The Foundations of General Schemas Theory

1
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
2
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

3
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
5
Systems Engineering a Transformative Discipline?

• SE is a nascent discipline
• It is attempting to gain academic respectability
• Part of this is the attempt to establish
  mathematical and philosophical foundations for
  the new discipline
• SE has no specific academic counterpart unlike SW
  Eng. has in Computer Science, rather, all
  Engineering disciplines are the academic
  counterpart of SE
• Much SE research merely attempts to validate what
  has been put already into practice in Industry

6
Systems Engineering a Transformative Discipline?

• Few SE Ph.D. programs exist
• Most SE academic departments concentrate on the
  masters level where the emphasis in on coursework
  rather than original research
• In-depth research into SE foundations is rare
• Most in-depth research at the Ph.D. level has a
  foreshortened horizon seeking to mostly validate
  what is already known or seeking to apply what is
  known from other disciplines to SE
• Very few researchers consider SE a transformative
  discipline

7
Systems Engineering a Transformative Discipline?

• A transformative discipline is one which changes
  the relations between other disciplines when it
  appears
• This is the highest possibility to which the SE
  discipline can aspire
• Rather than viewing SE as a discipline which
  calls for bolstering in order to become
  academically respectable, let us explore the
  transformative possibilities of SE

8
Systems Engineering a Transformative Discipline?

• If we consider SW Eng. as a model, we can clearly
  see its vibrancy slowly transforming computer
  science into a support for industrial practice by
  bringing new problems and new applications for
  computer science to explore
• SW Eng. has its own subject matter as well, which
  concerns products, processes, methods and tools
  that support large scale software development

9
Can Systems Engineering be a Transformative
Discipline?

• Systems Engineering has no specific complementary
  academic discipline
• Instead every sub-division of engineering in
  academia is its complement, as well as the
  meta-discipline of Systems Theory which has no
  dedicated department within the university
• There is a gap between SE and all other
  Engineering disciplines which makes it difficult
  for these engineering disciplines to reap the
  benefits that SE has to offer
• Systems Theory is too nebulous and diffuse since
  it lacks autonomy when spread throughout other
  engineering disciplines

10
Systems Engineering a Transformative Discipline?

• For the most part SE is adopting SW Eng.s
  processes, methods, and tools
• SE thus appears as a surrogate of SW Eng. at a
  higher level of abstraction
• The unique needs of SE are not being considered
  very deeply
• Unlike SW Eng., SE is neither driving academic
  research agendas nor is it fostering its own
  innovative research agenda
• SE seems to be a late arrival with little new to
  offer other disciplines
• Instead, it is borrowing and begging from other
  disciplines hoping for recognition because of its
  place at the top of the food chain in industry

11
How can we reverse this situation?

• One way is to realize that SE is the place where
  all the diverse industrial disciplines come
  together to produce the emergent effects of a
  whole working system being developed on a large
  scale
• The key thing that SE has as its focus is
  Emergence, while other disciplines do not have
  this focus the same way or with the same intensity

12
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

13
Emergence Engineering

• Emergence is a hot topic in complex Systems
  Theory and science in general
• It is related to Chaos Theory and Complex
  Adaptive Systems Theory
• SE has an intimate hands-on knowledge of how
  large scale complex systems are built to produce
  holistic emergent effects
• And SE is concerned with the huge and open
  problem of how to deal with these systems of
  greater scale and complexity

14
Emergence Engineering

• By studying the successes and failures of the
  development of large complex systems, SE has a
  ready-made focus for inquiry
• No other discipline attempts such large scale
  production of emergent wholes, and it is
  essential to note that differences in scale can
  produce qualitatively different problems
• Effects come into play which do not appear on
  smaller scales
• This is one of the lessons of Hegelian
  Dialectics, i.e., Differences in quantity produce
  differences in quality in relation to dialectical
  synthesis

15
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

16
Emergence Engineering

• In our new vision of SE, we can see it as an
  emergent event within industry and academia
• The study of Emergence comes into it own in a
  practical sphere of industrial practice which
  gives a ground for theories of emergence that are
  developed in Complex Systems Theory
• In the advent of an emergent event, it is natural
  to see SE as a radically transformative
  discipline changing itself and other disciplines
  profoundly when it is considered from this new
  viewpoint

17

MAP
(of the argument)
Emergence Engineering Meta-levels
de-emergence
supervenience
emergence
meta-levels of emergence
meta-levels of Being
18

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
19

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
20
Emergence

• An emergent system gestalt must be based on
  supports from the next lower level of phenomena
• Its dependence on these supports, although it
  rises above them, is called supervenience
• However, the emergent system gestalt must add new
  properties and characteristics that go beyond the
  limitations of these supports opening up new
  horizons of combination and complexification that
  produce other higher properties with their own
  reality which cannot be reduced

21
Supervenience

• All systems designed and built by SE
  practitioners attempt to produce wholes with
  emergent effects on a large scale
• These wholes are supervenient on the supports of
  their subsystems and parts, but attempt to go
  beyond these sub-system or parts to produce
  characteristics and properties not contained in
  the parts themselves which go beyond what the
  parts can accomplish in isolation from each other

22
Philosophy of Science

• From the point of view of Philosophy of Science
  it is clear that there is no method for producing
  emergent leaps to the whole greater than the sum
  of its parts, which is the emergent whole
• As Paul Feyerabend says, The only method is NO
  METHOD, so that anything goes when it comes to
  design and construction of emergent wholes
• This gives SE its character which is based on
  trial and error and applying the best of
  engineering judgment

23
Uniqueness

• Because there is no method, nor royal road for
  producing emergences in SE practice it is
  necessary to bring creativity and innovation into
  the development of Emergent Systems
• This is also why Engineering practice seems so ad
  hoc and why it is so difficult to estimate and
  predict outcomes
• Each new system presents unique challenges and
  requires unique configurations of products,
  processes, methods, and tools to create the
  required emergent effects

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Godel

• One way to think about the production of sui
  generis emergent characteristics in creative
  systems design and construction is in terms of
  Godelian statements
• Godelian statements are undecideable with respect
  to supervenient lower level axiomatic foundations
• The emergent excess of the designed and
  constructed system can be thought of as equal to
  the undecidable Godelian statements that cannot
  be designated as inside or outside the system
• They are beyond what is definitely inside the
  system, yet not outside it

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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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Large Scales

• All engineering attempts to produce emergent
  effects on a small scale
• SE attempts to produce these effects on a large
  scale by integrating small scale emergent
  sub-systems into large scale systems or systems
  of systems
• This is, in effect, an attempt to produce an
  emergence of emergences

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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
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Meta-levels

• The idea that there can be different meta-levels
  of emergence changes our concept of emergence
  itself by fragmenting it into an infinite series
  of possible meta-levels using the Higher Logical
  Type Theory of B. Russell and A.N. Whitehead from
  Principia Mathematica (cf I. Copi)
• This theory can be used as a means of teasing out
  the different meanings of emergence

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Radical Possibility

• Emergence is a radical possibility of Being
• Emergence is what allows different technologies
  to be combined to produce new levels of synthesis
  which gives rise to new possibilities of Being
• The levels of emergence are another face of the
  meta-levels of Being
• Our attempt to understand the levels of Emergence
  leads us directly into what Heidegger calls
  fundamental ontology as developed in Continental
  Philosophy

30

MAP
(of the argument)
repeated
Emergence Engineering Meta-levels
de-emergence
supervenience
emergence
meta-levels of emergence
meta-levels of Being
31

Correspondence between meta-levels of Emergence
and meta-levels of Being
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Characteristics of Emergence

• Each kind of Being expresses itself in a
  characteristic of emergence
• Emergence is a phenomena in the world that brings
  to bear all the kinds of Being as a face of the
  world transforming one face of the world into
  another
• Emergence and kinds of Being have a reciprocal
  relationship
• Each allows us to understand the other better if
  we study them together

33
Ontological Difference

• Ontological Difference is a kind of
  meta-difference that distinguishes between
  Being and beings
• It appears as the difference between genuine and
  Artificial Emergence
• Artificial emergence is incremental change that
  is not genuinely new but merely combinatorially
  different
• Genuine emergence clears the stage for the advent
  of the utterly unheard of here-to-fore rewriting
  of the past and production of new horizons of
  possibility

34

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
35
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
38
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
39
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

40
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

42
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
43
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

44
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

46
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
47
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

48
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

49

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
50
Torn between alternatives

• In SE we are always recombining existing
  components when attempting to build new systems
• We are constantly torn between, reuse,
  subcontracting, and new development
• When we engage in new development we recognize
  that process plays an important part
• There are certain stages that force themselves on
  us
• It takes a certain time to build a system from
  scratch and many times shortcuts cost more in the
  end

51
Design

• In the design process there are many possible
  workable designs for the same system and many
  more which will not work
• When walking though the design landscape there
  are myriad decisions to be made which all must
  cohere to produce the desired emergent effects
  that will meet requirements
• Design elements must have synergy to fit together
  so that each element performs multiple roles with
  respect to the entire ensemble of elements that
  make up the system

52
Genuine emergence is based on
Ultra Being
Ultra Being is the interspace between void and
emptiness, i.e. between the two non-duals, odd
and even zero
53
Emptiness / Void

• Inter-penetration mutual synergistic
  interlocking
• Intra-penetration mirroring of other parts of
  the system in each part
• Inter-surfacing fitting interfaces
• Intra-surfacing interchange protocols in
  interim between interfaces

54
Ultra Being is . . .

• Ultra Being is external view of projection
• A face of the world including all four
  meta-levels of Being that embody projection
• Ultra Being is the standing upon which
  schematization is based

55

MAP
(of the argument)
repeated
Emergence Engineering Meta-levels
de-emergence
supervenience
emergence
meta-levels of emergence
meta-levels of Being
56

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
57
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

58
MAP
Meta-Levels of Being
(of the argument)
Aspects of Being
Properties
Perice/Fuller Categories
Face of world
Path into world for Emergence
Worldhood
59
Peirce / Fuller Categories
objects
relations between objects
system synthesis
simulation of interactions through behaviors of
object methods
class templates of objects
60
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
61
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
62
Worldhood

• Pure
• Present-at-hand
• Subject/Object dualism
• No context
• Pointing
• Determinate and continuous

• Process
• Ready-to-hand
• Dasein (prior to split)
• Being-in-the-world
• Grasping
• Probabilistic

63
Worldhood

• Hyper
• In-hand
• Query
• Expansion of being-in-the-world
• Bearing
• Possibility

• Wild
• Out-of-hand
• Enigma
• Contaction of being-in-the-world
• Encompassing
• Propensity

64
Science
Quantum Mechanics
Relativity theory
macro
micro
Present-at-hand
Local flat spacetime
Newtonian Mechanics
Experienced
speed of light
Copenhagen interpretation
Superimposed probability waves
Global Curved Spacetime
Not-experienced
Ready -to-hand
65
Science
Infinite temperature
Phase transition
Phase transition
Phase transition
Phase transition
Absolute zero
Plasma
Gas
Liquid
Solid
Condensate
The kinds of Being are like the differences
between the states of matter
66
Science
pure
conserved
particle
virtual
process
wild
hyper
creation
annihilation
anti-process
black hole
67
Science
singularity
existence as void
pure
conserved particles
wild
Hawking Radiation
ultra
event horizon
virtual particles
process
wild
hyper
68
Levels of the World Duals and Non-duals
Info-energy Entropy-matter
Physics / Thermodynamics
order
Physus / Logos
right
Finite / Infinite
good
Have / Have not
fate
Existence / Non-Existence
source
Actualized / Non-Actualized
root
Non-manifest / Manifest
69
Non-Dual means . . .
Not One! one
Not Two! many
Info-energy physics/thermodynamics Order
logos/physus Right finitude Good
possessed Fate existence Source
actualization Root -- manifestation
70
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?

71
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

72

Mathesis
Order
logos of physus Schema
Physus of logos Logic
Physus / Logos
Finite / Infinite
73

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
74

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
75

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
76

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
77

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
78
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
79

Open Problems
Normal / Deviant
Set / Mass Syllogism / Pervasion
Diamond Logic Vajra Logic Matrix Logic
80
Logics
Syllogism
Pervasion
Universal
Boundary
Set Attribute difference
Mass Containment identity
particular
instance
Non-dual
Conjunction
Conglomerate Metonymy Sameness belonging together
Ipsity
81

Open Problems
semantics
syntax
Reality
Truth
Presence
Identity
syntax
syntax
Model theory
82

Aspects and Properties
syntax
semantics
Coherence
Reality
Truth
Consistency
Validation
Verification
Completeness
Presence
Identity
Clarity
syntax
syntax
83

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
84
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
85

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
86

Open Problems
mimesis
Form 3d
Building
Model
perspective
rendering
mimesis
Form 2d
Picture
Plans
Representation
Repetition
87

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
88
End of Talk

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

89
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
90
Ontic Levels of Emergence
Gaia Society Species Organism Multi-cell Cell Prot
o-cell Macro Molecule Molecule Atom Particle Quark
String
Pressure of reductionism
91
Types of Schemas Ontological levels of Emergence
Pluriverse Kosmos World Domain Meta-system System
Form Pattern Monad Facet
Ontic Level
Reflexive Special System Autopoietic Special
System Dissipative Special System
92
Anaximander Advent of Metaphysical
Writing
Map of World
two dimensional
Prose
Model of Kosmos
Metaphysical Principle
Apeiron
three dimensional
93
Plato Timaeus
Triangles
Platonic Solids
two dimensional
three dimensional
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Kant
Quantity of Judgment Universal, Particular,
Singular
Relation Categorical, Hypothetical, Disjunctive
Time-order, connecting representations with one
another under a rule
Time-series, generation of time
Quality Affirmative, Negative, Infinite
Modality Problematic, Assertoic,
Apodeictic (affirmation as merely possible, as
true (real), as necessary)
Time-content, filling of time
Scope of time, time itself as correlate of
determination of whether and how objects belong
to time
95
Heidegger
Transcendental Imagination
Dasein
96
Unfamiliar and Surprise
projection of spacetime
Individual differences
Suchness
Schema
Kind
Significance
Mathematical or Geometrical Schemas Umberto
Eco Kant and the Platypus
97
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
98
The Nature of Schemas

• Schemas are the first projection of
  differentiation of spacetime onto experienced
  things
• Spacetime is not a plenum, but is a
  differentiation into dimensions, and beyond that,
  into meta-dimensions
• The overflow of dimensions beyond experience is
  part of the ecstasy of dasein
• Dimensional scale gives us a way to measure
  distance between schemas
• Dimensional scale helps clarify the emergent
  differences between schemas

99
Context of Design

• Understanding the emergent hierarchy of schemas
  gives us a context for understanding the design
  and construction of large complex systems,
  because beyond the nesting of systems, there are
  other schemas that need to be understood and used
  and other relevant characteristics that impinge
  on systems design and construction

100
Move to General Schemas Theory

• We need to move from using General Systems Theory
  as a basis for Systems Engineering to General
  Schemas Theory as a basis for Schemas Engineering
• In this way we will be recognizing the wider
  context of the systems we build and the schemas
  that control the articulation and the
  understanding of those contexts

101
Next Step Special Systems

• Meta-System
• Reflexive Social Special System
• Autopoietic Symbiotic Special System
• Dissipative Ordering Special System
• System

102
Emergent Meta-System
Dissipative Monad
Autopoietic View
System Seed
Reflexive Pod
Meta-system Ground
103
Mathematical Operations

• Unicity unitary operations like negation
• Duality compementarity
• Triality octonion
• Quadrality Tits Magic Square EMS
• Quintality ?
• Plotnitsky was right there is multi-way
  complementarity.