Transcript The Foundations of General Schemas Theory

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 [email protected]
http://archonic.net
1
*
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
2
*
Horizons of SE
Schemas Engineering
Current SE
Emergence Engineering
3
*
MAP
(of the argument)
Ontic and Ontological
Levels of Emergence
Complex
Systems
Theory
Complex
Adaptive
Systems
Systems
Engineering
Discipline
•A transformative
discipline is one
which changes the
relations between
other disciplines
when it appears
Other
Disciplines
SW Eng /
Comp Science
All Engineering
Disciplines are
the Academic
counterpart of
SE
Scope Broader
Chaos Theory
4
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
5
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
6
discipline
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
7
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
8
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
9
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
10
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
11
*
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; subsystem/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
12
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
13
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
14
relation to dialectical synthesis
*
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
15
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
16
*
MAP
(of the argument)
Emergence Engineering Meta-levels
supervenience
de-emergence
emergence
meta-levels of emergence
meta-levels of Being
17
*
Supervenience & Emergence
Gestalt = Whole greater than sum of parts
Emergence
Excess
organism
Supervenience is
Homomorphism
with lower level
supports cell
LEVEL N+1
LEVEL N
new characteristics
supports
Synthesis
Qualitative and
Quantitative Jump
18
*
De-emergence
Proto Gestalt = Whole less than sum of parts gives
knowledge of implicate order
Emergent Lack
Loss of knowledge or information
Cannot
reconstitute
the whole
LEVEL N
LEVEL N+1
Part Part Part Part Part
Parts don’t add up to the whole
Analysis/
Architecture
There is normally a cycle between emergence and de-emergence
19
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
20
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
21
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”
22
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
23
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
24
*
Conjecture: Emergent Properties are Godelian
This could be the basis for formalizing the concept of emergence
emergent
excess
decidable
inside
decidable
outside
emergence
de-emergence
Undecidable means non-reducible
25
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”
26
*
Emergence of Emergences
E2b
E3
Can’t get to E3
directly from
lower levels of
Emergence
E2a
E1
E0
Current view of SE as concerned with Integration
27
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
28
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
29
*
MAP
(of the argument)
repeated
Emergence Engineering Meta-levels
supervenience
de-emergence
emergence
meta-levels of emergence
meta-levels of Being
30
*
Correspondence between meta-levels of Emergence and meta-levels of Being
Meta-levels of Emergence
Ontology
Meta-levels of Being
Emergence7
Thatness/Suchness
Emergence6
Manifestation
Emergence5
Ultra-Being
Emergence4
Wild Being
Emergence3
Hyper Being
Emergence2
Process Being
Emergence1
Pure Being
Emergence0
beings
existence
threshold
ontological
difference
31
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
32
Ontological Difference
• Ontological Difference is a kind of metadifference 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
33
Existence
Being
*
Stairs to Nowhere: Meta-levels of Emergence
Emptiness / Void
E4
E2
chiasm between
actualities, errors, voids
Radically Unpredictable,
unknown
essencing
forth in time
Supervenient
Lack
E3
E1
excess
E5
Ultra Being
genuine
emergence
horizon
combinatoric or
additive change
undecidable
E0 non-emergent change
34
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
35
origin
*
0
Emergence
• Non-new change
• More of the same
• Random alteration
*
= beings
• beings, entities, things
Emergent Difference and Ontological Difference
• Entry of the New
Example: Car wear
• Entry of Being
Example: Projection
36
*
Aspects of Being
•
•
•
•
Truth
Reality
Identity
Presence
These change
at the
different
meta-levels of
Being
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.
37
1
Emergence
• Pure Artificiality
• Combinatoric
expansion
• Superficial newness
• Additive or
incremental
improvement
• Nothing fundamental
changes
*
= Pure Being
• Determinate and
continuous
• Present-at-hand
• Pointing
• Standing reserve
• Subject/object dichotomy
• Form level
– Symbol
– Shape
Example: New cars
38
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
39
*
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-theworld)
• Pattern Level
–
–
–
–
Value
Sign
Flux
Structure
Example: From Buggy to Car
40
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
41
Emergence3
• Projects new
possibilities on new
horizon
• Emergence itself is
undecidable
• Emergent excess is
Godelian
*
= Hyper Being
•
•
•
•
•
•
Possibility
In-hand
Bearing
Query (expansion)
Trace Level
Differance
– Differing/Deferring
• Excess / Supplement
Example: Car with Software
42
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
43
4
Emergence
• Actualizes new
possibilities on new
horizon
• Emergence is intrinsically
unpredictable
• Reveals unexpected,
unheard of, unthought,
anomalous appearances
from a direction
previously unknown
*
= Wild Being
•
•
•
•
•
•
•
•
Propensity
Out-of-hand
Encompassing
Enigma (contraction)
Tendency
Rhizome
Chiasm (reversibility)
Flesh
Example: Car with AI
44
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
45
5
Emergence
• Genuinely emergent
existent appears from
itself in its own time
and a place of its
choosing
• No projection
• Face of the World
*
= Existence
• Interpretations
– Ultra Being
– Emptiness
– Void
• Inter/intra
penetration/surfacing
• Being seen from outside
as a found thing beingout-of-the-world
Example: Flying Car,
New Media
46
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
47
*
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
48
Existence
Being
*
Meta-levels of Emergence
Emptiness / Void
E4
Lack
E5
Radically Unpredictable, unknown
E2 essencing forth in time: event
Supervenient
E1
E3
excess
Ultra Being
genuine
emergence
horizon
combinatoric or
additive change
undecidable
E0 non-emergent change
49
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
50
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
51
Genuine emergence is based on …
Inter
penetration
Intra
surfacing
Ultra Being
Ultra Being is the interspace between void and emptiness,
i.e. between the two non-duals, odd and even zero
52
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
53
Ultra Being is . . .
• Ultra Being is … external view of
projection
– A face of the world including all four metalevels of Being that embody projection
• Ultra Being is … the standing upon which
schematization is based
54
*
MAP
(of the argument)
repeated
Emergence Engineering Meta-levels
supervenience
de-emergence
emergence
meta-levels of emergence
meta-levels of Being
55
Existence
Being
*
Meta-levels of Emergence Engineering
Meta-system
eg., manufacturing, Eng. disciplines
Inter
Intra
penetration
surfacing
Niche
synthesis
E4
E2
chiasm between actualities,
errors, voids
essencing
forth in time
Products
Supervenient
Specialties
E5 System
Architecture/Analysis
E3 excess
Process
interim artifacts
E0 vicissitudes
of work
horizon
Design
Possibilities
Change Control
E1
combinatoric or
additive change
SE
genuine
emergence
undecidable
Trade-offs
56
*
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
57
MAP
(of the argument)
Meta-Levels of Being
Aspects of Being
Properties
Perice/Fuller
Categories
Face of world
Path into
world for
Emergence
Worldhood
58
groundless
ground
class
templates
of objects
objects
relation
logic
relations
between
objects
Third
continuity
logic
Fuller
Fourth
synergy
geometry
Ultra
arising
logic
Second
Peirce
Pure
First
Peirce
Process
Zeroth
Peirce
Hyper
Void or
emptiness
Wild
Ultra
Peirce / Fuller Categories
simulation of system
interactions synthesis
through
behaviors of
object
59
methods
Path of Emergence into the World
•Emergent characteristics
Artificial Nihilistic
Emergences
•Emergent Event produces
new kinds
•Emergent possibilities
rewrite history
•Emergence inherently
unpredictable
Repatterned
world of
beings
60
Face of the World
All four kinds of Being working together
SE is a face of the world
Ultra
Actuality
Possibilities
Hyper
Wild
propensity
diversions due to
differences in ontic
physus
probability
distribution
Process
61
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
62
Worldhood
• Hyper
– In-hand
– Query
– Expansion of being-inthe-world
– Bearing
– Possibility
• Wild
– Out-of-hand
– Enigma
– Contaction of being-inthe-world
– Encompassing
– Propensity
63
Present
-athand
Local flat
spacetime
speed of light
Ready
-tohand
Global
Curved
Spacetime
micro
Relativity
theory
macro
Science
Quantum
Mechanics
Newtonian
Mechanics
Experienced
Copenhagen
interpretation
Superimposed
probability
waves
Notexperienced
64
Solid
Ultra
continuity
logic
Fuller
Fourth
synergy
geometry
Condensate
The kinds of Being are like the differences between the
states of matter
65
Absolute zero
Liquid
Third
Pure
relation
logic
Peirce
Phase transition
Gas
Second
Process
arising
logic
Peirce
Phase transition
Plasma
Phase transition
Infinite temperature
groundless
ground
First
Hyper
Zeroth
Peirce
Phase transition
Void or
emptiness
Wild
Ultra
Science
Science
pure
conserved
particle
virtual
process
wild
hyper
creation
annihilation
anti-process
black
hole
66
Science
singularity
existence as void
pure conserved
particles
wild
Hawking Radiation
ultra
event horizon
virtual particles
wild
process
hyper
67
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
68
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
69
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?
70
*
*
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
71
*
Mathesis
Order
logos of physus
Schema
Physus of logos
Logic
Physus / Logos
Finite / Infinite
72
*
Mathematical Categories
Mathesis
strong
Representation
kernel
Theory
||
representations
Schema
weak
Mathematical
Model Theory
Philosophical Categories
Episteme
Paradigm
Theory
Facticity
real
Semantics
Syntax
presence
identity
truth
Logic
strong
73
*
Circulation of Projection
meta-dimensionality
set/mass
Mathesis
Phenomenological View
•Preontological
•Ontic
•Ontological
Anomalies
Being
Order
non-dual
ontic
Physus
logos of physus
Schema
Phil. Cat.
existence
ontos
episteme
paradigm
theory
Logos
ontological
physus of logos
Logic
Example: Projection of System
Experience
kind
individual
facticity
Reason
doxa
ratio
74
*
Gaia
Society
Species
Organism
Multi-cell
Cell
Proto-cell
Macro Molecule
Molecule
Atom
Particle
Quark
String
Pressure of reductionism
Ontic Levels of Emergence
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.
75
*
Types of Schemas
Ontological levels of Emergence
Ontic
Level
Pluriverse
Kosmos
World
Domain
Meta-system
System
Form
Pattern
Monad
Facet
Different
possible
projections
onto the Ontic
levels
76
*
Research in General Schemas Theory
Schemas
Pluriverse
Kosmos
World
Domain
Meta-system
System
Form
Pattern
Monad
Facet
Dimensions
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
77
*
Open Problems
mathesis
schema
logic
Phil. Categories
Existence
Ontos
Episteme
Paradigm
Theory
Facticity
Aristotle
Kant
Hegel
Heidegger
Johannson
Social levels
of
knowledge
• 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
78
*
Open Problems
mathesis
schema
logic
Normal / Deviant
Diamond Logic
Vajra Logic
Matrix Logic
Set / Mass
Syllogism / Pervasion
79
Logics
Set
Attribute
difference
Syllogism
Pervasion
Universal
Boundary
particular
Mass
Containment
identity
Non-dual
instance
Conjunction
Conglomerate
Metonymy
Sameness
belonging together
Ipsity
80
*
Open Problems
semantics
syntax
Reality
Truth
Presence
Identity
syntax
syntax
mathesis
Model theory
schema
logic
81
*
Aspects and Properties
Coherence
Validation
Reality
syntax
Presence
syntax
Truth
Consistency
semantics
Clarity
Identity
syntax
82
*
Open Problems
Mathematics ignores
mass approaches and
relies solely on set
approaches, so
mathematical categories
are fundamentally
lopsided
N-conglomerates
N-category
N-blob
Set / Mass
mathesis
schema
logic
83
1 - Conglomerate conjunction
2-?
3-?
4-?
N-conglomerates
N-blob
Blob boundary - 1
Tissue - 2
Bag - 3
Tweak - 4
N-category
1 - Category arrow
2 - Functor
3 - Natural transformation
4 - Modification
84
*
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
mathesis
Representation theory
schema
logic
85
*
Open Problems
Form 3d
Building mimesis
perspective
Form 2d
Picture
Representation
Model
rendering
mimesis
Plans
Repetition
86
*
Open Problems
mathesis
Pluriverse
Kosmos
World
Domain
Meta-system
System
Form
Pattern
Monad
Facet
schema
logic
Schemas are relatively unknown
and a General Schemas Theory
has not yet been developed, but
the schemas are the basis of all
“formalization”
87
End of Talk
See http://archonic.net and http://holonomic.net
for more information concerning this ongoing
research project.
88
MAP
(of the argument)
Schema
Ultra Being
and Existence
Types of schema
Opposite of
Emergence
Genealogy of
the schema
Anaximander
Plato
Kant
Heidegger
Unfamiliarity
Dimensions
Negative
Dimension
Meta-dimension
Pascal
Triangle
Simplicies
89
Gaia
Society
Species
Organism
Multi-cell
Cell
Proto-cell
Macro Molecule
Molecule
Atom
Particle
Quark
String
Pressure of reductionism
Ontic Levels of Emergence
90
Types of Schemas
Ontological levels of Emergence
Ontic
Level
Pluriverse
Kosmos
World
Domain
Meta-system
System
Form
Pattern
Monad
Facet
Reflexive Special System
Autopoietic Special System
Dissipative Special System
91
Anaximander
Advent of Metaphysical
Writing
Prose
Model of Kosmos
three dimensional
Map of World
two dimensional
Metaphysical Principle
Apeiron
92
Plato
Timaeus
Triangles
two dimensional
Platonic Solids
three dimensional
93
Kant
Quantity of Judgment
Relation
Universal, Particular, Singular
Categorical, Hypothetical, Disjunctive
Time-series, generation of time
Time-order, connecting
representations with one another
under a rule
Quality
Modality
Affirmative, Negative, Infinite
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
94
Heidegger
Transcendental
Imagination
Dasein
95
Unfamiliar and Surprise
projection of
spacetime
0
Suchness
1
Schema
2
Kind
3
Individual
differences
4
Significance
Mathematical or Geometrical Schemas
Umberto Eco
Kant and the Platypus
96
Research in General Schemas Theory
Schemas
Pluriverse
Kosmos
World
Domain
Meta-system
System
Form
Pattern
Monad
Facet
Dimensions
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
97
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 metadimensions
• 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
98
differences between schemas
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
99
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
100
Next Step … Special Systems
• Meta-System
– Reflexive Social Special System
• Autopoietic Symbiotic Special System
– Dissipative Ordering Special System
• System
101
Emergent Meta-System
Dissipative
Monad
Autopoietic
View
System
Seed
Meta-system
Ground
Reflexive
Pod
102
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.
103