Hi Craig,
On 15 Aug 2012, at 11:21, Craig Weinberg wrote:
in case the special characters don't come out...
I was thinking about your primitive of arithmetic truth (numbers, 0,
+, and *, right?) and then your concept of ‘the dreams of
numbers’, interviewing Lobian Machines, etc and came up with this.
One single irreducible digit ॐ (Om) which represents a self-
dividing continuum of infinite perpendicular dialectics between
eidetic dream states (in which dream~numbers escape their numerical
identities as immersive qualitative experiences) and entopic non-
dream states (in which number~dreams escape their dream nature as
literal algebra-geometries).
I use such term more literally. I am not sure I can understand this,
even if there is some genuine analogy.
The dreaming number are usually very big concrete number. They dream
by encoding computational state of person, relatively to some
universal number, which are encoding universal machine relatively to
some other one, and the initial one can be chosen arbitrary. Those are
not symbolic number, but real encoding number, a bit like the genome
if you want.
This continuum f (ॐ(Om)), runs from infinitely solipsistic/private
first person subjectivity (calling that Aleph ℵ)to infinitely
discrete/public third person mechanism (calling that Omega Ω), so
that at ℵ,any given dream is experienced as 99.99…9% dream and
0.00…1% number and at Ω (Omega), any given machine or number is
presented as 99.99…9% number and 0.00…1% dream.
?
The halfway point between the ℵ (Aleph) and Ω (Omega) axis is the
perpendicular axis f (-ॐ(Om)) which is the high and low
correspondence between the literal dream and figurative number (or
figurative dream and literal number depending on whether you are
using the dream-facing epistemology or the number-facing
epistemology). This axis runs from tight equivalence (“=”
equality) to broadly elliptical potential set membership (“…”
ellipsis)
So it looks something like this:
f(ॐ) ⊇ {ℵ “…” ⊥ “=” Ω}
function (Om) is superset or equal to the continuum ranging from
Aleph to ellipsis perpendicular/orthogonal to the inverse range from
equality to Omega).
To go further, it could be said that at Ω(Omega), ॐ (Om) expresses
as 10|O (one, zero, line segment, circle referring to the
quantitative algebraic and geometric perpendicular primitives) while
at ℵ (Aleph), ॐ (Om) expresses as
יהוה (tetragrammaton or yod, hay, vov, hay, or in perhaps more
familiar metaphor, ♣♠♥♦(clubs, spades, hearts, diamonds)
where:
♣ clubs (wands) =Fire, spiritual, tactile
♠ spades (swords) = Air, mental, auditory
♥ hearts (cups) =Water, emotional, visual
♦ diamonds (pentacles/coins) = Earth, physical, olfactory-gustatory
Note that tactile and auditory modalities tune us into ourselves and
each others sensemaking (selves and minds), while the visual and
olfactory/gustatory sense modalities are about objectifying realism
of the world (egos or objectified selves/self-images and bodies). It
should be obvious that ♣ clubs (wands) and ♠ spades (swords) are
stereotypically masculine and abstracting forces, while ♥ hearts
(cups) and ♦ diamonds (pentacles/coins) are stereotypically
feminine objectified fields.
Sorry for the mumbo jumbo, but it is the only way to be non-
reductive when approaching the qualitative side.
I don't think so. Aristotle invented modal logic to treat in the
quantitative way non reductive qualitative notion.
We can’t pretend to talk about the eidetic, dream like
perpendicular of number logic while using the purely empirical terms
of arithmetic reduction. We need symbols that can only refer to
named qualities rather than enumerated quantities.
This is exactly what happen when you define the first person by the
knower. Bp & p, or if you prefer
provable(p) and true(p),
gives a modality which can provably be shown qualitative, and non
formalizable in arithmetic. It leads to a logic (know as S4Grz) which
describes something which is absolutely impossible to reduce to any
number relations or even anything third person describable notion,
even infinite one.
You might think I just described it, by Bp & p, or by "provable(p) and
true(p)", but this is not the case, as I use some of your intuition
about truth, which cannot be arithmetized by itself, by a famous
result of Gödel and Tarski (independently).
It happens that we do have a good intuition of many truth, and machine
can indeed describe better and better approximations of the truth
concept, but the limit of it, used here, cannot be. So by using both
the comp hypothesis, and by studying simple (Löbian) machine (simpler
than us) we can develop a formal (quantitative in some sense, at some
level, from some point of view) theory concerning the non formal, and
even non-formalizable-at-all-by-the-machine, qualities that machine
can still refer about. And this can be used to explain why machine are
forced to be befuddled by the subjectively-real apparent gap between
third and first person attributes.
Let the ignoring and insulting begin!
We don't need that here, I think, nor anywhere. An insult is almost
always equivalent with "I have no argument".
Bruno
http://iridia.ulb.ac.be/~marchal/
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