## Foundations of Systems Architecture Design

A Series of papers on the Foundations of Systems Architectural Design: See https://independent.academia.edu/KentPalmer/Foundations-of-Systems-Architecture-Design

*Using Gödel’s Incompleteness Theorem to ground Systems Theory via Co-recursion based on Special Systems Theory. *— Abstract: A foundation for Systems Engineering is laid out based on Gödel’s Incompleteness theorem. This foundation gives the basis for Architectural Design of Systems including Software Systems. Systems Engineering has its roots in Systems Science. Systems Science propounds various General Systems Theories and all of them depend on Logic and Mathematics and their Foundations which have been brought into question by Gödel’s theorem. We use the Theorem of Gödel to provide the foundations for Systems Theory, and thus Systems Science via the Special Systems and Schemas Theory, which in turn ground Systems Engineering and thus Software Engineering Systems. These Systems are syntheses that are Designed using Architectural Design, the Afoundation discovered herein gives a basis for Emergent Design in general which leads to Architectural Design of Systems including Software Systems. Key Words: Systems, Architecture, Design, Special Systems, Pascal Triangle, Systems Engineering, Software Engineering, Software Ontology, Formal Systems, Schemas Theory, Godel’s Incompleteness Theorem, Afoundationalism, Foundations, Meta-systems.

2. **Steps toward and Ecology of Emergent Design**

*Differance that makes a difference* — Abstract: Bateson says that we need to explore the meta-levels of Learning in his Steps to an Ecology of the Mind. Here we explore the steps toward an ecology of Emergent Design. Notice we are not trying to found any specific Discipline directly. But instead we are trying to ground our specific designs that we produce as software systems architectures. In other words, it is concrete systematic structured compositions that we are grounding as dynamic syntheses. We do this by a fusion of Leibniz Characteristica Universalis as Symbolic Logic with his Analysis Situs the lost science of configurations of things which the mathematical contemporaries of Leibniz did not accept and therefore was only sketched by him. But this sketch is brought back into focus by our transformation of the proof of Gödel that gives a basis for Special Systems Theory. — Key Words: Systems, Architecture, Design, Special Systems, Systems Engineering, Software Engineering, Software Ontology, Formal Systems, Schemas Theory.

*A Mysterious Synthesis or How a Miracle Occurs Here* — Abstract: This paper attacks the core problem with Design: What is a synthesis and how is it possible. We begin by asking why this Transdisciplinary approach to the problem of design synthesis is necessary and significant. — Key Words: Systems, Architecture, Design, Special Systems, Systems Engineering, Software Engineering, Software Ontology, Formal Systems, Schemas Theory.

4. **Convolution**

*A Prelude to the Comprehension of the Supra-Rationality of the Dagger Formation* — Abstract: The internal view of worlds seen in terms of the relations between pairs of schemas and pairs of Foundational Mathematical Categories which are convoluted and reflected as inward relations between Dagger Theory elements that are external and appear in the interstices between the worlds or realms as defined by Ken Lloyd based on the delineations of worlds by Penrose and Popper, with the addition of the social world. — Key Words: Systems, Architecture, Design, Special Systems, Systems Engineering, Software Engineering, Software Ontology, Formal Systems, Schemas Theory, Dagger Theory.

*Quiddity and Internal Relations in Schemas* Abstract: We define the names of the “essences” of each Schema. We call these nerves after the “Nerve Category” in Category Theory. Examples are Essence of Form, Structure of Pattern, Nucleus of System. We discuss the implications for the understanding of internal relations in Hegel from a schematic point of view. Key Words: Systems, Architecture, Design, Special Systems, Systems Engineering, Software Engineering, Software Ontology, Formal Systems, Schemas Theory, Dagger Theory, Essence, Nerve, Internal Relations.

*Essence as a Model of Internal Relations and Projective Geometry.* Key Words: Systems, Architecture, Design, Special Systems, Systems Engineering, Software Engineering, Software Ontology, Formal Systems, Schemas Theory, Dagger Theory, Essence, Nerve, Internal Relations.

7. **Microgenesis of Internal Difference**

*From Internal Relations of Hegel to Internal Differences of Deleuze* — Abstract: This paper explains the difference between internal difference of Deleuze and internal relations of Hegel. — Key Words: Systems, Architecture, Design, Special Systems, Systems Engineering, Software Engineering, Software Ontology, Formal Systems, Schemas Theory, Dagger Theory, Projective Geometry, Essence, Internal Relations

8. **Nondual Difference **(TBD)