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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