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
<http://www.merriam-webster.com/dictionary/pedagogical>stance).
I cannot give sense to that paragraph.
Are you familiar with the concept of degeneracy
<http://en.wikipedia.org/wiki/Degeneracy_%28mathematics%29>?
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. 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).
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 in fact cannot occur in
the absence of interactions between "persons" however those might be
defined. The problem is that you have "thrown the baby out with the
bathwater" by the claim in step 8.
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 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)."
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. 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.
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". 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.
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
<http://iridia.ulb.ac.be/%7Emarchal/publications/SANE2004MARCHAL.pdf>.
"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
<http://en.wikipedia.org/wiki/Boolean_algebras_canonically_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
<http://en.wikipedia.org/wiki/Satisfiability_of_boolean_expressions>, 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.
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. 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!
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!
Let me ask you a seemingly unrelated question. Are you familiar
with the concept of "synthetic a priori
<http://www.britannica.com/EBchecked/topic/578646/synthetic-a-priori-proposition>"?
--
Onward!
Stephen
"Nature, to be commanded, must be obeyed."
~ Francis Bacon
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