indeed.

there are a) misperceptions b) perceptions c) lack of perceptions d)
impossibility of perception e) pseudo-perceptions.

It is interesting to check out what Penrose is talking about when he
talks about Fashion, Faith, and Fantasy in theoretical physics.

Fashion: String Theory
Faith: Quantum Mechanics at all levels
Fantasy: Inflationary Cosmology and other wild cosmological schemes

On Jun 7, 8:01 am, "Stephen Paul King" <stephe...@charter.net> wrote:
> Dear Bruno,
>
> From: Bruno Marchal
> Sent: Monday, June 06, 2011 9:00 AM
> To: everything-list@googlegroups.com
> Subject: Re: Mathematical closure of consciousness and computation
> Hi Stephen,
>
> On 06 Jun 2011, at 05:27, Stephen Paul King wrote:
>
>   Hi Bruno, Rex and Friends,
>
>       My .002$...
>
>   [BM]
>   No theories nor machine can reach all arithmetical truth, but few  
>   people doubt that closed arithmetical propositions are either true or  
>   false. We do share a common intuition on the nature of arithmetical  
>   truth.
>   I have doubt on any notion of global mathematical truth. Sets, real  
>   numbers, complex numbers, etc. are simplifications of the natural  
>   numbers. They are convenient fictions, I think. If we are machine, it  
>   is undecidable if ontology is more than N.
>
>   [SPK]
>
>       I think that there is some differences in opinion about this but it 
> seems to me that we need to look at some details. For example, there should 
> exist a theory that could reach all arithmetic truth given an eternity of 
> time or an unnamable number of recursions or steps.
> [BM]
> ?
>
> No this cannot exist. It is precluded by the incompleteness theorem. Eternity 
> can't help. Unless you take a non axiomatisable theory, or some God-like 
> entities.
>
> [SPK]
>
>     Yes, you are correct. I miswrote. I had even developed an informal proof 
> of this in my critique of Leibniz’ Monadology. But this still presents a 
> challenge.. Umm, maybe this is where Cantor et al considered this idea in 
> terms of unnamable cardinals...
> **
>
>   This by definition would put them forever beyond human (finite entity) 
> comprehension. Whether or not there is closure or a closed form of some 
> theory does not make it realistic or not. AFAIK, closed arithmetic 
> propositions are tautologies, no?
> [BM]
> They are not tautologies, unless you mean by this "propositions true in *all* 
> models of Peano Arithmetic. But then "tautology" means "theorem", and that 
> would be an awkward terminology. Ax(0 ≠ s(x)) is not a tautology (it is 
> already false in (Z,+), nor is Fermat last theorem.
>
> [SPK]
>     Yes, I did mean it that way, as in “propositions that are true in *all* 
> models” but not just of Peano Arithmetic. I was considering all Arithmetics, 
> especially Robinson’s. Usually one thinks of tautologies as A = A. What I am 
> trying to weaken is the way that the so called law of identity is usually 
> defined. I am working toward a notion of equivalence that allows for not just 
> strict equality but a more general notion of “bisimilarity”. In this way 
> theorems would be tautologies in this weaker form of Identity.
> **
>
>   That we share a common intuition of truth may follow from a common local 
> measure of truth within each of us. (Here the "inside" implied by the word 
> "within" is the logical/Arithmetic/abstract aspect of the duality that I 
> propose.)
>       Additionally, we should be careful not to conflate a plurality of 
> fungible individuals with a multiplicity of non-fungible entities. We can set 
> up a mental hall of mirrors and generate an infinite number of self-images in 
> it, but this cannot *exactly* map to all of the selves that could exist 
> without additional methods to break the symmetries.
>
>       I have been waiting a long time for you to state this belief of yours, 
> Bruno! That "Sets, real  numbers, complex numbers, etc." are simplifications 
> of (mappings on/in?) the Natural Numbers. This seems to be the Pythagorean 
> doctrine that I suspected that you believed.
> [BM]
> Would you take the time to study the papers, you would have understood that 
> this is a result of comp. Comp transforms the very banal arithmetical realism 
> in an authentic Pythagorean neoplatonist theology, i.e.  with some use of 
> OCCAM razor.
>
> [SPK]
>     I am studying the papers, but I need to clarify some ideas by asking 
> questions to the Professor. ;-) I do not think the way you do and must 
> translate your mental language into my own to understand them.
> **
>
>   It has a long history and a lot of apostles that have quite spectacular 
> histories. I think that there is a deep truth in this belief, but I think 
> that it needs to be more closely examined.
> [BM]
> It can be derived from Church thesis and the assumption that "we" are Turing 
> emulable.
>
> [SPK]
>     OK, but would you allow me to say that it seems that you are considering 
> a form of Turing emulation that is vastly more sophisticated and subtle than 
> the purely mechanical one that Turing, for example, considered with his A 
> machines? The fact that you are considering infinities of computations as 
> “running” each instance of us, is pushing the idea of a recursive algorithm 
> into places it is never been before.
> **
>
>   >
>   > Perhaps there is just human belief.
>
>   [BM]
>   Jason said it. If you follow that slope you may as well say that there  
>   is only belief by Rex. You can also decide that there is nothing to  
>   explain, no theories to find, and go walking in the woods. Science, by  
>   definition, assumes something beyond (human) belief.
>
>   [SPK]
>
>       I admit that I laughed out loud at this! Good point, Bruno! The 
> reduction of all truth to that which can be defined within a single human's 
> belief trivializes and renders it meaningless. That is one of the absurd 
> consequences that we lambast solipsism for, but I think that Rex should not 
> be to swiftly dismissed form maybe trying to make a deeper observation; he 
> has brought up a very good topic for discussion.
>       While it is absurd to reduce all truth to what a single finite entity 
> can "compute" - which is that we are actually saying if we follow the 
> Kleene-Turing-Church-Post road -
>
> [BM]
> Careful. It can be said that all ontological truth will be generated, but the 
> epistemological truth will never be generated, but they will emerge in a not 
> completely computable way. Remember that arithmetic, seen from inside, is 
> *much* bigger than arithmetic see from outside.
>
> [SPK]
>     OK, but that poses a difficult problem because it is epistemological 
> truth that we consider as reality! What we “know” to be true, even by the 
> Bp&p definition, is by definition what is “real” of us individually and via 
> consensus, no? I am not understanding what you mean by “arithmetic seen from 
> the outside”. Are you saying that there is more to Existence than numbers? My 
> apologies, I am confused.
> **
>
>   we are actually positing that "all truths can be defined in terms of N -> N 
> mappings".
>
> [BM]
> That would contradict Gödel's incompleteness. Unless you mean *all* N -> N 
> mappings, which is far to bigger and trivialize the theory (making it non 
> testable, and unable to derive anything in physics, cognitive science, etc.).
>
> [SPK]
>     Not provable truths, just the ones that we can bet on. Yes, to extend to 
> *all* N->N mappings would be like what we see in superstring theory – the 
> landscape that has almost completely reduced SUSY to a Scholastic type of 
> theory....
> **
>
>   Many such mappings to be sure, but N to N mappings nonetheless. We are back 
> to that strange belief that Bruno explicitly, albeit inadvertently, stated.
>       But this is not really a "strange" belief, partly because it seems to 
> be almost universally the default postulate within the basket of beliefs that 
> people operate with in our every day world. I would like to pose the question 
> of whether or not we are inadvertently painting ourselves into a corner with 
> this belief. IT seems to me, and this is just a personal prejudice of mine, 
> that there exists truths that cannot be named or represented exactly in terms 
> of N->N maps.
> [BM]
> In this context, you should clearly stated if you take all N->N mappings, or 
> the total computable one, or the partial computable one. The non triviality 
> of comp entirely resides in such nuances.
>
> [SPK]
>     I do not know yet how to do that parse. I am still learning the 
> vocabulary. My apologies.
> **
>
>   The source of this suspicion comes from what I have studied of G. Cantor's 
> work on transfinites and the histrionics of practitioners of mathematical 
> logic that have been examining the nature of cardinalities.
> [BM]
> With comp, the diagonalization of Kleene gives the information. Cantor's one 
> are far too crude.
>
> [SPK]
>     What text might you suggest that I study to understand Kleene’s 
> diagonalization? I have only found this paper on the 
> topic:www.columbia.edu/~hg17/naming-diag.pdf
> **
>
>   Additionally there is my belief that the Totality of Existence must be, at 
> least, Complete (not in the Gödel sense of just 1st order logics), Bicomplete 
> (in the Category theory sense) and Closed (in the topological sense). This 
> implies the existence of unnamable truths, or at least Truths that cannot be 
> exactly represented in terms of recursive functions on the Integers.
>
> [BM]
> That the totality of existence is complete seems to me to be a tautology, or 
> a truth by definition.
> That truth is beyond machine's means, is a theorem.
> That truth is beyond us is consequence of such theorem when we assume that we 
> are machines.
>
> [SPK]
>     Umm, not quite the same idea. I am following the reasoning in these 
> papers:http://arxiv.org/abs/math/0307090,http://arxiv.org/abs/physics/0212092and
>  my own ideas formed from studying Category theory. The difficulty that I see 
> in your definitions is that it makes the notion of a machine into something 
> altogether unknowable. People seem to interpret your word machine in the same 
> way that, for example, Descartes considered the idea of automata. I made that 
> mistake myself until I saw that you where not considering the notion of a box 
> full of levers, springs, gears and widgets.
> **
>
>       The question becomes one of the implications of this on our 
> metaphysical assumptions about the ontologies that we are using in our 
> thinking about the issue of mathematical closure of computation and 
> consciousness. As I see it, and this very well could be just an eccentric 
> thought, is that we need to be very careful that we do not tacitly assume 
> that all of the minds of entities are replicating the same ideas as one’s 
> own. The fact that we are continuously
> ...
>
> read more »

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