On 29 Oct 2012, at 22:38, Stephen P. King wrote:

On 10/29/2012 1:08 PM, Bruno Marchal wrote:

On 29 Oct 2012, at 14:36, Stephen P. King wrote:
[Bruno Marchal wrote:] So numbers are universal and can be treated mathematically as always.

I agree, but the concept of numbers has no meaning prior to the existence of objects that can be counted. To think otherwise is equivalent to claiming that unspecified statements are true or false even in the absence of the possibility of discovering the fact.

Dear Bruno

I think you confuse numbers, and the concept of numbers.

No, I do not. My claim is that Numbers are objects in the mind of conscious beings.

This contradicts what you said before. It contradicts comp immediately, as comp needs the understanding of what a computer can do, even in absence of any conscious observer.

If there does not exist worlds where entities to whom numbers are concepts then there is no such thing as a concept of numbers in such worlds.

But with comp, a conscious observer is explained by number relations. We explain the concept of numbers, and of human understanding of numbers, by number relations (computations).

My argument is that concepts of truth and provability of theorems apply only to the concepts of numbers and their constructions, not to numbers themselves.

Truth applies to proposition, or sentences representing them for some machine/numbers. If not, comp does not even makes sense.

And then your argument is not valid, as with numbers, the miracle is that we can specify the concept of numbers, as this result in defining some arithmetical sigma_1 complete theory in terms of 0, s(0), ... and the laws of addition and multiplication, that everybody understands (unless philosophers?).

I am a philosopher! My argument rests only on the fact that the 'miracle' is exactly as you state it here: we exist and have a concept of numbers and can ascertain the truth of arithmetic statements. My claim is that truth valuations supervene on the ability of consciousness to form concepts of numbers.

That is idealism, if not solipsism. In comp plotinus term, you confuse the outer God (the objective ultimate truth) and the inner God, or the sould of the individual inquirer.

I question the entire idea of numbers existing as separate Platonic entities. In the absence of consciousness, there is no such thing as a concept!

Again, we need only the relation between the numbers, not the concept of numbers, which with comp will be explained by computation occurring in the brain of some machine/number.

PS BTW, from a computer scientist perspective, your use of NP never succeed to make sense. I don't dare to ask you to elaborate, as I am afraid you might aggravate your case. The NP question is fundamental and has many interesting feature, but it concerns a local tractability issue, and is a priori, unless justification, not relevant for the arithmetical body issue, nor number's theology (including physics) issue, etc.

It is the argument is sound and is the same kind of argument as what Kripke used to discuss the idea of possible worlds. In http://en.wikipedia.org/wiki/Possible_world we read:

"There is a close relation between propositions and possible worlds. We note that every proposition is either true or false at any given possible world; then the modal status of a proposition is understood in terms of the worlds in which it is true and worlds in which it is false."

All this presuppose numbers at the outset. World in Kripke are only elements of any set having a binary relation. You must study the math, not use the naive interpretation based on the use of common terms.

Solutions to equations or computations are not available until after they are actually solved.

That is constructive thinking, again incompatible with comp, although retrieved and explain for the subject. This is akin to your solipsism above. Of course it is hard to guess what you think as long as you don't propose a theory.

My solution to this is to not go so far as you do in Step 8.

You can't make the conclusion of a reasoning false by stopping the reasoning. This will only make you ignorant of a conclusion.

Let me try to be more explicit:

From your paper http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf :

"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). "

Yes. That is already true in a concrete robust physical universe (robust = own a non stopping UD).

I am pointing out that the idea of computations "existing independently of our selves" is wrong in that it conflates the meaning and truth valuation of numbers with the existence of numbers as Platonic objects.

You seem to ignore that this conflation is not us, but the doing of the (universal) numbers themselves, and this independently of me, you, or universes.

It is absurd to refer to the claim that the truth of "17 is prime" depends on any one person or entity, but the claim that the truth of "17 is prime" is knowable by any person is not absurd.

It is absurd with comp, as knowing, despite NON arithmetical in the logical sense, is still defined in purely arithmetical terms. If not, you will not surive with an artificial brain, even concrete.

If we stipulate that the content of knowledge exists somehow prior to that which knowledge supervenes upon, we are being absurd.

This is just realism. The semantical content of knowledge as to exist independently of you if you don't want to fall into solipsism.

The content of knowledge and the ability of knowledge occur simultaneously or not at all.

With comp they "occur" as consequence of + and * laws.

Absent the "concept" of numbers there is no such thing as valuations of numbers

Then 17 is prime only since humans exist on the planet? or since insects use this to regulate mating?
This is solipsism/idealism.

because the notion of Platonic objects considers objects as existing independently as some singular "perfect" version that is then plurally projected somehow into the physical realm, as we see in the Allegory of the Cave. This is a one-to-many mapping, not a one-to- one mapping.

? (so you postulate conscious observer *and* physical universes?). Your theory looks more and more like Craig's non comp theory.

How exactly is a "type" or "sheaf" a singular and "perfect" version of each and every computation and yet be something that has individuated valuations? Individual valuations of computations are only those that occur as physical instantiations of computations

"physical instantiation of computations" is something in needed to be explaiend, not assumed, if we want to understand something (not just comp). Computation evaluation is a too fuzzy terming for me.

and thus they do not "exist" in Platonia.

Then Church thesis has no more meaning.

The Many exist in the physical worlds, no?

Primitive one?

I propose a rephrasing of your statement above: We identify the 1p qualia to a sheaf of computations (as bisimilar Boolean Algebras) that is dual to physical machine states at diffeomorphically equivalent space-time coordinates (x, y, z, t). This is a restatement of the Stone duality into COMP-like terms. ;-)

That does not make sense to me. Sorry.
it might make sense in some non comp analogical theory of mind, with mind and matter explicitly defined in term of non computable diffeomorphism. But this looks to me like making the mind-body problem more complex just for fun.

(The idea of diffeomorphic equivalence is discussed in detail here: http://plato.stanford.edu/entries/spacetime-holearg/Leibniz_Equivalence.html )

When you say:

Yes, this is the Pre-Established Harmony, but as I have argued before this concept is deeply flawed because it tries to claim that the solution to NP-Hard problem (of choosing the best possible world) is somehow accessible (for the creation of the monads by God) prior to the availability of resources with which to actually perform the computation of the solution. One cannot know the content of a solution before one computes it, even if one is omniscient!

I don't find any sense.

How is this so difficult for you to comprehend? The Platonic Realm is defined as timeless, everything in it just 'exists', no?

Only in the sense that if some proposition P(n) is true independently of me, then ExP(x) is true independently of me.

Therefore any argument that shows that "if A does not exist then neither does B if B requires A to exist" is true in Platonia as well, (we stipulate the existence of Platonia as defined for the sake of this statement). If a solution to a computation cannot exist until the computation is run then if the resources required to run the computation do not exist then there does not exist a solution to the computation!

So you cannot compute 10^1000 + 10^1000, and your theory is ultrafinitist (and so non-comp).

I propose that we can easily resolve this conundrum by stating Computational universality as: "A computation is universal if and only if it is independent of any particular physical implementation."

Universal applies to finite entity (numbers, humans, machines, language). Not to computations, although the running of a universal dovetailer can be said universal in some context, but only by abuse of language.

This allows for the existence of physical implementations,

Comp allows this too; without the need of assuming physical realities.

even those that are themselves defined by correlations between sheaves for computations. This sets up a relation between computations - as abstract or immaterial objects - and physical systems that seems consistent with "COMP minus Step 8". We can recover the picture of step 8,

<Sane 04 Bijection.gif>

Step 8 is a consequence of comp, like all steps in the UDA. 'Comp minus step 8' implies that 0 = 1.

in a way that is truly neutral ontologically, by changing its single directed arrow to a pair of oppositely directed arrows, but this one that occurs only in the ultimate sense of the elaboration of all possible physical worlds consistent with Pratt's idea.


This idea, BTW, is consistent with the concept of Indra's Net, as an inversion of the idea that every Jewel reflects all others: Every jewel is a physical world that is defined by all computations of it. Note also that this naturally includes self-computation as jewels also reflect themselves. ;-)

I have no more any understanding by what you mean by "physical world". It seems like a God-of-the-Gap.

I hope you don't mind my frankness. I wouldn't say this if I did not respect some intuition of yours. But math and formalism can't be a pretext for not doing the elementary reasoning in the philosophy of mind. If you use math, you have to be clearer on the link with philosophy or theology. To be understandable by others.

I am trying to be clear. I will correct and rephrase my verbiage until you understand it.

It would help to tell us what you assume at the start. from what I understand it is just contradictory. Pratt assumes more than arithmetic. All paper you refer too assumes more than arithmetic. Your notion of consciousness and of physical universe seems to be very fuzzy and clearly not comp-compatible.

I reject the idea of an entity, 'God', whose total purpose is to "observe" the Reality of the Universe!

Comp too. Comp rejects also the primitive reality of a physical universe.

If we accept the idea that numbers exist in our complete absence, then it follows that an entity like us cannot exist just to observe the existence of numbers (or anything else).

? ? ?

Why postulate the existence of a special entity that does what we collectively are already doing?

Why postulate physical computations, and comp, when comp explains how physical computations emerges in our mind through the existence of the computations in arithmetic?

It is our collective consciousness that Constitutes the Platonic Realm, IMHO. A theory that there is some independently existing realm is a gross violation of Occam.

But you do it for the physical computations, like in this post, despite you often pretend the contrary in other posts.



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