On 01 Feb 2012, at 21:48, Stephen P. King wrote:
On 2/1/2012 3:06 PM, Bruno Marchal wrote:
I don't get it.
Many people have discussed this idea that Existence, in-itself,
is primitive and neutral (has no properties or divisions). It is not
original with me. For example, Bertrand Russell's discussion of
neutral monism and Russell Standish's ToN explain it well.
There might exist phenomenological hermeneutic of the monist kind, but
this, once we chose to do science, is a private affair, which can
inspire but cannot be communicated.
So by a neutral monist theory, its is meant a theory which does not
assume mind, nor matter, and explain them from something else. That
something else needs to be able to be described in first order logic,
at least. It should have terms for the existing objects, and axioms
for the laws to which those objects obey. Without those two
components, we can do nothing.
What I ask is a scientific theory, by which I mean a first order
logical theory about what you assume to exist, and then theorems
justifying the other form that "existence" can take.
All that does not contradict itself and is thus necessarily
possible exists, thus I claim that existence is necessary
possibility.
That's an old idea in philosophy. It is the indexical idea that
existence is consistence seen from inside. In first order logic it
makes a lot of sense, given that consistence is equivalent with the
existence of a model.
And in AUDA, the necessity of the possibility of p, BDp, is the
consequence of sigma_1 truth, and its leads to an arithmetical
quantization. Here Bp is for (Bew(p) & Diamond("1=1")), and Dp is
(Diamond(p) v Bew(f) 'relative consistency)). p is sigma_1.
Once you are using notion of necessity or possibility, being
precise forces you to suggest in which modal logic you are working,
and how you justify it. There are infinities of modal logics.
UDA justifies the use of the self-reference modal logic, and their
variants. Gödel's results (and Löb's one, and Solovay) don't let
many possible choice for the ideally correct machines. The variant
described above are the one needed to find the correct physic
(correct with respect to comp, if you get UDA).
I don't know if comp is true or not, but comp makes theoretical
computer science a lantern to find the key. It allows a
mathematical formulation of many subproblems of the (comp) mind
body problem.
Bruno
http://iridia.ulb.ac.be/~marchal/
Hi Bruno,
On these particulars we can agree. Our only disagreement is that
you seem to consider that Arithmetic is at the same level as bare
Existence and I see bare existence as neutral and that both logics
(including arithmetic) and physicality are non-primitive.
Then tell me what you mean by "Existence", and show me how you derive
logics, arithmetic and physicality from that.
Unfortunately, people mature enough in logic know that you can't do
that. No formal arithmetic can be deduced from anything less than
itself.
Our beliefs in the natural numbers is authentically mysterious. But
with comp we can, and we must, explain everything from them. And it
works, because arithmetic emulate the ... self-referential resonance
of numbers, which appears to be very rich and full of surprise.
Have you noticed that I claim that the duality that I am considering
vanishes at the level of Existence itself?
I have still not the slightest clue of what you mean by "Existence".
This is because we cannot consider Existence to be partitioned
without specifying a basis for the partition, in other words our
ontological models have to start at our level of substitution and
cannot remain coherent if we subtract out our existence as entities
that can distinguish, for example, 0 from 1.
This does not follow logically. We, the distinguishers of 0 and 1,
certainly exist at some level, from some point of view. But that
existence might be derivable (and is derivable) in arithmetic, once we
assume comp.
Some aspect of it are not derivable, and yet are still true and
existing, and can be meta-justified for simpler machines than us, so
that we can grasp them indirectly, including our incompleteness with
respect to those truth, and which comes from our local relative
finiteness.
If not, like Craig, perhaps like Rex Allen and Benjayk, you are
postulating that comp is false.
If that is the case, I encourage you to make that precise, and to
study comp and computer science to even just define "non-comp".
That will not be easy. AUDA works, for example, for many transfinite
sequences of weakening of comp.
Bruno
http://iridia.ulb.ac.be/~marchal/
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