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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