On 10 Nov 2012, at 11:41, Roger Clough wrote:

Hi Bruno Marchal

OK, so it's not numbers alone (pure numbers),
something else is required.

Yes the laws of numbers. We believe in zero, and we believe that zero has a successor, and then the successor itself has a successor. Two common notation for the successor of x is s(x) and x + 1. We agree that two different numbers and two different successors, and we accept the laws of addition and multiplication:

x + 0 = x
x + (y + 1) = (x + y) + 1

 x *0 = 0
 x*(y + 1) = x*y + x

The "crazy" thing, but which results from the work of Gödel & Others, is that you can already define in that language, the very minimal believer in those laws. That one is already intelligent, in the sense that he can understand that he can crash. It is the price of creativity or universality. The machine is such that if she believes p and if she believes p -> q, she will soon or later believe q.

To be sure, to define a believer in the laws above, in the language using only the logical symbols, and the symbols: 0, s, (, ), +, *, is a very long ingenuous but also tedious work, like defining correctly a low level programming in itself. I will give some glimpse how to do that more quickly by using non trivial result.



At the very minimum that
something else must be intelligence,
the ability to essentially freely make choices of one's own.

You are right. Numbers, then, relatively to other numbers got it. Trivially, with comp, and arguably from computer science and the classical theory of knowledge.



Nothing can be done without intelligence.

But if you can do that, what's special about numbers ?

Nothing.

Numbers are just easier for most, when reasoning "exactly". Programs, engrams, digital machines, two dimensional cellular automata, one dimensional cellular automata, hereditarily finite sets, hereditarily finite n-category, topological computer, modular functor, ... We can start from any of those, but we explain more by choosing the simplest. The universal beings are very multiple, and one you have one of them, you automatically inherit all of them. You get also, for the internal 1p, the result of a sort of competition of all of them below your substitution level (the global first person indeterminacy). I think the universal numbers (or the Löbian one) play the roles of the supreme monads. They are intermediates between earth and heaven.



Geometry, such as created network, would make more sense.
Or natural language. or arithmetic functions.

Keep in mind that I assume comp, and *then* reason in computer science/ mathematics/arithmetic.

Bruno





Roger Clough, rclo...@verizon.net
11/10/2012
"Forever is a long time, especially near the end." -Woody Allen


----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-11-09, 14:26:09
Subject: Re: How can words be transformed into numbers ?


On 09 Nov 2012, at 13:41, Roger Clough wrote:

Hi Bruno Marchal

So how would

"I see a cat."

be transformed into numbers ?

Maybe 63 7 89 ?

I am afraid that will not be enough. "I see a cat", to get put in
number, with the 1-I and 3-I of you, you will need to scan your brain
at the correct comp subst level (which exist by comp assumption), and
this when you are looking at a cat.
Then the real 1-I is not in that number, but in all the computation
going through the state described by that number relatively to our
most probable environment. The number can be used to reimplement you
in some computer, and then you will be able to manifest your seeing a
cat to us.






I could do that if I indexed all of the words in Roget's thesaurus,
but I don't think the numbers would mean anything besides numbers.
Because the meanings of words come from context -- not only in where
they are placed in a text but how they arose from culture.
Language is culture.

You are right.




And in mandarin, three characters placed together might not
have anything to do with literal meaning. For example, the
characters for

I touch flowers in vase

can mean


Final touch


No problem with this.

Bruno




Roger Clough, rclo...@verizon.net
11/9/2012
"Forever is a long time, especially near the end." -Woody Allen


----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-11-08, 10:36:49
Subject: Re: Peirce's concept of logical abduction-- a possible
moneymaker


Hi Roger Clough ,

On 08 Nov 2012, at 11:03, Roger Clough wrote:

Hi Bruno Marchal

My principal interest over the years has been to
come up with some self-sustaining self-generating
method of autopoeisis. That's why I found the I Ching
fascinating. It contains sensible links between binary numbers and
metaphors.

When I look up methods of data mining, all they give is
hierarchy diagrams and numbers. How do they link
numbers and metaphors or words in general ?
Perhaps there is some sort of bayesian scheme to do that.

Roget's thesaurus might also be a starting point,
since they have words of similar meanings clustered,
but where you go from that beats me.

You should perhaps study how works a computer (or a universal number).
They transforms numbers into words and actions all the time, and this
in a non metaphorical way. And they can do much more, like referring
to themselves in the 3p but also in the 1p and other senses. There is
no more magic than in computer science, imo.

Bruno







Roger Clough, rclo...@verizon.net
11/8/2012
"Forever is a long time, especially near the end." -Woody Allen


----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-11-07, 12:57:14
Subject: Re: Peirce's concept of logical abduction-- a possible
moneymaker


On 07 Nov 2012, at 18:12, Roger Clough wrote:

Hi Bruno Marchal

Cool. Shows you how little I know.



Those things are virtually unknown by most. Computer science is very
technical, and the number of publications is explosive, almost an
industry. It is also a gold mine, alas, most philosophy curriculum
does not have good courses in the field. We separate the human and
the
exact sciences, which does not help.
In science we still kill the diplomats, and this means that science
is
still run by unconscious (pseudo)-religion, if not simply "the boss
is
right" theory. Of course the degree of graveness is very variable in
time and places.

Bruno




Roger Clough, rclo...@verizon.net
11/7/2012
"Forever is a long time, especially near the end." -Woody Allen


----- Receiving the following content -----
From: Bruno Marchal
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Time: 2012-11-07, 12:05:11
Subject: Re: Peirce's concept of logical abduction-- a possible
moneymaker




Hi Roger Clough,


Hi Bruno Marchal

Yes, by new I mean contingent. But Kant, although his examples
are debatable, at least sought a synthetic a priori,
which of course would be a gold mine, or perhaps a stairway
to the divine.

Pragmatism rejects the idea of there being any
such universals, but I think by abduction strives
to obtain completly new results (if actually new I can't say).
I think that's why Peirce came up with the concept of abduction.
The concept is very seductive to me for its possible
power of discovery of something unknown or new.
If comp could do this, I'd not spend a moment more on
simulating the brain. Such a program might be worth a lot of
money in venues such as AI, the defense industry, medicine
and criminal investigation a la Sherlocki Holmes.





Abduction is just one technic among many to do inductive inference
(predicting theories from fact, synthesizing programs from input-
output sequences, finding explanations from data, etc.).


The mathematical theory of inductive inference is a very large
subfield of theoretical computer science and theoretical artificial
Intelligence, or Learning theory. AI is the practice and/or
experimental part of it.


Behavioral Comp is the idea that machines can emulate all 3p aspect
of experience and consciousness.
STRONG AI is the thesis that machine can have 1p experience.
COMP is the thesis that *you* are emulable by a computer.


Famous theorem in theoretical learning theory:


Roughly speaking we measure the "intelligence" (really competence)
by the largeness of the class of computable processes recognized
(explained, inferred) by a machine, or by the number of such classes
(or comobinations).


What is *much* more clever than a machine? Answer: two machines. It
is the non union theorem of Blum and Blum. Actually, and in general,
the gap of intelligence is incomputably big.


A machine which can change its mind n times is also incomputably
more "clever" than a machine which changes its mind m times, if m <
n. (Case and Smith)


A surprising result: a machine which is able to change its mind,
despite he got a correct theory, is again *much more* clever than a
machine which sticks on the correct theory! (Case and Smith).


Case & Al. refuted also a form of strict Popperianism. Machines able
to infer irrefutable theories can learn larger classes, and more
classes, of computable process.


Most result are, as we could expect, non constructive. No machine
can really construct a machine and prove that such machine is more
clever than herself. But of course machine can do that
serendipitously, and machine can build other hierarchies, close to
form of biological self-extension.


References below.


Theoretical computer science is a *very* large part of mathematical
logic. With both a deductive and an inference inductive part.


Computer are very peculiar objects. They seem close to what you say
about the supreme monads, but the supreme monads are not Gods, they
are only God reflector, or God mirror. God is more like the whole
truth, I mean the whole arithmetical truth, which contains the many
truth concerning many universal numbers and universal relation
between numbers. The monads are windows through which God can take a
look at itself, but the supreme-monads the universal numbers, are
window enough large so that God can begin to "recognize" itself, so
to speak.


Bruno






BLUM L. & BLUM M., 1975, Toward a Mathematical Theory of Inductive
Inference.
Information and Control 28,.pp. 125-155.


CASE J. & SMITH C., 1983, Comparison of Identification Criteria for
Machine Inductive
Inference. In Theoretical Computer Science 25,.pp 193-220.


CASE J. & NGO-MANGUELLE S., 1979, Refinements of inductive inference
by Popperian
machines. Tech. Rep., Dept. of Computer Science, State Univ. of New-
York, Buffalo.











http://en.wikipedia.org/wiki/Abductive_reasoning


"Abduction[1] is a form of logical inference that goes from data
description of something to a
hypothesis that accounts for the reliable data and seeks to explain
relevant evidence.
The term was first introduced by the American philosopher Charles
Sanders Peirce (1839?1914) as
"guessing".[2] Peirce said that to abduce a hypothetical explanation
from an observed surprising circumstance
is to surmise that may be true because then would be a matter of
course.[3] Thus, to abduce
from involves determining that is sufficient (or nearly sufficient),
but not necessary, for [b, unclear symbol].

For example, the lawn is wet. But if it rained last night, then it
would be
unsurprising that the lawn is wet. Therefore, by abductive
reasoning, the
possibility that it rained last night is reasonable. (But note that
Peirce did
not remain convinced that a single logical form covers all
abduction.)[4]
Peirce argues that good abductive reasoning from P to Q involves not
simply
a determination that, e.g., Q is sufficient for P, but also that Q
is among the
most economical explanations for P. Simplification and economy are
what call
for the 'leap' of abduction.[5] In abductive reasoning, unlike in
deductive
reasoning, the premises do not guarantee the conclusion. Abductive
reasoning
can be understood as "inference to the best explanation".[6]
There has been renewed interest in the subject of abduction in the
fields of law,[7] computer science, and artificial intelligence
research.[8] "



Roger Clough, rclo...@verizon.net
11/7/2012
"Forever is a long time, especially near the end." -Woody Allen


----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-11-07, 09:07:59
Subject: Re: (mathematical) solipsism


On 06 Nov 2012, at 15:30, Roger Clough wrote:

Hi Bruno Marchal

OK. That's analytic uncertainty.

Yes indeed. Almost the opposite of the comp indeterminacy. With comp
we get many form of indetermlinacies and uncertainties.




And analytic deduction cannot really tell us anything new,
it can only give us a fresh perspective.

Yes. But nor can a God, or a universe. I am not sure what you mean
by
"new".



But a new thing can be created with synthesis
(intuiition,inference, induction, abduction),
which is the trick that Einstein performed when
he showed (very simply) that time is relative.

OK, but this happens in arithmetic too, even without comp. And more
easily shown with comp.



This was invented I think, entirely new, not deduced.

So by new, you mean contingent. But arithmetic is full of many
contingencies. Even many type of very different sort of
contingencies.




I suppose this might be construed as a form of nominalism,
and if so, realism can be expanded with intuition.

Tell me what you mean by nominalism, as this term is often used
differently by different people.

Bruno






Roger Clough, rclo...@verizon.net
11/6/2012
"Forever is a long time, especially near the end." -Woody Allen


----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-11-06, 07:48:07
Subject: Re: (mathematical) solipsism


On 05 Nov 2012, at 13:48, Roger Clough wrote:

Hi Bruno Marchal

Isn't strong AI just an assumption ?

Yes. Comp too. The existence of the moon also.

The fact that I am conscious, can only be an assumption for you,
and
vice versa.

The only thing which is not an assumption is private consciousness.
All the rest are assumptions.
Strictly speaking.

Science uses only assumption and develop only *relative*
certainty. A
difficulty comes from the fact that the brain wired in us already
many
assumptions, which we are not conscious of the hypothetical nature.
for example some birds assumes that the first things they see
moving
after birth is their parent, and we tend to do the same. But having
parent is of the type "theoretical hypotheses".

Bruno





Roger Clough, rclo...@verizon.net
11/5/2012
"Forever is a long time, especially near the end." -Woody Allen


----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-11-04, 09:43:16
Subject: Re: (mathematical) solipsism




On 03 Nov 2012, at 13:00, Stephen P. King wrote:


On 11/3/2012 5:39 AM, Bruno Marchal wrote:

[SPK] In the absence of a means to determine some property, it is
incoherent and sometimes inconsistent to claim that the property
has
some particular value and the absence of all other possible
values.


In math this is called (mathematical) solipsism.


Dear Bruno,

How is it solipsism? Solipsism is: "Solipsism is the
philosophical idea that only one's own mind is sure to exist. The
term comes from the Latin solus (alone) and ipse (self). Solipsism
as an epistemological position holds that knowledge of anything
outside one's own mind is unsure. The external world and other
minds
cannot be known, and might not exist outside the mind. As a
metaphysical position, solipsism goes further to the conclusion
that
the world and other minds do not exist."

My point is that numbers, by your notion of AR, are solipsistic
as there is literally nothing other than the numbers. I reject AR
because of this! Numbers alone cannot do what you propose.



Comp entails Strong AI, which attributes consciousness to
machines,
and thus to others. You argument is not valid because it beg the
question that number (related through the laws of + and *)
emulated
computation to which comp attribute consciousness. So comp is not
solipsism.


Bruno









This post argues similar to my point: 
http://mathforum.org/kb/message.jspa?messageID=5944965

"Conventional solipsism is a logical philosophy whose underlying
views
apply equally to mathematical philosophies of neopythagoreanism
and
neoplatonism as well as mathematical realism and empiricism
generally.

The well established philosophical principle of solipsism is that
only
the individual is or can be demonstrated to exist. But the problem
is
that if this principle were actually demonstrably true it would
also
make it false because the "truth" established would ipso facto
make
the principle beyond control of any individual.

Nobody really thinks solipsism is true. But the difficulty is no
one
can prove or disprove the concept because no one can prove the
foundations of truth in absolute, necessary, and universal terms."


This article 
http://digitalcommons.macalester.edu/cgi/viewcontent.cgi?article=1020&context=philo
argues against the claim that Intuitionism is solipsistic. I
reject
Intuitionism as a singular coherent theory of mathematics, but I
do
accept it as a member of the pantheon of "interpretations" of
mathematics.

-- Onward!

Stephen


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