The Foundations of General Schemas Theory
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Transcript of 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 040413Kent D. Palmer, Ph.D.
PO Box 1632 Orange CA 92856714-633-9508 [email protected]
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
Cur
rent
SE
Schemas Engineering
Emergence Engineering
*
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Chaos Theory
Complex Systems Theory
Complex Adaptive Systems
Ontic and Ontological Levels of Emergence
Systems Engineering Discipline
Other Disciplines
SW Eng / Comp Science
All Engineering Disciplines are the Academic counterpart of SE
Transformative ?MAPMAP
(of the argument) *
Scope Broader
•A transformative discipline is one
which changes the relations between other disciplines when it appears
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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/super-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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Emergence Engineering Meta-levels
supervenience de-emergence
emergence
meta-levels of emergence
meta-levels of Being
MAPMAP(of the argument) *
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LEVEL N+1
LEVEL N
Supervenience & Emergence
Emergence Excess
emer
genc
e
Qualitative and Quantitative Jump
Gestalt = Whole greater than sum of parts
Supervenience isHomomorphism with lower level supports
*
Synthesis
new characteristics
supportscell
organism
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LEVEL N+1
Part
Emergent Lack
<Red
uctio
nism
De-
emer
genc
e>
Proto Gestalt = Whole less than sum of parts gives knowledge of implicate order
De-emergence
Part Part Part Part
Cannot reconstitute the whole
Parts don’t add up to the whole
LEVEL N
*
Analysis/Architecture
Loss of knowledge or information
There is normally a cycle between emergence and de-emergence
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10Undecidable means non-reducible
decidable outside
undecideable
decidable inside
emergent excess
Conjecture: Emergent Properties are Godelian *
emergence
de-emergence
This could be the basis for formalizing the concept of emergence
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E0
E1
E2a
E2b
Emergence of Emergences *E3
Can’t get to E3 directly from
lower levels of Emergence
Current view of SE as concerned with Integration
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Emergence Engineering Meta-levels
supervenience de-emergence
emergence
meta-levels of emergence
meta-levels of Being
MAPMAP(of the argument) *
repeated
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*
Emergence7
Meta-levels of Emergence Meta-levels of Being
Emergence6
Emergence5
Emergence4
Emergence3
Emergence2
Emergence1
Emergence0
Thatness/Suchness
Manifestation
Ultra-Being
Wild Being
Hyper Being
Process Being
Pure Being
beingsontological difference
existencethreshold
Ontology
Correspondence between meta-levels of Emergence and meta-levels of Being
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Lack
E0 non-emergent change
E1
E2 E3
E5
Supervenient
essencing forth in time
excess
E4 chiasm between actualities, errors, voids
horizon
horizon
horizon
undecidable
Stairs to Nowhere: Meta-levels of Emergence
Ultra Being
Emptiness / Void
genuine emergence
Bei
ngE
xist
ence
combinatoric oradditive change
*
Radically Unpredictable, unknown
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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 self’s and other’s identity and difference
• Presence4 – Chiasm between self’s and other’s presence and absence
• Reality4 – Chiasm between nature’s and artificiality’s reality and illusion
• Truth4 – chiasm speech’s and silence’s 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 IR&D
*
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Lack
E0 non-emergent change
E1
E2 E3
E5
Supervenient
essencing forth in time: event excess
E4
horizon
horizon
horizon
undecidable
Meta-levels of Emergence
Ultra Being
Emptiness / Void
genuine emergence
Bei
ngE
xist
ence
combinatoric oradditive change
*
Radically Unpredictable, unknown
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Emergence Engineering Meta-levels
supervenience de-emergence
emergence
meta-levels of emergence
meta-levels of Being
MAPMAP(of the argument) *
repeated
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System
Niche
Products E1
E2 E3
E5
Supervenient
combinatoric oradditive change
essencing forth in time
excess
E4 chiasm between actualities, errors, voids
horizon
horizon
horizon
undecidableTrade-offs
Meta-levels of Emergence Engineering
genuine emergence
Bei
ngE
xist
ence
Process
Change Control
Architecture/Analysis
Specialties
InterIntra
penetrationsurfacing
DesignPossibilities
interim artifactsE0
Meta-system
vicissitudes of work
synthesis
*eg., manufacturing, Eng. disciplines
SE
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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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Meta-Levels of Being
Perice/FullerCategories
Path into world for Emergence
Face of world
Worldhood
Aspects of Being
Properties
MAPMAP(of the argument)
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Genuine Emergence
false
abortiv
e new
ness
Artificial Nihilistic Emergences
ultra
wildhy
per
proc
ess
pure
Repatterned world of beings
•Emergent characteristics
•Emergent Event produces new kinds
•Emergent possibilities rewrite history
•Emergence inherently unpredictable
Path of Emergence into the World
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Face of the WorldAll four kinds of Being working together
ideal determinate
probability distribution
propensitydiversions due to
differences in ontic physus
Possibilities
Actuality
continuous pathPure
Process
Hyper
Wild
Ultra
SE is a face of the world
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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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Finite / Infinite
Physus / Logos
Mathesis
Order
logos of physusSchema
Physus of logosLogic
*
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Schema Logic
Mathesis
Model TheoryRepresentation
Theory
Mathematical Categories
Philosophical CategoriesEpistemeParadigmTheory
Facticity
SemanticsSyntax
strong
strongweak
real
presenceidentity
truth
kernel||
representations
Mathematical
*
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ontological
facticity
Physus
Mathesis
Order
logos of physusSchema
physus of logosLogic
Model TheoryRepres
entat
ion th
eory
LogosPhil. Cat.ontic
Experience Reasonkind
individual
projection
Anomalies
perception
Being
para
dox
contrary
cont
radi
ctio
nty
pe th
eory
doxaratio
meta-dimensionalityset/mass
existenceontos
epistemeparadigm
theory
non-dual
Phenomenological View•Preontological•Ontic•Ontological
Circulation of Projection *
Example: Projection of System
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Ontic Levels of EmergenceGaia
SocietySpecies
OrganismMulti-cell
CellProto-cell
Macro MoleculeMolecule
AtomParticle
QuarkString
Pre
ssur
e of
red
ucti
onis
m
*
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.
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PluriverseKosmosWorld
DomainMeta-system
SystemForm
PatternMonadFacet
OnticLevel
Types of SchemasOntological levels of Emergence
*
Different possible
projections onto the Ontic
levels
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Pluriverse
Kosmos
World
Domain
Meta-system
System
Form
Pattern
Monad
Facet
Schemas Dimensions
Important result:
Two dimensions per schema
Two schemas per dimension
See “General Schemas Theory” paper by author CSER conference 2004
Research in General Schemas Theory *10 - 9
9 - 8
8 - 7
7 - 6
6 - 5
5 - 4
4 - 3
3 - 2
2 - 1
1 - 0
0 - -1
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Open Problems
• 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
mathesis
schema logic
Phil. Categories
ExistenceOntos
EpistemeParadigmTheory
Facticity
AristotleKantHegel
HeideggerJohannson
Social levels of
knowledge
*
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mathesis
schema logic
Open Problems
Normal / Deviant
Diamond LogicVajra LogicMatrix Logic
Set / MassSyllogism / Pervasion
*
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LogicsSyllogism
Universal
SetAttributedifference
particular
Pervasion
Boundary
MassContainment
identity
instance
Non-dual
Conjunction
ConglomerateMetonymySameness
belonging together
Ipsity
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Open Problems
mathesis
schema logic
Model theory
Reality Truth
Presence Identitysyntax syntax
syntaxsemantics
*
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Reality Truth
Presence Identitysyntax syntax
syntaxsemantics
Aspects and Properties
Coherence
Verification
Completeness
Val
idat
ion
Clarity
Con
sist
ency
*
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Open Problems
mathesis
schema logic
Set / Mass
N-category N-blob
N-conglomeratesMathematics ignores mass approaches and
relies solely on set approaches, so
mathematical categories are fundamentally
lopsided
*
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N-blob N-category
N-conglomerates
Blob boundary - 1Tissue - 2
Bag - 3Tweak - 4
1 - Category arrow2 - Functor3 - Natural transformation4 - Modification
1 - Conglomerate conjunction2 - ?3 - ?4 - ?
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Open Problems
mathesis
schema logicRepresentation theory
Representational Theory taken for granted but not
explicitly defined
See . . .Deleuze, GDifference and RepetitionTaussig, M.Mimesis and Alterity
Representation vs. Repetition
*
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Open Problems
Form 3d
Form 2d
Building Model
Picture Plans
RepresentationRepresentation RepetitionRepetition
mimesis
mimesis
perspective rendering
*
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Open Problems
mathesis
schema logicPluriverseKosmos
WorldDomain
Meta-systemSystem
FormPatternMonad
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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Schema
Types of schema
Genealogy of the schema
UnfamiliarityDimensions
Opposite of Emergence
Ultra Being and Existence
MAPMAP(of the argument)
AnaximanderPlatoKantHeidegger
NegativeDimension
Meta-dimension
PascalTriangle
Simplicies