Dear John,
On 22 Oct 2011, at 23:07, John Mikes wrote:
my thanks for taking the time in your busy schedule to reflect to my
babbling to Stephen.
If you don't mind, I reflect to some of them just in plain text
above your post copied hereunder.
*
So "numbers' ARE markers for quantity? what are "quantities"? (they
may not be so abstract!) And: of WHAT?
*
Numbers can do many things. Mainly measure a discrete quantity (like
bank account, spermatozoids in a drop, etc), and they can put linear
order on discrete sets, like in the 546th avenue. They can also be
code for description of any finitely describable things. Then by
virtue of the explosive richness of the laws of addition and
multiplication, which makes the prime numbers already, all alone,
emulating (at the least) quantum chaos, and which makes the existence
of the Indra Net of self-reflecting universal numbers, the number
reality becomes locally, from *their* points of view full of qualities
which go well beyond what the numbers can describe with only numbers.
Numbers cannot avoid unsolvable conflicts between heart and reason.
In the mind? an abacus is pretty real <G> in material construct.
*
Each time I use the term machine, it is in the well definite
mathematical sense of Church Turing Post, etc. A physical machine is
just an observable digital pattern seeming to obey to the laws of
numbers.
Later on you question 'my' WORLD, which is(?) the infinite
complexity of everything in a fashion that is beyond us.
As I imagine (in my faith???) it's both a-temporal and a-spatial so
I do not consider a "LOCAL" reality (to describe quantities or
anything else).
*
I am interested in the relation between the global and the local. The
outer god and the inner god.
I cannot understand 'logic' or 'logics' without knowing what could
be "THINKING" (the WAY of which logic should be).
Thinking, in a large sense, is what universal numbers do.
Classical thinking is when they obeys to the Boole's laws of thought.
Then they inherit a Löbian mind once they believe in the numbers, or
in the machines.
I have a pretty ignorant image of 'mentality' all in those parts of
the "WORLD"?? which is still not explainable in our informational
basis - with a (material) -tool- we apply for it, called the neural
brain,
The brain, like the universe is in your head. Indeed, in the head of
all UNs. The LUNs know that.
UN = Universal Number.
LUN = Löbian Universal Numbers.
I don't go for a mechanistic neuronal interaction-firing scheme
becuase it does not answer several of my questions (no repeat here).
Low level description of something can account of a higher level
reality, but usually cannot explain it. You need higher levels.
People confuse an account for, and an explanation.
*
Br: If you agree that there is something unknown, you believe
that there is something to be known or believed OK?
I dislike to be though with MY mind by someone else (ha ha). No, I
don't 'believe' there is something we know. We think we know.
OK.
I do think we know that we are conscious though. (Although I doubt we
know who we are, or who "we" is).
The rest, from the existence of parents, moon, bosons, galaxies and
dark (or not) matter: those are (theoretical beliefs).
About the numbers, I have no definite opinion.
I accept some of it to have something to go on/by, call it "MY
belief system" because such is the human way we think (?).
In science we call that an assumption. It is your theory. We need
theories to go on, indeed.
After Robert Rosen I hold a view of a 'model-world' made of known
ingredients (topical/functional) as the sole domain we can THINK
within. In addition to that is the rest of the infinite complexity
(unknown to us) influencing our model-content (I think) .
Yes. And since Gödel, we are like that already in front of the
arithmetical truth: we can only scratch the surface (provably so if we
are machine-emulable).
This is why we cannot pinpoint THE cause of a change chosen from the
known model-content only.
OK.
And if we try to pinpoint the thing, we change it.
We speak in processes: it may be a change in relations (between much
more than what we can imagine and totally different from even
'aspects' we can think of.
I take my agnostic ignorence for real.
Yes, good. Now, with the mechanist ASSUMPTION, there is a dessert! The
LUNs can access a part of their ignorance. Enough, for taking their
agnostic ignorance for real. They can do science in the cold way
without wishful thinking because they know that they don't know. They
hope for the best, and fear the worst.
*
A machine? Feel free to identify it as MORE than what WE are.
That's the case for the physical machine. But, in the theory I suggest
(yes doctor), we have to distinguish the mathematical machines from
the physical machines. The first are emulable by one universal machine
in a quasi-direct way. The second, the physical one, result from very
deep long and competitive struggle between all universal machines.
Would you restrict (your) machine to structural components within
our inventory of today?
Not at all. They can have many clothes, and many different type of
relative clothes.
HER functions to restricted into OUR present sortiment of
activities? I like to call it an ORGANIZATION and no such
restriction emerge. It is only a name. "WE" are orgqnizations as
well, with unlimited (into our models that is) connections into the
WORLD (infinite complexity of everything). Your Universal Computer
may be even more compact and outreaching. (I am not talking about
our present binary embryonic digital Kraxlwerks - we call our
computers).
*Assuming* "yes doctor", you and me are such universal machine, but
here "you" and "me" does not refer to our special earth-local
incarnation, but all the arithmetical incarnations.
Thanks for your thoughts
With pleasure,
Best,
Bruno
On Sat, Oct 22, 2011 at 9:26 AM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 21 Oct 2011, at 22:09, John Mikes wrote:
Hi Stephen,
it seems you are closing to 'my alley'.
First: if you don't think of T R U T H (in any absolute sense,
meaning it's acceptable 'meaning') how can you abide by a version
of it? - What are the "REALS"?
I do not consider 'Arithmetic' the one and only ontological
primitive: I cannot 'see' ontology at all in a world that changes
ceaselessly and the 'being' (ontology) turns into 'becoming' (sort
of epistemology?) with changing away at the instant you would
realize it "became".
Idem per idem is not a workable position. You can explain a
'system' only in terms looking at it from a different (outside?)
view. Platonism is such a system. I try a "common sense" platform.
I asked Bruno several times how he explains as the abstract
'numbers' (not the markers of quantity, mind you) which makes the
fundamentals of the world. He explained: arithmetically 2 lines
(II) and 3 lines (III) making 5 (IIIII) that is indeed viewable
exactly as quantity-markers (of lines or whatever).
That's the idea.
Of course a zero (no lines) would introduce the SPACE between lines
- yet another quantity, so with the 'abstract' of numbers we got
bugged down in measurement techniques (physics?).
Here you might be too much literal already. The numbers are more of
the type of mind ability to distinguish quantities of similar
things. It is more in the mind, than in the way we might use a local
reality to describe them.
Logic? a human way of thinking (cf the Zarathustrans in the Cohen-
Stewart books Collapse of Chaos and The Figment of Reality) with
other (undefinable and unlimited) ways available (maybe) in the
'infinite complexity' of the world
- IF our term of a 'logic' is realizable in it at all.
If logic is a human way of thinking, is not logics ways of thinking
(note the plural). There are infinities of logic. Classical logic is
the way of the greek human thinking, and of the he ideally
arithmetically correct machine, which can be studied to learn about
us, like the bacteria Escherichia coli can studied for learning
something about us.
You know a lot more in math-related terms than I do, so I gave only
the tips of my icebergs in my thinking.
Then there is my agnosticism: the belief in the unknown part of the
world that yet influences whatever we think of.
But here is the problem: what do you mean by "world"? Is there a
world? Why not a dream. If you agree that there is something
unknown, you believe that there is something to be known or believed
OK?
We continually learn further parts of it, but only to the extent of
the capabilities of our (restricted) mental capacity. So whatever
we 'know' is partial and inadequate (adjuste, incomplete) into our
'mini-solipsism' of Colin Hales.
What is the difference with the first person's beliefs? And with the
first person knowledge. Are you OK with the idea that a machine can
also have her mini-solipsism? (this would not imply that "we" are
machine, just that a machine could think). I just try to have a more
precise idea of your thinking.
Best,
Bruno
Regards
John M
On Fri, Oct 21, 2011 at 7:07 AM, Stephen P. King <stephe...@charter.net
> wrote:
Hi John,
I was not thinking of truth in any absolute sense. I'm not even
sure what that concept means... I was just considering the
definiteness of the so-called truth value that one associates with
Boolean logic, as in it has a range {0,1). There are logics where
this can vary over the Reals!
My question is about "where" does arithmetical truth get coded
given that it cannot be defined in arithmetic itself? If we
consider Arithmetic to be the one and only ontological primitive,
it seems to me that we lose the ability to define the very
meaningfulness of arithmetic! This is a very different thing than
coding one arithmetic statement in another, as we have with Goedel
numbering. What I am pointing out is that if we are beign
consisstent we have to drop the presumption of an entity to whom a
problem is defined, i.e. valuated. This is the problem that I have
with all forms of Platonism, they assume something that they
disallow: an entity to whom meaning is definite. What distinguishes
the Forms from each other at the level of the Forms?
Onward!
Stephen
On 10/20/2011 10:18 PM, John Mikes wrote:
Dear Stephen,
as long as we are not omniscient (good condition for
impossibillity) there is no TRUTH. As Bruno formulates his reply:
there is something like "mathematical truth" - but did you ask for
such specififc definition?
Now - about mathematical truth? new funamental inventions in math
(even maybe in arithmetics Bruno?) may alter the ideas that were
considered as mathematical truth before those inventions. Example:
the zero etc.
It always depends on the context one looks at the problem FROM and
draws conclusion INTO.
John M
On Sun, Oct 16, 2011 at 12:48 AM, Stephen P. King <stephe...@charter.net
> wrote:
Hi,
I ran across the following:
http://en.wikipedia.org/wiki/Tarski%27s_indefinability_theorem
"Tarski's undefinability theorem, stated and proved by Alfred
Tarski in 1936, is an important limitative result in mathematical
logic, the foundations of mathematics, and in formal semantics.
Informally, the theorem states that arithmetical truth cannot be
defined in arithmetic."
Where then is it defined?
Onward!
Stephen
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