On 05 Aug 2012, at 19:18, Stephen P. King wrote:
On 8/5/2012 4:01 AM, Bruno Marchal wrote:
On 04 Aug 2012, at 17:19, Stephen P. King wrote:
Hi Bruno,
There was a typing error in what I wrote originally. Please
try it again.
On 8/4/2012 7:50 AM, Bruno Marchal wrote:
[SPK]
Yes, and that is exactly why I am asking you to reconsider
the idea that "arithmetic is ontologically primitive"! When we
reduce a class to the ontological primitive level (meaning that
all else supervenes upon that class or some subclass thereof),
then we make the relational structure of that class degenerate.
We literally eliminate the meaningfulness of the class if we
make it uniquely primitive. This is why a primitive class is
denoted as "neutral". It cannot be "any particular thing", it is
either "Everything" or "Nothing" or both simultaneously
(depending on your pedagogical stance).
I cannot give sense to that paragraph.
Are you familiar with the concept of degeneracy?
Yes.
Explain why assuming addition and multiplication makes arithmetic
or reality degenerate.
Dear Bruno,
Addition and multiplication, as the operators alone, do not
cause degeneracy and that is not what I am claiming. It is the act
of taking Godel numberings of arithmetic strings that induces
degeneracy.
?
When one defines a number in terms of other numbers, it makes the
identity - the uniqueness - of particular numbers degenerate. 2+2=4
is no longer just a single transcendental fact when we include Godel
numberings in our model as we are literally requiring that numbers
(and their combinations) to have multiple meanings.
? I can be OK, and the "meaning" variates with respect of the
universal numbers. But from the 1pov, this just make the measure
problem more difficult.
This effectively destroys 3p meaningfulness, as it will take an
infinite tower of levels and indexing to sort which numbers have
which meanings and even in this case we have to allow for non-well-
founded cases (such as a number that names itself).
Indeed. But that is what I defend since the beginning. No need to
postulate non-well-foundedness because we have it for free from
computer science.
Again, even if true, it cannot be relevant, given that I explain
why and how physics (both the sharable part (quanta) and the non
sharable part (qualia) are entirely reduced to number's theology,
and this in a way which refutes once and for all any reductionist
conception of the soul/person.
On the theology part of your result we agree 100%. Reductionism
fails utterly. What you are not understanding is that the actions
that you are assuming occur at the arithmetic level
OK in a large sense of "action", but the physical actions does not
occur at the arithmetical level, but at the level of the material
hypostases (povs).
in fact cannot occur in the absence of interactions between
"persons" however those might be defined.
Yes, that is the point. You need persons and souls to get physics.
That is the result. But you don't and can't use matter and person to
get them. You can use only the numbers and their laws (or equivalent).
The problem is that you have "thrown the baby out with the
bathwater" by the claim in step 8.
But it is a logical, semi-axiomatic deduction, so you have to find the
flaw.
You seem to always start from the conclusion, and criticize it for
philosophical reason. You should proceed in the other way round:
start from the assumption (comp) and use your philosophical idea to
find a flaw in the reasoning.
If and when an argument yields an absurd conclusion, one can
only start at the end and work backwards to see where and when the
absurdity vanishes (if at all). Sometimes the absurdity is is a
step near the end, sometimes it could be at the beginning. Comp
only is absurd, IMHO, at step 8. By denying the necessity of any
physical world you are effectively removing the means by which the
elementary arithmetical constructs can both have unique identities
and interact with each other.
You get it wrong. UDA shows the necessity of the physical worlds. It
just shows also the necessity of not making it primitive, but a number
(psycho)-logical consequence in the comp theory.
You do not seem to understand that concepts that you are using such
as "interviewing the Modest Machine" become the meaningless
statements by a single solipsistic entity when you make claims such
as this:
"Instead of linking [the pain I feel] at space-time (x,t) to [a
machine state] at space-time (x,t), we are obliged to associate [the
pain I feel at space-time (x,t)] to a type or a sheaf of
computations (existing forever in the arithmetical Platonia
which is accepted as existing independently of our selves
with arithmetical realism)."
This is just the first person indeterminacy on the whole UD*, or on
arithmetic.
Meaningfulness is a public fact. It is not a private truth.
Consider what would happen in your narrative of the UDA if one where
not permitted to keep a diary of the experiences of the
teleportations.
But this does not occur. In UD* observers can take note of result in
diaries. They are just not primitively real.
It is the "diary" that acts as a publicly accessible source that
allows meaningfulness to emerge for the statements like "I am in
Washington". The diary is a proxy for a physical world, just as the
yes Doctor is a proxy for the physical world. Please understand that
I am claiming that the physical world cannot be "ontologically
primitive" in agreement with you, but I am also claiming that
neither can elementary arithmetics be ontologically primitive.
This means you have not studied logic and arithmetic. Arithmetic has
to be primitive in any theory (except physicalist ultrafinitism, which
is incomptaible with comp).
It is the "existing forever in the arithmetical Platonia" idea
that is the poison that is causing the absurdity in your result. As
I have been trying to explain, "existing" is not a state of "being
definite of property"; it is merely "necessarily possible".
No, that will be "physically existing", which is defined in the higher
level hypostases. For the ontology, existence is defined by the rules
obeyed by the existencial quantifier. ExP(x) is true if it exists a
number n such that it is the case that P(n).
It is not even a state of being as it cannot be contingent of
anything or supervene on anything. The truthfulness of a arithmetic
statement is contingent on the ability of entities to both
subjectively ascertain the validity of a claim and the public
( which is emergent from the intercommunication between many
entities) availability to prove the claim (as in demonstrative
profs). It is not an a priori definite property as there cannot be
any such thing.
That is arithmetical idealism, and if that is true, comp does not make
sense at all.
The degeneracy can be see in your illustrations in SANE04, in
the figures 7 and 8. You are identifying the DU operations with the
1 of sigma_1 sentences of arithmetic. Here are your exact statements
in SANE04.
"Suppose now, for the sake of the argument, that our concrete and
‘‘physical’’ universe is a sufficiently robust expanding
universe so that a ‘‘concrete’’ UD can run forever, as
illustrated in figure 7."
and then later you write:
"Figure 8 illustrates our main conclusion, where the number 1 is
put for the so called Sigma1 sentences of arithmetic."
This makes the infinite set of distinct identities of all of the
quantities and qualia that are supervening on the DU collapse into
the singleton of a sigma_1 sentence (not a plurality of sigma_1
sentences!).
?
How so you ask? Because the diagonalization of Godel numberings
strips away the unique identity of numbers or combinators or any
other entity that is isomorphic to the N of {+,*, N}.
?
You even allude to this yourself in SANE04: "If comp is correct,
the appearance of physics must be recovered from some point of
views emerging from those propositions. Indeed, taking into
account the seven steps once more, we arrive at the conclusion
that the physical atomic (in the Boolean logician sense)
invariant proposition must be given by a probability measure
on those propositions. A physical certainty must be true in
all maximal extensions, true in at least one maximal extension
(we will see later why the second condition does not follow
from the first) and accessible by the UD, that is
arithmetically verifiable. "
An atom in the Boolean logic sense is defined as: "... those
elements x such that x∧y has only two possible values, x or 0." But
guess what, there does not exist a atom for a Boolean algebra what
has an infinite number of propositions *prior* to the solution of an
Np-complete problem, as Boolean Satisfiability is an NP-complete
problem.
?
Let me be more explicit here on this claim. We cannot make any
claims of the definiteness of a truth value when such is not
available for inspection.
*that* is solipsism/idealism. Even Gödel's incompleteness would not
have sense if that was the case.
You are effectively asking for the read to believe that an action
that requires an infinity of steps occur prior to (so as to be
available for) the truthfulness of the Sigma_1 sentence.
This comes from the first person indeterminacy on the whole UD*. It
makes sense because we have that p -> Bp for the sigma_1 sentences,
and thus p -> [] <> p, in Z1*, and X1* (and S4Grz1), and this provides
the arithmetical quantization defining already the "measure one" and
its (quantum-like) logic.
We cannot assume that that which requires an actual eternity to
obtain is available any time prior to the end of that eternity. This
statement is absurd itself!
No problem, because that infinity is a machine pov. We don't need an
actual infinity in the ontology. But we cannot avoid it in the
epistemology, and thus in physics.
It just occurs to me that this is a possible problem for your
Bp&p theory of knowledge; the "accidentalist" theory. An
accidentalist theory of knowledge requires an infinitely extendible
string of uncorrelated "lucky accidents" to justify arbitrary claims
of a priori truth. The probability measure of such is already known.
It is measure zero. It never happens! Therefore the Bp&p concept
must be augmented with some postulates that force the accidents to
happen "regularly", but this removes the "accidental" nature of
theory!
A good thing, done by the presence of "Bp". Bp & p is not accidental
at all. Indeed, before Gödel, everyone thought that Bp -> p would be a
theorem. Since Gödel we know that this is false with p = f, and since
Löb we know that Bp -> p implies p. So the "accidental" feature is in
Bp and is a consequence of incompleteness. We have to live with that
if we assume comp and our local correctness. But this accidental
feature is exactly the one needed to relate the "dream argument" to
comp in the formal setting, so Gödel's incompleteness makes a bridge
between classical metaphysics and computer science.
Let me ask you a seemingly unrelated question. Are you familiar
with the concept of "synthetic a priori"?
You keep escaping forward. Just use any notion you want to find a
flaw, or assess the result, please.
Bruno
http://iridia.ulb.ac.be/~marchal/
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