Hi Bruno,
I mean logical implication and definitely -not- in the sense of production
and -most definitely not- causation.
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 <marchal.domain.name.hidden> 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/>
>
>
> >
>
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Received on Wed May 14 2008 - 11:51:29 PDT