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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 Kent D. Palmer, Ph.D. PO Box 1632 Orange CA 92856
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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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Emergence Engineering
* Horizons of SE Schemas Engineering Emergence Engineering Current SE
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* MAP Transformative ? Systems Engineering Discipline
(of the argument) Transformative ? Systems Engineering Discipline Other Disciplines Ontic and Ontological Levels of Emergence SW Eng / Comp Science A transformative discipline is one which changes the relations between other disciplines when it appears Complex Systems Theory All Engineering Disciplines are the Academic counterpart of SE Complex Adaptive Systems Scope Broader Chaos Theory
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Systems Engineering means . . .
* 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
* 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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meta-levels of emergence
* MAP (of the argument) Emergence Engineering Meta-levels supervenience de-emergence emergence meta-levels of emergence meta-levels of Being
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* Supervenience & Emergence organism LEVEL N+1 emergence Synthesis
Gestalt = Whole greater than sum of parts Emergence Excess organism LEVEL N+1 new characteristics Supervenience is Homomorphism with lower level supports emergence Synthesis cell LEVEL N supports Qualitative and Quantitative Jump
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* De-emergence LEVEL N+1 <Reductionism De-emergence> Part Part
Proto Gestalt = Whole less than sum of parts gives knowledge of implicate order Emergent Lack Loss of knowledge or information LEVEL N+1 Cannot reconstitute the whole <Reductionism De-emergence> Part Part Part Part Part LEVEL N Analysis/ Architecture Parts don’t add up to the whole There is normally a cycle between emergence and de-emergence
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Undecidable means non-reducible
* Conjecture: Emergent Properties are Godelian This could be the basis for formalizing the concept of emergence emergent excess decidable inside decidable outside undecideable emergence de-emergence Undecidable means non-reducible
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* E3 Emergence of Emergences E2b Can’t 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 of emergence
* MAP (of the argument) repeated Emergence Engineering Meta-levels supervenience de-emergence emergence meta-levels of emergence meta-levels of Being
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* Emergence7 Meta-levels of Emergence Meta-levels of Being Emergence6
Correspondence between meta-levels of Emergence and meta-levels of Being 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 beings ontological difference existence threshold Ontology
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Radically Unpredictable, unknown
* Stairs to Nowhere: Meta-levels of Emergence Existence Emptiness / Void Lack Radically Unpredictable, unknown E4 chiasm between actualities, errors, voids E5 genuine emergence Being Ultra Being horizon essencing forth in time E3 E2 excess Supervenient combinatoric or additive change E1 undecidable E0 non-emergent change
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* Emergent Difference Ontology covers the various standings of everything that presents or absences itself phenomenologically Ontological Difference distinguishes those standings from the various beings which have those various standings Emergent difference relates to the intensification of nihilism Artificially emergent events are additive, incremental, and combinatoric intensifications of nihilism Genuine Emergent events are quantum leaps that reset all parameters and recalibrate by producing a new origin
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Emergent Difference and Ontological Difference
* 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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These change at the different meta-levels of Being
* 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
* 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
* 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 Propensity Out-of-hand Encompassing
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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Radically Unpredictable, unknown
* Meta-levels of Emergence Existence Emptiness / Void Lack E4 Radically Unpredictable, unknown E5 genuine emergence Being Ultra Being horizon E3 E2 essencing forth in time: event excess Supervenient combinatoric or additive change E1 undecidable E0 non-emergent change
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meta-levels of emergence
* MAP (of the argument) repeated Emergence Engineering Meta-levels supervenience de-emergence emergence meta-levels of emergence meta-levels of Being
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eg., manufacturing, Eng. disciplines
* Meta-levels of Emergence Engineering Existence Meta-system Inter penetration Niche Intra surfacing eg., manufacturing, Eng. disciplines synthesis SE E4 chiasm between actualities, errors, voids System genuine emergence Being Specialties E5 Architecture/Analysis horizon essencing forth in time E2 Process E3 excess horizon Design Possibilities Change Control horizon Products E1 Supervenient combinatoric or additive change undecidable Trade-offs interim artifacts E0 vicissitudes of work
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* Main Point The whole discipline of Systems Engineering is structured by the meta-levels of Emergence Systems Engineering is intrinsically Emergence Engineering But is Systems Engineering enough even when viewed as Emergence Engineering? Perhaps we need something even broader than the focus on the Emergence of Systems which is dependent on the Systems Schema alone
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MAP Meta-Levels of Being Aspects of Being Properties Perice/Fuller
(of the argument) Aspects of Being Properties Perice/Fuller Categories Face of world Path into world for Emergence Worldhood
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Path of Emergence into the World
Artificial Nihilistic Emergences Emergent characteristics Emergent Event produces new kinds Emergent possibilities rewrite history Emergence inherently unpredictable false abortive newness ultra wild hyper process pure Genuine Emergence Repatterned world of beings
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Face of the World Actuality SE is a face of the world Possibilities
All four kinds of Being working together Ultra Actuality SE is a face of the world Possibilities Hyper Pure continuous path ideal determinate Wild propensity probability distribution diversions due to differences in ontic physus Process
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What about the System Schema?
* What about the System Schema? Are there other possible Schemas that might be important to SE? What are the other Schemas that give systems their meaning through contrast? Do the set of all possible schemas have a structure? Can SE use this structure of schemas to help formalize its work?
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* Non-dual Order Einstein noted how amazing it was that mathematics can be used to connect theory to physical phenomena through instruments Theory is the Logos, Physical Phenomena are the Physus, and the non-dual between and before their split is Order
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* Mathesis Order logos of physus Physus of logos Schema Logic
Physus / Logos Finite / Infinite
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* Mathesis Schema Logic Mathematical Categories Representation Theory
strong Representation Theory real kernel || representations Mathematical Semantics Syntax Model Theory presence identity truth Schema Logic weak Philosophical Categories Episteme Paradigm Theory Facticity strong
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* Circulation of Projection Mathesis Order ontic Physus Logos
meta-dimensionality set/mass Phenomenological View Preontological Ontic Ontological Mathesis Anomalies Being Representation theory Model Theory Order non-dual ontic Physus Phil. Cat. Logos ontological existence ontos episteme paradigm theory type theory contradiction projection logos of physus Schema physus of logos Logic contrary perception Example: Projection of System paradox Experience facticity Reason doxa ratio kind individual
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* Ontic Levels of Emergence Gaia Society Species Organism
Multi-cell Cell Proto-cell Macro Molecule Molecule Atom Particle Quark String We discover the levels of Emergence by trying to reduce everything. Those things that cannot be reduced are emergent ontic levels. Different possible ontic hierarchies are possible. Pressure of reductionism
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* Types of Schemas Ontological levels of Emergence Pluriverse Kosmos
World Domain Meta-system System Form Pattern Monad Facet Different possible projections onto the Ontic levels Ontic Level
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* Research in General Schemas Theory Schemas Dimensions Pluriverse
Kosmos World Domain Meta-system System Form Pattern Monad Facet 10 - 9 9 - 8 8 - 7 7 - 6 6 - 5 5 - 4 4 - 3 3 - 2 2 - 1 1 - 0 0 - -1 Important result: Two dimensions per schema Two schemas per dimension See “General Schemas Theory” paper by author CSER conference 2004
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Social levels of knowledge
* 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 Paradigm Theory Facticity Social levels of knowledge
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* Open Problems mathesis schema logic Normal / Deviant Set / Mass
Syllogism / Pervasion Diamond Logic Vajra Logic Matrix Logic
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Logics Syllogism Pervasion Universal Boundary Set Mass particular
Attribute difference Mass Containment identity particular instance Non-dual Conjunction Conglomerate Metonymy Sameness belonging together Ipsity
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* Open Problems Reality Truth Presence Identity mathesis schema logic
semantics syntax Reality Truth Presence Identity syntax syntax mathesis schema logic Model theory
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Aspects and Properties
* Aspects and Properties syntax semantics Coherence Reality Truth Validation Consistency Verification Completeness Presence Identity Clarity syntax syntax
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* Open Problems N-conglomerates N-category N-blob Set / Mass mathesis
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
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1 - Conglomerate conjunction
2 - ? 3 - ? 4 - ? N-conglomerates N-blob N-category Blob boundary - 1 Tissue - 2 Bag - 3 Tweak - 4 1 - Category arrow 2 - Functor 3 - Natural transformation 4 - Modification
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* Open Problems Representational Theory taken for granted but not explicitly defined Representation vs. Repetition See . . . Deleuze, G Difference and Repetition Taussig, M. Mimesis and Alterity mathesis schema logic Representation theory
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* Open Problems mimesis Form 3d Building Model perspective rendering
Picture Plans Representation Repetition
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* Open Problems mathesis Pluriverse schema logic Kosmos World Domain
Meta-system System Form Pattern Monad Facet Schemas are relatively unknown and a General Schemas Theory has not yet been developed, but the schemas are the basis of all “formalization”
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End of Talk See http://archonic.net and http://holonomic.net
for more information concerning this ongoing research project.
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MAP Schema Ultra Being and Existence Types of 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
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