On 3 October 2011 16:43, Stephen P. King <stephe...@charter.net> wrote:
> [SPK] > But why some particular type of primitive rather than some other? It > seems to me, for symmetry reasons, that a truly ultimate primitive would > have no particular properties associated with it at all! I think that there > is a flaw in this reductionist idea, the idea that there exists a > fundamental primitive that both is irreducible (by definition!) and has some > properties rather than some others. We have been considering some form of > Number as our primitive and I have been raising objections to this because > while numbers definitely do seem to be irreducible primitives, the very > notion that they are numbers vanishes when we consider them at this > primitive level because the structure of Arithmetic, which gives meaning and > haecceity to them, was dissolved away by the Aqua Regia of Reduction. > One cannot have properties and not the means that generates them, to > claim otherwise is a contradiction Stephen, I don't know if the following will help (and I don't know either if Bruno will agree with it), but there are a few intuitions that have helped me to get intuitively closer to these topics (to the extent that I can). First, I try not to be too literal-minded about "number", at least in any of its "local instantiations". Obviously, if we try to picture ourselves as being in some way literally "made out of numbers" in any of their ordinary manifestations, it's very difficult to make any sense of AR. I'm not suggesting that you are being this literal-minded, by the way. But speaking for myself, I tend to intuit comp's starting position on "ontology" as something like: in order to make sense of CTM, assume some "primitive" analytical-combinatorial principle which is equivalent to arithmetic in *all relevant respects*. What remains (almost everything!) is then to discover whether and how, within precisely these limitations, we can recover what we're ultimately in pursuit of - mind and matter - also *in all relevant respects*. It turns out that, to have any hope of doing this, some key supplementary ideas are in fact required, and the easiest one to lose sight of, perhaps, is the critical additional assumption (if indeed it is correct to call it merely an assumption) of the knower - the "inside view", or "epistemological reality". Now, however one nuances terms like "ontology" and "epistemology", we cannot but acknowledge the personal manifestation of the knower - the first person - as some intimate amalgam of knowing and being. This "amalgam" I take to be an irreducible fact, but nonetheless what comp seeks to show is how the "logical ontology" of AR can both underpin (i.e. form the structural basis of), and permit reference to, such epistemological facts. This last point - i.e. that of reference - actually seems to me to be the strongest motivation for a combinatorial approach to the mind-body conundrum. Try as I might, I have never succeeded in imagining another ontologically primitive assumption capable of capturing the fundamental aspects of reference (and particularly self-reference); and unless the basis of such reference is built into our foundational assumptions, it seems to me that the possibility of recovering it "later" (say, from the ramifications of a physicalist theory) is a stark impossibility. I hope this may help, or at least may lead to some helpful amplification. David > On 10/1/2011 9:50 AM, Bruno Marchal wrote: > > On 01 Oct 2011, at 02:18, David Nyman wrote: > > On 30 September 2011 16:55, Bruno Marchal <marc...@ulb.ac.be> wrote: > > They are ontologically primitive, in the sense that ontologically they are > > the only things which exist. even computations don't exist in that primitive > > sense. Computations already exists only relationally. I will keep saying > > that computations exists, for pedagogical reasons. For professional > > logicians, I make a nuance, which would look like total jargon in this list. > > I've been following this discussion, though not commenting (I don't > understand all of it). However, your remark above caught my eye, > because it reminded me of something that came up a while back, about > whether reductive explanations logically entail elimination of > non-primitive entities. I argued that this is their whole point; > Peter Jones disputed it. Your comment (supporting my view, I think) > was that reductionism was necessarily ontologically eliminative, > though of course not epistemologically so. > > Yes. This makes sense. Certainly a wise attitude, given that UDA shows that > if Mechanism is correct then both consciousness and matter are reduced to > number relations. If reduction was elimination, we should conclude that > consciousness does not exist (that would be nonsensical for any conscious > creature) and that the physical reality does not exist, which does not make > much sense either. > A physicalist would also be obliged to say that molecules, living organism, > etc. don't exist. Note that James Watson seemed to have defended such a > strong reductive eliminativism. > But I don't see any problem with reduction, once we agree that some form of > existence can be reduced to other, without implying elimination. > Mechanism makes it clear that machine are *correct* when they believe in > material form. Indeed all LUMs can see by themselves the rise of matter, or > the correct laws of matter by introspection, and they will all see the same > laws. > > [SPK] > Let me try to be sure that I understand this comment. When you write: > "they will all see the same laws" are you referring to those invariant > quantities and relations/functions with respect to transformations of > reference frames/coordinate systems (which has become the de facto > definition of physical laws) or are you referring to our collective human > idea of physical laws? > Why does it seem to me that you assume that the physical laws that we > observe are the only possible ones? To badly echo Leibniz: How these and not > some others? It seems to me that we observe exactly the physical laws that > are consistent with our existence as observers within this universe, a > universe where we can communicate representations of the contents of our 1p > to each other. Communication requires a plurality of possible 1p for each > and every separate observer in one universe to act as the template from > which signal is distinguished from noise, plurality is insufficient to > communications between observers. One needs something like the > Hennessy-Milner property for a coherent notion of communication. > There seems to be no a priori reason why we do not experience a universe > that contains only a single conscious entity or a universe with completely > different laws along with completely different physicality for the observers > wherein. IMHO, There is something to the self-selection that Nick Bostrom > tedand others have writen about that needs to be included in this discussion > in addition to the contraints that communications between many separate > entities generates. > > > > > Indeed this seemed to me > uncontroversial, in that the whole point of a reductionist program is > to show how all references to compound entities can be replaced by > more primitive ones. > > Your remark above seems now to be making a similar point about > arithmetical "reductionism" in the sense that, presumably, > computations can analogously (if loosely) be considered compounds of > arithmetical primitives, a point that had indeed occurred to me at the > time. If so, what interests me is the question that inspired the older > controversy. If the primitives of a given ontology are postulated to > be all that "really" exist, how are we supposed to account for the > apparent "existence" of compound entities? > > We need two things. The primitive objects, and the basic laws to which the > primitive objects obeys, and which will be responsible of making possible > the higher level of organization of those primitive objects, or some higher > level appearances of structures. > > [SPK] > But why some particular type of primitive rather than some other? It > seems to me, for symmetry reasons, that a truly ultimate primitive would > have no particular properties associated with it at all! I think that there > is a flaw in this reductionist idea, the idea that there exists a > fundamental primitive that both is irreducible (by definition!) and has some > properties rather than some others. We have been considering some form of > Number as our primitive and I have been raising objections to this because > while numbers definitely do seem to be irreducible primitives, the very > notion that they are numbers vanishes when we consider them at this > primitive level because the structure of Arithmetic, which gives meaning and > haecceity to them, was dissolved away by the Aqua Regia of Reduction. > One cannot have properties and not the means that generates them, to > claim otherwise is a contradiction > > > In the case of mechanism, we can take as primitive objects the natural > numbers: 0, s(0), s(s(0), etc. > And, we need only the basic laws of addition and multiplication, together > with succession laws: > 0 ≠ s(x) > s(x) = s(y) -> x = y > x+0 = x > x+s(y) = s(x+y) > x*0=0 > x*s(y)=(x*y)+x > There is some amount of latitude here. We could consider that there is only > one primitive object, 0. Given that we can define 1, 2, 3, by Ex(x= > s(0)), Ex(x= s(s(0))), etc. > > [SPK] > But that definitive arithmetic structure does not even exist at the > level of our one Primitive, 0, therefore we are wrong to claim that our > primitive is a number! It is no more a number than a purple and pink > polka-dotted Pony! It is the (0, +, *, =) that gives our primitive > "number-ness", and it by definition cannot be an ontological primitive > because it lacks the necessary multiplicity of extrinsic possible positions > that a physical space generates. Just because it is possible to fully > express Arithmetic via Goedelian sentences coded as numbers does not require > us to believe that the primitive is a number and that that quality of being > a number is itself irreducible. Unless there is some form of manifold or > non-singular set unto which valuations can be compared and contrasted, each > and every number collapses into 0. There is simply no *space* for multiple > copies of numbers. "No cloning" follows from "no room to put the clones". > > > > [Or we could take the combinators (K, S, SK, KS, KKK, K(KK), etc.) as > primitive, and the combinators laws: > Kxy = x > Sxyz = xz(yz) ] > It might seems amazing but those axioms are enough to prove the existence of > UMs and LUMs, and the whole "Indra Matrix" from which consciousness and > physical laws appears at some (different) epistemological levels. > > [SPK] > The Indra Matrix (aka Net of Indra) is a *non-well founded* set, it has > no true primitives and reductionism goes very wrong in it. Every jewel in > the Matrix reflects and is defined by relations to all others. It has no > *One* primitive in the well founded sense of a minimal element. > > > It is the same as the brick in the house example. You need the primitive > elements (brick) and some laws which makes them holding together (ciment, > gravitation, for example). > The same occur with physicalism. You need elementary particles, and > elementary forces which makes them interact. What I show is that IF > mechanism is correct, elementary particles and elementary forces are not > primitive but arise as the "border of some universal mind" (to be short), > which lives, at some epistemological level, in arithmetic. > > [SPK] > > I agree, physicalist, as a form of material monism is incomplete; but so > is any for of idea monism! Only a neutral monism escapes this but at the > price of dissolving Everything into Nothing at all. This is why I am > motivated to rehabilitate dualism, it solves the incompleteness problems of > both material and idea monism and becomes neutral monism in the limit of all > possible reductions, thus my proposal is more like dual-aspect monism but > not exactly. > > > If the supposedly > fundamental underlying mechanism is describable (in principle) > entirely at the level of primitives, there would appear to be no need > of any such further entities, and indeed Occam would imply that they > should not be hypothesised. > > Yes. And that is indeed why we can say that we explain them. We can explain > the DNA structure entirely from the atoms quantum physical laws. So DNA does > not need to be taken as a new "elementary" particle. With digital mechanism, > atoms and particles are themselves reducible to the non trivial intrinsic > unavoidable consequences of addition and multiplication laws. > > [SPK] > What needs to be understood about reductionism is that is is showing us > that *meaningfulness* itself vanishes at some point in the dissolving. > Reduction leads, eventually, to Neutral and Unnameable Monism, not to Number > or Arithmetic Realism. > > > Yet the bald fact remains that this is > not how things appear to us. > > Why? DNA seems clearly to be explainable by the atoms and their laws, like > house seems clearly to be explainable in term of bricks and cement. > > [SPK] > At the level of atoms there in no such thing as Van Der Walls forces, > for instance, just as there is no such thing as temperature at the level of > atoms. So I am skeptical of this claim of explainability. Why? DNA seems > clearly to be explainable by the atoms and their laws, like house seems > clearly to be explainable in term of bricks and cement. Brick and cement can > be used to construct a blue print of the house, but the process of using > concrete and bricks to build blueprints is a tiny bit different from > building a house of those same brick. There is nothing inherent in a brink > that demands that it build a house... > > > For the reduction of physics to numbers, it might seems less obvious, > because we are programmed to take seriously our "epistemological beliefs". A > cat would have less chance of surviving in case he doubts the existence of > the mouth. So brain have emerged by simplifying the possible world view, but > this is due to habitude, and is comparable with many illusion we have had in > the past: the sun looks like moving around the earth, but on close > inspection, it is the earth rotating on itself, and the move of the sun is a > local "illusion". Matter seems to exist in some ontological primitive way, > but on closer inspection, it emerges from group symmetries, which themselves > emerges from the provable symmetries of the sigma_1 arithmetical sentences > when observed by machine. > > [SPK] > That very same emergence from symmetries is true for numbers!!!!! THis > is shown by how we can identify numbers as the equivalence over a class of > arithmetic operations. There is not thing *special* about numbers that > allows us to violate the neutrality principle that I mentioned above. You > seem to ignore the fact that to be "observed by a machine" is not a purely > arithmetic act. Numbers, in themselves, do not act at all. They are static > relations. A static relation cannot implement an observation or any other > kind of action. > > > > So should such compound appearances be > considered entirely a matter of epistemology? > > Yes, but there are many layers of realities available inside arithmetic, and > nuances can be introduced. Take the example of prime number, or even of > universal numbers. Those can be said, if we want to, as existing as much as > the primitive 0, 1, 2, 3, ... After all they are only special numbers. > But consciousness and matter are more properly epistemological (first person > singular and first person plural respectively). Those are not numbers, but > are number experiences, and those, mainly due to our self-multiplication in > arithmetic, are related to infinities of arithmetical relations. > A notion like a computation, or a computable functions is intermediate, they > can have description, which will be numbers, and extension which will be, > usually, sequences of numbers. > > [SPK] > Layers which reduction dissolves into nothingness. Eventually the very > property of being distinguishable dissolves away too and no properties at > all are left with which to distinguish 0 from anything else. > > > > IOW, is the > first-person - the "inside" view - in some sense the necessary arena - > and the sole explanation - for the emergence of anything at all beyond > the primitive ontological level? > > You don't need a notion of first person to say that prime numbers exist, or > that universal numbers exist. Those are just numbers having special property > due to the richness of the laws of addition and multiplication when taken > together. But UDA shows (I think) that matter and consciousness are first > person collective constructs of all the numbers. > Usually, and conventionally I consider that numbers exist primitively even > if they have special properties. > > [SPK] > *special properties*? How so? Where does the difference between being a > number and not being a number remain at the most primitive level? > > > So I gave the same type of existence to prime numbers, even numbers, or > universal numbers. They are captured by sentences with the shape: > Ex ( ... x ...), where (... x ...) represent some arithmetical proposition > (which contains only the symbols 0, x, y, ..., +, *, s, and the logical > symbols). > (The proper epistemological existence will be defined by the modal logics > like BEx(B(.... x ...), or <>Ex(<>(... x ...). The last one are still > pure arithmetical formula (thanks to Gödel translation of B in arithmetic), > but they have a special "meta-role", and describe what machines can believe, > feel, observe, etc. > OK? > Bruno > > [SPK] > Idealism is an epic fail, not matter how sophisticated it is, just as > materialism fails and for exactly the same reason. > > Onward! > > Stephen > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to email@example.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to firstname.lastname@example.org. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. 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