Hi Bruno, I mean logical implication and definitely -not- in the sense of production and -most definitely not- causation.

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I sat down for once and wrote something down and here's basically what the statement of my idea (which could easily be "wrong"): [+1] If x is a (Wolpert) device, then (if "x is complex in a sense" then "x is conscious in a sense"). [+1] is just a label for this forum of scant formatting power... ;) Now I must describe what is meant by "x is complex in a sense" and "x is conscious in a sense." The definitions are pretty dismal in terms of how insightful they are at encapsulating complexity (or, loosely speaking, -pseudo-randomness-) and consciousness; however, the definitions I will give will be open-ended enough so that someone can certainly come along, like a cognitive scientist who knows enough about the language we're using, and narrow down these to-be-general definitions. (So instead of random, which is a quite loaded term, I am using complexity now though the notation I use for complexity will be a predicate R <for random but it's more akin to pseudo-randomness> also since C is a predicate reserved for consciousness.) First, let x be a Wolpert device. At this point, the least number of 'axioms', defining traits, should be placed on what a device is so as to more readily prove facts about our world (e.g., that a human mind is conscious). Second, consider the aggregate of all possible outputs x can "produce" if it is fed all possible, relevant, inputs and notate this aggregate (which may not be a set, but a class) as [x]. [x] is the aggregate of all outputs of x. Let's call this the -range- of the device x. Second, let t be the set of all truth values one is using for the moment. The only assumptions on t are that t is a carrier (truth set) of an MV-algebra, that {0,1} is a subset of t (so the contextual logic either is classical logic or generalizes classical logic), and that t is a (not necessarily proper) subset of [0,1]. One example is t is {0,1}, the classical case, the entire interval [0,1] the fully fuzzy logic, and another is this set, denoted L_n after Łukasiewicz's rational logics: L_n = (by definition) {0, 1/(n-1), ..., (n-2)/(n-1), 1} , so, L_2 = {0,1}, L_3 = {0, 1/2, 1}, and L_6 = {0, 1/2, 2/3, 3/4, 4/5, 1}. Again, t is just some truth set -in an MV-algebra- that contains {0,1} and is a subset of [0,1]. Further abstractions are possible but I believe especially in light of Chang's theorems regarding the connection between arbitrary MV-algebras and the real unit interval, no further abstract MV-algebras would be needed for this discussion. Device measures Call a function a device measure if it can accept as input any set or class of the form [x] where x is a device and whose range is t. Device measures say -something- about a device. Examples: R, C, S, and O, meaning complexity/randomness, consciousness, self-awareness, and omniscience will all be device measures. In the literature, t can be partitioned into three disjoint pieces called the set of designated truth values, anti-desgniated truth values, and a possibly empty set of elements of t that are neither. For example, on {0,1/2,1}, one can say that 0 is anti-designated and the designated truth values are 1/2 and 1. There is flexibility here but all designated truth values must be lattice-larger than all other types of elements of t and all anti-designated truth values must be lattice-less than elements of t that are designated or neither. Let D_t be any such partitioning of t into three pieces. My intuition is that if the truth value of a statement is designated, it is -essentially true-, anti-designated is -essentially false-, and neither means -essentially- neither. Device Typing Let f be a device measure with a partitioning of t, called D_t. Then define the (f, D_t)-type of x to be either -1, 0, or 1, as follows: T(x; f, D_t) = 1 iff ( f( [x] ) is a designated truth value ), T(x; f, D_t) = 0 iff ( f( [x] ) is a non-designated truth value ), and, lastly, T(x; f, D_t) = -1 iff ( f( [x] ) is an anti-designated truth value ). So the typing scheme brings everything back to classical logic, aka crisp logic. Senses Say that device x has property (related to) f -in a sense- iff x is a type 1 device for some partitioning D_t of t. What I mean here can be stated now: Let R be a device measure pertaining to complexity, such as akin Kolomogorov complexity and C be a to-be-determined device measure about consciousness. For all devices x, if T(x; R, D_t) = 1, for some D_t, THEN On Wed, May 14, 2008 at 6:55 AM, Bruno Marchal <[EMAIL PROTECTED]> wrote: > > > Le 13-mai-08, à 18:27, Brian Tenneson a écrit : > > > > I must admit to a little hand waving. OK, maybe a lot. > > > > > Actually you are not. Not necessarily so, I mean. *I* could have been > wrong. Let me explain: > > When you said: > > <<Randomness implies consciousness.>> > > I interpreted as: "Randomness causes or produces consciousness". But > UDA (the first three steps) shows that it is consciousness (or first > person awareness) which causes, or produces, or makes it possible that, > randommess feeling. Just think about the iterated self-duplication > thought experiment. In that case randomness implies not only > consciousness or at least first person apprehension. > > So the question is: what do you mean by "implies". Is it "material > implication" like the classical logical implication, or do you mean > that there is some third person ("objective") notion of randomness > playing some role in the rise of consciousness. Something like that > could also exist, but not at the same level of the first person > indeterminacy which is a form of subjective uncertainty occurring > *thanks* to the third person, objective determinacy. > > Also, your repeating non ending post, has made still more obscure the > reason why you want a universal set. If such a set "exists" (in which > set theoiry?) it should be used to cut out such infinite behavior, in > some theory of meaning, not to produce them. If not, then the best > "universal set" is the universal machine. It seems to me. > > And then you seem to distinguish awareness and consciousness, or > self-awareness and self-consciousness. Am I right? What is the > relevance of that distinction (and which one?) for your message? > > I try to get your point, You should perhaps try to write a short > informal text "for the children". That could help. > You could also make some economy of thought by first studying the UDA > perhaps. It shows that he comp hyp put very strong constraints on the > possible mind-body relationships. If you dfend a non-computationalist > hyposthesis, it is ok, but even in that case the UDA can help you to > learn something, I sincerely think. > > To be sure, I will be more and more busy, and so expect my > aswers/comments/questions to be more and more delayed. I'm sorry for > that. > > > Bruno > > > > > > http://iridia.ulb.ac.be/~marchal/ <http://iridia.ulb.ac.be/%7Emarchal/> > > > > > --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. 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