactly what they can do when they
believe in enough induction axioms.
Then I define the set of beliefs of the ideally correct machine
*in* the language of the machine, which here will be elementary
arithmetic, given that we have fixed that one. The most typical
machine/number/theory/belief-set is Peano Arithmetic.
RA can prove that PA exists (trivially actually), and RA imitate
all machine, notably in proving all the details of the computations
that PA does when doing her "thinking".
I write []A for "PA proves A", and I think about it as translated
in the language of the machine. In our case this makes []A an
arithmetical proposition.
Then you get all the sort of existence by the quantified modal
logics:
ExP(x)
[]ExP(x)
[]Ex []P(x)
With [] put for []p, and for []p & p, and for []p & <>t, and for
[]p & <>t & p, and some infinity of graded variants, depending on
the points of view.
The apparent primary matter is given by the quantization:
[]<>ExP(x)
[]<>Ex []<>P(x)
(but here only on []p & p, []p & <>t, []p & <>t & p, with p obeying
p -> []p).
So there are indeed many sort of existence, and most error in
philosophy and theology can be reduced to a confusion between such
existence, or a confusion between the corresponding hypostases.
If you define [1]p = []p & p, [2]p = []p & <>t and [3]p = []p & <>t
& p, and [0]p = []p, you get the five hypostases, and even 8, as
three of them split between a provable and true part. The
incompleteness makes the true part extending properly the provable
part, and that split is inherited by [2]p and [3]p.
Lucas-Penrose invalid use of Gödel's incompleteness can be seen as
a confusion between [0] and [1]. The separation between science and
theology can be sees as a confusion between [0] ans [0]* for the
logic which split along proof and truth. Obviously some confusion
entail others.
I recall the epistemological the plotinian lexicon:
p
[]p
[]p & p
[]p & <>t
[]p & <>t & p
One
Intellect
Soul
Intelligible Matter
Sensible Matter
Truth
Provability
Knowledge
Observable
Sensible
Only One (God) and the Soul do not split along proof and truth.
Up to now it works. It is a pure mathematical theory, and physics
is determined by them, so just let us look if it works. Thanks the
quantum weird logic and possible interpretations, it works.
The neoplatonism of the universal (Turing) machine suggests that
the Heisenberg relations *are* consequence of the (mathematical)
self-reference limitations. Aristotelians cannot see that because
they tend to confuse the One with the Observable.
The theory gives the tools to test all this, and measure a possible
departure from the neopythagoreanism or neoplatonism canonically
associated to the universal machine.
If the quantum logic we got is good enough, we can apply Gleason
theorem and prove the unicity of the measure on the computations
(when seen from inside, observed), and if some quantum logicians
are correct (hard paper!), the whole standard model might follow.
UDA is for the human babies, AUDA, the translation, is for all
universal Löbian number, where a number is Löbian when it can prove
p -> []p for all Sigma_1 arithmetical sentences.
Note that the ontology is given by RA, for which p -> []p is true,
but RA don't know that. For PA, which exists in the mind of RA (so
to speak) p->[]p is not only true, but provable. She knows, like
you, that she is Turing universal, and Löbian.
Keep this post, as further conversation could help to make all this
clear and simple. You might put some good book on logic (Mendelson,
Boolos and Jeffrey, Epstein & Carnielli) near your bed.
Bruno
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