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: firstname.lastname@example.org
> 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$...
> 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
> 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.
> 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.
> 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
> 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?
> 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.
> 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
> 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.
> 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.
> 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.
> It can be derived from Church thesis and the assumption that "we" are Turing
> 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.
> 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.
> 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 -
> 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.
> 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
> 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.).
> 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
> 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.
> 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.
> 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.
> With comp, the diagonalization of Kleene gives the information. Cantor's one
> are far too crude.
> What text might you suggest that I study to understand Kleene’s
> diagonalization? I have only found this paper on the
> 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.
> 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.
> Umm, not quite the same idea. I am following the reasoning in these
> 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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