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From: Brian Tenneson <tennesb.domain.name.hidden>

Date: Wed, 14 May 2008 08:51:17 -0700

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

Date: Wed, 14 May 2008 08:51:17 -0700

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:

--~--~---------~--~----~------------~-------~--~----~

You received this message because you are subscribed to the Google Groups "Everything List" group.

To post to this group, send email to everything-list.domain.name.hidden

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Received on Wed May 14 2008 - 11:51:29 PDT

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