The Foundations of General Schemas Theory

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The Foundations of General Schemas Theory

• As an Extension to Systems Theory to Form a
  Mathematical and Philosophical Basis for Systems
  Engineering

Draft 12 040413 Kent D. Palmer, Ph.D. PO Box 1632
Orange CA 92856 714-633-9508 kent_at_palmer.name http
//archonic.net
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Significant Points

• The current most likely foundation for SE is
  Systems Theory
• Emergence is an important viewpoint on SE
• There are specific levels of Emergence some of
  which are addressed in current SE and others of
  which are not addressed yet, but should be
• SE is a discipline structured by Emergence
• Other schemas besides the system schema are
  important to SE
• Ultimately SE needs to become Schemas Engineering
  based on Schemas Theory

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Horizons of SE

Schemas Engineering
Current SE
4

MAP
Transformative ?
(of the argument)
Systems Engineering Discipline
Other Disciplines
Ontic and Ontological Levels of Emergence
SW Eng / Comp Science

• A transformative discipline is one which changes
  the relations between other disciplines when it
  appears

Complex Systems Theory
All Engineering Disciplines are the Academic
counterpart of SE
Complex Adaptive Systems
Scope Broader
Chaos Theory
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Systems Engineering means . . .

• Engineering Large Scale Emergence
• SE is where emergence is the appearance of new
  properties at the level of a whole not seen in
  the parts,
• E.g., cell/organism Hydrogen,Oxygen
  elements/Water (H2O) molecule sub-system/system/s
  uper-system
• The problem of emergence appears in other
  engineering disciplines but it comes to a head in
  SE because of the scale of SE projects

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Emergence Engineering

• If we begin to think of Systems Engineering as
  Large Scale Emergence Engineering, then our view
  of the discipline begins to change radically
• When we change our vision of SE, it changes its
  relation to other disciplines
• The biggest problem is our own limited vision of
  SE, not the subject matter of SE itself
• Emergence Engineering must be a transformative
  discipline in relation to other disciplines, and
  what it studies will have a profound effect on
  itself

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MAP
(of the argument)
Emergence Engineering Meta-levels
de-emergence
supervenience
emergence
meta-levels of emergence
meta-levels of Being
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Supervenience Emergence
Gestalt Whole greater than sum of parts
Emergence Excess
organism
LEVEL N1
new characteristics
Supervenience is Homomorphism with lower level
supports
emergence
Synthesis
LEVEL N
cell
supports
Qualitative and Quantitative Jump
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De-emergence
Proto Gestalt Whole less than sum of parts
gives knowledge of implicate order
Emergent Lack
Loss of knowledge or information
LEVEL N1
Cannot reconstitute the whole
ltReductionism De-emergencegt
Part
Part
Part
Part
Part
LEVEL N
Analysis/ Architecture
Parts dont add up to the whole
There is normally a cycle between emergence and
de-emergence
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Undecidable means non-reducible

Conjecture Emergent Properties are Godelian
This could be the basis for formalizing the
concept of emergence
emergent excess
decidable outside
decidable inside
undecideable
emergence
de-emergence
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Emergence of Emergences
E2b
E3
Cant get to E3 directly from lower levels of
Emergence
E2a
E1
E0
Current view of SE as concerned with Integration
12

MAP
(of the argument)
repeated
Emergence Engineering Meta-levels
de-emergence
supervenience
emergence
meta-levels of emergence
meta-levels of Being
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Correspondence between meta-levels of Emergence
and meta-levels of Being
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Stairs to Nowhere Meta-levels of Emergence
Existence
Emptiness / Void
Lack
Radically Unpredictable, unknown
E5
E4
chiasm between actualities, errors, voids
genuine emergence
Being
Ultra Being
E3
essencing forth in time
E2
excess
Supervenient
combinatoric or additive change
E1
undecidable
E0 non-emergent change
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Emergent Difference

• Ontology covers the various standings of
  everything that presents or absences itself
  phenomenologically
• Ontological Difference distinguishes those
  standings from the various beings which have
  those various standings
• Emergent difference relates to the
  intensification of nihilism
• Artificially emergent events are additive,
  incremental, and combinatoric intensifications of
  nihilism
• Genuine Emergent events are quantum leaps that
  reset all parameters and recalibrate by producing
  a new origin

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Emergence0 beings

• Non-new change
• More of the same
• Random alteration
• Entry of the New

• beings, entities, things
• Entry of Being

Emergent Difference and Ontological Difference
Example Car wear
Example Projection
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Aspects of Being

• Truth
• Reality
• Identity
• Presence
• I am only going to describe the differences
  in the meta-levels of emergence not the
  differences and the kinds of Being or the aspects
  of Being in this talk.

These change at the different meta-levels of Being
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Emergence1 Pure Being

• Pure Artificiality
• Combinatoric expansion
• Superficial newness
• Additive or incremental improvement
• Nothing fundamental changes

• Determinate and continuous
• Present-at-hand
• Pointing
• Standing reserve
• Subject/object dichotomy
• Form level
• Symbol
• Shape

Example New cars
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Aspects of Being at Emergence Level 1

• Identity1 Change and difference occur but make
  no fundamental difference
• Presence1 Changed Emergent characteristics
  appear
• Reality1 Emergent characteristics are embodied
• Truth1 Emergent characteristics can be
  described in language

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Emergence2 Process Being

• Emergence becomes an event
• It takes time for something to be what it is
• Emergent change reveals the essence of the thing
  seen
• Like Catalysis in Transformations

• Probability
• Ready-to-hand
• Grasping
• Dasein (being-in-the-world)
• Pattern Level
• Value
• Sign
• Flux
• Structure

Example From Buggy to Car
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Aspects of Being at Emergence Level 2

• Identity2 Self identity revealed though change
  sameness belonging-together family
  resemblance
• Presence2 showing and hiding
• Reality2 Physus - unfolding of new kinds in
  nature
• Truth2 Logos unfolding of new kinds in
  language

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Emergence3 Hyper Being

• Projects new possibilities on new horizon
• Emergence itself is undecidable
• Emergent excess is Godelian

• Possibility
• In-hand
• Bearing
• Query (expansion)
• Trace Level
• Differance
• Differing/Deferring
• Excess / Supplement

Example Car with Software
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Aspects of Being at Emergence Level 3

• Identity3 Self Identity revealed though Other
  (Alterity)
• Presence3 secrecy, lies, deception,
  dissimulation
• Reality3 Simulacrum unreality of reality is
  more real than reality
• Truth3 Fiction lies tell truth deeper than
  the facts alone can tell

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Emergence4 Wild Being

• Actualizes new possibilities on new horizon
• Emergence is intrinsically unpredictable
• Reveals unexpected, unheard of, unthought,
  anomalous appearances from a direction previously
  unknown

• Propensity
• Out-of-hand
• Encompassing
• Enigma (contraction)
• Tendency
• Rhizome
• Chiasm (reversibility)
• Flesh

Example Car with AI
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Aspects of Being at Emergence Level 4

• Identity4 Chiasm between selfs and others
  identity and difference
• Presence4 Chiasm between selfs and others
  presence and absence
• Reality4 Chiasm between natures and
  artificialitys reality and illusion
• Truth4 chiasm speechs and silences between
  truth and fiction

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Emergence5 Existence

• Genuinely emergent existent appears from itself
  in its own time and a place of its choosing
• No projection
• Face of the World

• Interpretations
• Ultra Being
• Emptiness
• Void
• Inter/intra penetration/surfacing
• Being seen from outside as a found thing
  being-out-of-the-world

Example Flying Car, New Media
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Aspects of Existence at Emergence Level 5

• Identity5 uniqueness
• Presence5 Fully and Genuinely Emergent Alterity
• Reality5 Phenomena bodies forth in itself in
  its own style of non-nihilistic distinctions in
  action
• Truth5 Wipes nihilistic background clean -
  clears the clearing-in-being and makes
  non-nihilistic distinctions as phenomena speaks
  for itself in its own voice

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Emergence means . . .

• History is rewritten
• New future possibilities appear while old future
  possibilities vanish
• What is presence is seen in a new way
• New Theory
• New Paradigm (assumptions) Kuhn
• New Episteme (categories) Foucault
• New Ontos (projection, intelligibility) Heidegger
• New existence (found)
• Mythos is reformatted
• SE does not deal with all of Emergence in its
  current form
• Realm of Futurology, Venture Capital, or IRD

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Meta-levels of Emergence
Existence
Emptiness / Void
Lack
E5
E4
genuine emergence
Radically Unpredictable, unknown
Being
Ultra Being
E3
E2
excess
essencing forth in time event
Supervenient
combinatoric or additive change
E1
undecidable
E0 non-emergent change
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MAP
(of the argument)
repeated
Emergence Engineering Meta-levels
de-emergence
supervenience
emergence
meta-levels of emergence
meta-levels of Being
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Meta-levels of Emergence Engineering
Existence
Inter
penetration
Meta-system
Niche
Intra
surfacing
eg., manufacturing, Eng. disciplines
synthesis
SE
genuine emergence
E4
chiasm between actualities, errors, voids
System
E5
Specialties
Being
horizon
Architecture/Analysis
E3
essencing forth in time
Process
E2
excess
horizon
Design Possibilities
Change Control
horizon
Products
E1
Supervenient
combinatoric or additive change
undecidable Trade-offs
interim artifacts
E0
vicissitudes of work
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Main Point

• The whole discipline of Systems Engineering is
  structured by the meta-levels of Emergence
• Systems Engineering is intrinsically Emergence
  Engineering
• But is Systems Engineering enough even when
  viewed as Emergence Engineering?
• Perhaps we need something even broader than the
  focus on the Emergence of Systems which is
  dependent on the Systems Schema alone

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MAP
Meta-Levels of Being
(of the argument)
Aspects of Being
Properties
Perice/Fuller Categories
Face of world
Path into world for Emergence
Worldhood
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Path of Emergence into the World
Artificial Nihilistic Emergences

• Emergent characteristics
• Emergent Event produces new kinds
• Emergent possibilities rewrite history
• Emergence inherently unpredictable

false abortive newness
ultra
wild
hyper
process
pure
Genuine Emergence
Repatterned world of beings
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Face of the World
All four kinds of Being working together
Ultra
Actuality
SE is a face of the world
Possibilities
Hyper
Pure
continuous path
ideal determinate
Wild
propensity
probability distribution
diversions due to differences in ontic physus
Process
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What about the System Schema?

• Are there other possible Schemas that might be
  important to SE?
• What are the other Schemas that give systems
  their meaning through contrast?
• Do the set of all possible schemas have a
  structure?
• Can SE use this structure of schemas to help
  formalize its work?

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Non-dual Order

• Einstein noted how amazing it was that
  mathematics can be used to connect theory to
  physical phenomena through instruments
• Theory is the Logos, Physical Phenomena are the
  Physus, and the non-dual between and before their
  split is Order

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Mathesis
Order
logos of physus Schema
Physus of logos Logic
Physus / Logos
Finite / Infinite
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Mathematical Categories
Mathesis
strong
real
Representation Theory
kernel representations
Mathematical
Semantics Syntax
Model Theory
presence identity truth
Logic
Schema

Philosophical Categories Episteme Paradigm Theory
Facticity
weak
strong
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Circulation of Projection
meta-dimensionality set/mass

• Phenomenological View
• Preontological
• Ontic
• Ontological

Mathesis
Anomalies
Being
Representation theory
Model Theory
Order
non-dual
ontic
ontological
Physus
Logos
Phil. Cat.
existence ontos episteme paradigm theory
type theory
contradiction
projection
physus of logos Logic
logos of physus Schema
contrary
paradox
perception
Example Projection of System
facticity
Experience
Reason
doxa ratio
kind individual
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Ontic Levels of Emergence
Gaia Society Species Organism Multi-cell Cell Prot
o-cell Macro Molecule Molecule Atom Particle Quark
String
We discover the levels of Emergence by trying to
reduce everything. Those things that cannot be
reduced are emergent ontic levels. Different
possible ontic hierarchies are possible.
Pressure of reductionism
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Types of Schemas Ontological levels of Emergence
Pluriverse Kosmos World Domain Meta-system System
Form Pattern Monad Facet
Different possible projections onto the Ontic
levels
Ontic Level
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Research in General Schemas Theory
Schemas
Dimensions
Pluriverse Kosmos World Domain Meta-system
System Form Pattern Monad Facet
10 - 9 9 - 8 8 - 7 7 - 6 6 - 5 5 - 4 4 - 3 3 -
2 2 - 1 1 - 0 0 - -1
Important result
Two dimensions per schema
Two schemas per dimension
See General Schemas Theory paper by author CSER
conference 2004
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Open Problems

mathesis

• There is no clear definition of categories
• Many different systems are proposed
• The relation of Philosophical Categories, as they
  are defined by Kant, to schemas is vague
• The relation if the Philosophical Categories to
  other social levels of knowledge is unclear

schema
logic
Aristotle Kant Hegel Heidegger Johannson
Phil. Categories Existence Ontos Episteme Paradig
m Theory Facticity
Social levels of knowledge
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Open Problems
Normal / Deviant
Set / Mass Syllogism / Pervasion
Diamond Logic Vajra Logic Matrix Logic
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Logics
Syllogism
Pervasion
Universal
Boundary
Set Attribute difference
Mass Containment identity
particular
instance
Non-dual
Conjunction
Conglomerate Metonymy Sameness belonging together
Ipsity
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Open Problems
semantics
syntax
Reality
Truth
Presence
Identity
syntax
syntax
Model theory
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Aspects and Properties
syntax
semantics
Coherence
Reality
Truth
Consistency
Validation
Verification
Completeness
Presence
Identity
Clarity
syntax
syntax
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Open Problems
N-conglomerates
Mathematics ignores mass approaches and relies
solely on set approaches, so mathematical
categories are fundamentally lopsided
N-category
N-blob
Set / Mass
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1 - Conglomerate conjunction 2 - ? 3 - ? 4 - ?
N-conglomerates
N-blob
N-category
Blob boundary - 1 Tissue - 2 Bag - 3 Tweak - 4
1 - Category arrow 2 - Functor 3 - Natural
transformation 4 - Modification
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Open Problems
Representational Theory taken for granted but not
explicitly defined
Representation vs. Repetition
See . . . Deleuze, G Difference and
Repetition Taussig, M. Mimesis and Alterity
Representation theory
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Open Problems
mimesis
Form 3d
Building
Model
perspective
rendering
mimesis
Form 2d
Picture
Plans
Representation
Repetition
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Open Problems
Pluriverse Kosmos World Domain Meta-system System
Form Pattern Monad Facet
Schemas are relatively unknown and a General
Schemas Theory has not yet been developed, but
the schemas are the basis of all formalization
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End of Talk

• See http//archonic.net and http//holonomic.net
• for more information concerning this ongoing
  research project.

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MAP
Schema
(of the argument)
Ultra Being and Existence
Types of schema
Opposite of Emergence
Genealogy of the schema
Anaximander Plato Kant Heidegger
Dimensions
Unfamiliarity
Pascal Triangle Simplicies
Negative Dimension
Meta-dimension