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@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. * Emergence Engineering Horizons of SE Schemas Engineering Current SE

4. * MAP (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

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

8. * Supervenience & Emergence Gestalt = Whole greater than sum of parts Emergence Excess organism LEVEL N+1 new characteristics Supervenience is Homomorphism with lower level supports emergence Synthesis LEVEL N cell supports Qualitative and Quantitative Jump

9. * De-emergence 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

10. * Conjecture: Emergent Properties are Godelian Undecidable means non-reducible This could be the basis for formalizing the concept of emergence emergent excess decidable inside decidable outside undecideable emergence de-emergence

11. * 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

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

13. * Ontology Meta-levels of Emergence Meta-levels of Being Emergence7 Thatness/Suchness Emergence6 Manifestation Emergence5 Ultra-Being existence threshold Wild Being Emergence4 Hyper Being Emergence3 Process Being Emergence2 Pure Being Emergence1 ontological difference beings Emergence0 Correspondence between meta-levels of Emergence and meta-levels of Being

14. * horizon horizon horizon 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 essencing forth in time E3 E2 excess Supervenient combinatoric or additive change E1 undecidable E0 non-emergent change

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. Non-new change More of the same Random alteration Entry of the New beings, entities, things Entry of Being * Emergence0 = beings 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. 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 * Emergence1 = Pure Being 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. 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 * Emergence2 = Process Being 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. 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 * Emergence3 = Hyper Being 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. 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 * Emergence4 = Wild Being 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. 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 * Emergence5 = Existence 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. * horizon horizon horizon Meta-levels of Emergence Existence Emptiness / Void Lack E4 E5 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

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

31. * 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 essencing forth in time E3 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

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. MAP Meta-Levels of Being (of the argument) Aspects of Being Properties Perice/Fuller Categories Face of world Path into world for Emergence Worldhood

34. 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

35. 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

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

39. * 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

40. * Circulation of Projection meta-dimensionality set/mass • Phenomenological View • Preontological • Ontic • Ontological Mathesis Anomalies Being Representation theory Model Theory Order non-dual ontic Physus Logos ontological Phil. Cat. existence ontos episteme paradigm theory typetheory contradiction projection physus of logos Logic logos of physus Schema contrary paradox perception Example: Projection of System facticity Reason Experience doxa ratio kind individual

41. * 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

42. * 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

43. * 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

44. * 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

45. * mathesis schema logic Open Problems Normal / Deviant Set / Mass Syllogism / Pervasion Diamond Logic Vajra Logic Matrix Logic

46. Logics Syllogism Pervasion Universal Boundary Set Attribute difference Mass Containment identity particular instance Non-dual Conjunction Conglomerate Metonymy Sameness belonging together Ipsity

47. * mathesis schema logic Open Problems semantics syntax Reality Truth Presence Identity syntax syntax Model theory

48. * Aspects and Properties syntax semantics Coherence Reality Truth Consistency Validation Verification Completeness Presence Identity Clarity syntax syntax

49. * mathesis schema logic 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

50. 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