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 040413Kent D. Palmer, Ph.D.

PO Box 1632 Orange CA 92856714-633-9508 kent@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

Cur

rent

SE

Schemas Engineering

Emergence Engineering

*

4

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

5

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

*

6

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

*

7

Emergence Engineering Meta-levels

supervenience de-emergence

emergence

meta-levels of emergence

meta-levels of Being

MAPMAP(of the argument) *

8

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

9

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

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

11

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

12

Emergence Engineering Meta-levels

supervenience de-emergence

emergence

meta-levels of emergence

meta-levels of Being

MAPMAP(of the argument) *

repeated

13

*

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

14

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

15

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

*

16

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

17

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

18

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

19

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

20

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

21

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

22

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

23

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

24

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

25

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

26

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

27

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

28

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

*

29

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

30

Emergence Engineering Meta-levels

supervenience de-emergence

emergence

meta-levels of emergence

meta-levels of Being

MAPMAP(of the argument) *

repeated

31

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

32

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

*

33

Meta-Levels of Being

Perice/FullerCategories

Path into world for Emergence

Face of world

Worldhood

Aspects of Being

Properties

MAPMAP(of the argument)

34

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

35

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

36

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?

*

37

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

*

38

Finite / Infinite

Physus / Logos

Mathesis

Order

logos of physusSchema

Physus of logosLogic

*

39

Schema Logic

Mathesis

Model TheoryRepresentation

Theory

Mathematical Categories

Philosophical CategoriesEpistemeParadigmTheory

Facticity

SemanticsSyntax

strong

strongweak

real

presenceidentity

truth

kernel||

representations

Mathematical

*

40

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

41

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.

42

PluriverseKosmosWorld

DomainMeta-system

SystemForm

PatternMonadFacet

OnticLevel

Types of SchemasOntological levels of Emergence

*

Different possible

projections onto the Ontic

levels

43

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

44

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

*

45

mathesis

schema logic

Open Problems

Normal / Deviant

Diamond LogicVajra LogicMatrix Logic

Set / MassSyllogism / Pervasion

*

46

LogicsSyllogism

Universal

SetAttributedifference

particular

Pervasion

Boundary

MassContainment

identity

instance

Non-dual

Conjunction

ConglomerateMetonymySameness

belonging together

Ipsity

47

Open Problems

mathesis

schema logic

Model theory

Reality Truth

Presence Identitysyntax syntax

syntaxsemantics

*

48

Reality Truth

Presence Identitysyntax syntax

syntaxsemantics

Aspects and Properties

Coherence

Verification

Completeness

Val

idat

ion

Clarity

Con

sist

ency

*

49

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

*

50

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 - ?

51

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

*

52

Open Problems

Form 3d

Form 2d

Building Model

Picture Plans

RepresentationRepresentation RepetitionRepetition

mimesis

mimesis

perspective rendering

*

53

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”

*

54

End of Talk

See http://archonic.net and http://holonomic.net

for more information concerning this ongoing research project.

55

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