Convergence to a universal framework
Explorations in the unification of thought
Notes in progress, July 2019  January 2022
The vision
This project explores ways to interconnect all levels and types of abstract symbolic representation ("conceptual form") within a single closed algebraic framework defined by boundary values. This is an algebraic method to construct and define all objects commonly called "concepts".
 It is based on the atomic concept of "distinction"
 All "concepts" are constructed from (defined as) nested composites (or "assemblies") of distinctions
 Any mathematical or semantic object can be constructed in this way and its "meaning" explicitly defined
Fundamental thesis
 It is possible to define the notion of "concept" (or "abstract symbolic representation") with technical and algebraic precision, in a format that makes sense in cognitive psychology and in computer science. This is a stipulative process defined as constructive method based on the algebraic concept of distinction or "cut".
 All concepts and ideas arise from within the continuum, and are contained within the continuum.
 It seems there is a motivated "bootstrapping" process in human psychology that coalesces conceptual form from dim/vague/uncertain/fuzzy intuition into explicitly coded specifics.
 All symbolic coding involves abstract representation across levels of scale; this is true in computer science, and in human cognition.
 The general form of concepts is "distinctions nested within distinctions", defined in a recursive process that extends across levels of scale from more abstract and general to more concrete and particular, in a cascade that terminates in actual concrete instances. A common taxonomy illustrates this principle.
 The continuum can be interpreted as a differentiated unit interval (the bounded range from 0 to 1), where all decimal fractional numbers are defined in a recursive cascade as taxonomic subunits within that interval. This process approaches "real numbers" and continuity of differentiation at the bottom level. This decomposition of integer values is algebraically isomorphic to ("takes the same general form as" or "can be put into a onetoone correspondence with") the structure of any other categorical taxonomy.
 The "space" between lowestlevel terminating decimal numbers is the real actuality of "the continuum", and takes the form of "pure uncertainty". "The continuum is the space between lowestlevel defined partitions."
 Differing levels of coding (numbers, alphabets, words) can be explicitly linked across levels, and defined in terms of one another. This creates a way to map or link highlevel composite abstractions into specific lowerlevel implications.
 All of these elements can be defined within a single integral structure where differences and attributes are crisply defined in terms of boundary values.
 This thesis is a postulate, an exploratory hypothesis for testing.
Motivation
 World culture is experiencing a dangerous crisis of fragmentation.
 This fragmentation extends across many or all facets of human cooperation and interaction, as well as technical interconnection ("the silo effect").
 It might be possible to grow an integrating movement, perhaps assisted by an illuminating holistic or integral ontology.
Visionary hypothesis and integrating interpretation
 We are exploring an interpretation of the continuum defined as a "closed loop" and based on the concept "moebius strip". See the animated graphics in the header for hints on how this works.
 We are developing an interpretation of this twosided twoedged topological form that maps to the real number line in traditional ways and contains the general form of hierarchical semantic ontology, where categories range from the specific to the general. This is the general form of taxonomy, which can be adapted to any special case instance.
 One edge of the strip is the unbounded infinite and the other edge is the infinitesimal. Both edges are continuous unbroken closed circles defining unity. Between the edges, across the strip, is defined all levels of taxonomic differentiation. Logical processes operate across this topdown/bottomup spectrum.
 We supposing that this spectrum defined across the strip and contained in the boundary between the unbounded infinite and the infinitesimal defines the range from the universal upper ontology into all domains and specialcase instances.
 This hierarchical form is defined by "cuts" and "distinctions" creating "boundary values" ("min/max value in a dimension") which we suggest can define all possible categories and distinctions at any level of abstraction.
 This boundary value range accounts for ambiguity in abstraction.
 These boundary values (lowest and highest value in any defined dimension) define all possibilities of category formation, determining "what is inside the category and what is not". This is similar to a database search using AND or OR or GTE or LTE (Boolean) operators in SQL, which narrow the search range to select items that meet all criteria ("are within the envelope"). "In what dimensions is this thing defined; what are its values in those dimensions; how can we narrow this down to specifics?"
 If this hypothesis can be validated, this structure might form a "universal container" for all possibilities of human cognition, ranging from mathematics to natural language, including along the way all concepts developed in science and based on traditional definitions of numbers and measurement.
 In this context, tremendous creative and cultural diversity could be maintained under harmonic global guidelines, supporting informed governance and cooperative collective action.
Compositional semantics and a universal language for primitives
 We are exploring ways that the notion of "primitive concept" can be generalized and universalized.
 The "atomic" level of this process is a minimal coded (finitestate, discrete) distinction, defined in dimensions and coded in bits. How can we build this object in the abstract (its meaning) and in the concrete (represent it symbolically in a medium)?
 The objective is to develop a uniform compositional language that can "construct anything" as a composite of coded distinctions and dimensionality at some appropriate level of granularity
 Objects ("nouns") can be fully characterized by dimensional measurements, and categorized across (taxonomic) levels of generality
 Processes and actions ("verbs") can be described as linear sequences ("state transitions") in time
"Tower of Babel problem"
 In this context, we explore negotiated convergence in the context of high diversity
The absolute frame
 We explore a simple generalization of fundamental taxonomic principles defined across levels of generality and similarity
 This form is defined within the closed loop interval framework
 Its structure is "isomorphically recursive", taking a repeating identical form at descending levels of scale, like the parsing of the unit interval into terminating decimal numbers in the finitestate cascade that converges into the real numbers and the continuum
 Its definitions and logic structure are 100% linear in every facet
 The objective is a simple linear form and container that can interpret and possibly interconnect all complex special cases instances
The history of intuitive integral visions
 Visionaries and mystics and serious scholars have envisioned various versions of the "tree of knowledge" for thousands of years
 We draw inspiration from their work
This project
 This project runs on a database, and is intended to gather together many facets and aspects of a single larger vision. Of course this vision is experimental, but it is driven by a sustained deep intuition with deep roots in the classical history of philosophy, and is informed by brilliant work today in ontology and network science.
 The categories and themes and terms are intended to build a holistic momentum illuminating the largescale holistic thesis intended as possible and feasible to "integrate many parts into a single whole"
 We are supposing that all of semantic ontology can be defined by "cuts" across a single topological object, in a form that contains and illustrates the continuum and supposedly all algebraic and logical operations, and functions as an interpretive spectrum for any highly complex but specialcase process linked to a domain or particular context or particular application
 The entire project is an exploratory postulate testing for convergence and integration. The objective is integration across the entire spectrum from top to bottom across and incorporating every domain. It is supposedly an algebraic construction in applied/practical engineering mathematics
 Obviously this is a grand scheme, of something like infinite breadth and inclusion. We apologize for the pretension and ambition.
Technical areas
 This project attempts to "build a bridge across coding structures at multiple levels"
 These levels include purely abstract  symbolic, etc. (meaning triangle)
 Cognitive psychology: the formation of concepts
 Models: how maps and descriptions of reality correspond to reality
 Semantics: how is meaning expressed and intended in coded symbols
 Computer architecture: constructing symbols from bits
 Mathematics: how computation is defined in symbols
What is original
 All types of categories and concepts can be constructed by crisp boundary values grounded in the continuum (real number line and decimal measurement in dimensions). This is an original theory of concept structure, based on current literature in cognitive science. This model embraces both practical psychological theory, and can be documented in those terns, and practical working mathematics in in its most fundamental terms
 Quantitative and qualitative dimensionality can be generalized and defined along a single taxonomic cascade. All categories and concepts can be defined within this single allcontaining framework.
 There are innumerable alternative ways to describe aspects of general semantic ontology, many of which are very insightful and undoubtedly sound. But these models tend to compete with one another as microfragments of an undefined supercontext, going over and over the same or similar subjects, but in fragmentary ways. This does not makes the alternative microtheories wrong, but it does make them incommensurate. We believe the full context of these theories can be defined with precision, and their value combined and intersected. This is not a pretentious undertaking, because we are wellaware of the challenges involved, and are unfolding these ideas in the context of the best literature and critique available.
 The implications of the closed loop interval ontology span the content of mathematics, semantics and logic. It is proposed as an exacting container for all possible of conceptual form. Development strategy: 1) define this form properly; 2) document its sources and influences; and 3) test and correlate its implications.
 NOTE: It is probably true that "there is nothing new under the sun" and every idea suggested within this project has been looked at and considered by philosophers and scientists, and any value in this project is indebted to their work.
This project is in development and brandnew as of July 2019



Fundamentals
 The continuum
 The real line
 The definition of numbers
 Measurement
 Dimensions
 Dimensions of measurement  quantitative, linear
 Dimensions of models  qualities, properties, attributes, characteristics, aspects, facets, "nonlinear" ("multidimensional")
 Units
 Units of measurement
 Models
 How reality is represented in symbols
 The correlation between these symbols and reality  scientific testing of conceptual maps
 Differing philosophic positions on these questions
 Alphabets
 Fonts
 Syllables
 Computer language semantics
 Natural language semantics
 Quantitative and qualitative dimensionality
 Levels and types of variables
 Information structures and computerconsistent algebra that can map and model all of these elements in a common and systematic language
The structure of concepts
 Concepts can and should be understood as "information structures" ("data structures")
 This approach enables an isomorphism between (abstract/theoretical/psychological) concept theory and actual working computer language
 Intuitive concepts can be represented "perfectly" by this approach, and nothing of value is lost in this interpretation
 This approach opens the way to powerful new methods in compositional semantics
 Concepts and information structures must be defined in terms of ("composed of") truly primitive elements, that do not contain any inherent structure or potential decomposition
 The development of ontological systems based on "nonprimitive primitives" is a fundamental cause of weakness and failure (or ambiguity and controversy) in traditional ontology
 Ontological fundamentals cannot contain implicit potential decompositions. They must be absolutely atomic.
 In computers, this fundamental atomic level is the bit; in human cognition, the fundamental atomic level is a boundary value distinction in the continuum, which can be perfectly represented by a bit or composite of bits.
 Claim: all categories and concepts are or can be defined by boundary values; those boundary values form an "ndimensional container" (or "envelope") and the meaning of the term is the content of that container.
The continuum
 The continuum is the common ground of all human experience and human conceptualization
 All ideas and concepts emerge from it, and are grounded in it
 This includes all "levels and types of language and logic"  all of which embody motivated and symbolicallyencoded interpretations of some aspect of the continuum
 Intuitive interpretations of the continuum might be the foundation of most world religions
Dimensionality
 Dimensionality and dimensions are the natural and most commonly used ways to describe properties of anything in the real world. It's how we actually do it.
 Dimensionality can also be defined in "qualitative" terms, as the attributes or characteristics or properties of some complex item
 The concept of dimensionality can be generalized as a connective unit to map continuous variation defined from the real number line and integer measurement to any level of composite construction or abstraction, creating a direct mapping from "the empirical plane" to "any level of abstraction and universality".
Semantics
 Through a process of intentional topdown stipulation, the meaning of words can be defined precisely in terms of dimensionality across levels of abstraction
 human intention and stipulation
contextspecific cascades across levels of intentional/intended boundary values
Compositional semantics
 bottomup definitions grounded in bit and distinction as the fundamental primitive
 topdown definitions grounded in the undifferentiated continuum
 bottomup and topdown connected through a taxonomy of scale ("levels of abstraction")
Psychological dynamics
 the origin of concepts
 infant/child psychology
 basic concept formation
 the emergence of concepts from the continuum
Epistemology
 definition of all basic concepts in epistemology
 similarity
 difference
 comparison
 abstraction
 holism
 all terms are "information structures" defined in a common language grounded in dimensionality
Logic
Boundary values and taxonomy
 An object or instance is "in a class" (a genus or taxon) because its characteristics are defined within the boundary range of its defining dimensions
Categories and concepts
 all categories and concepts defined as a contextspecific or ad hoc partitioning of the continuum
 all concepts defined as "data structures" with defined explicit characteristics
Quantitative and qualitative dimensionality
 types and levels of variables  Stanley Smith Stevens  spectrum of types
 stipulative definition
 measurement
 measurement units
 conversion between measurement units, based on the dimensionality of their definition
Fundamental structures of ontology
 Universal container  upperlevel ontology
 Taxonomy
 Abstraction
 Topdown / bottomup spectrum
The meaning of "integral"
 All things brought together into unity and oneness while supporting infinitely fluent diversity
 All things held in unity expanding into endless diversity
 All things at the same time
 All things interdependent
 No sector of human experience or area of thought defined in isolation or logical independence from any other
The necessity of an integral method
 Existing methods and models, particularly those based on axiomatic methods, are inherently fragmenting and somewhat blind
 We have innumerable alternative fundamental frameworks and postulate systems, all of which are "partial" and "shortsighted"  and not "holistic" or "integral"  this creates fragmentation and inherent incommensurateness between elements
 the proper approach to integral method does not invalidate existing systems or frameworks; it is a reinterpretation of their particular content in universal terms, thereby enabling full inclusion across the entire spectrum of human experience, interconnecting "disciplines" or sectors of thinking traditionally thought of as incommensurate (e.g., "science" and "religion")
Major themes
 The fundamental partition or differentiation of the continuum is contextspecific or "ad hoc", depending on local motivation
 Development of a universal language based on dimensionality  "universal language" means "can interpret or fully express any existing concept defined in any language"
 Compositional semantics defined in terms of absolutely atomic binary primitives  every conceivable idea can be interpreted in terms of cascaded dimensions defined in bits
terms of data structures
 concepts
Integral container
 The continuum "implicitly contains all concepts" because all concepts arise as distinctions within it
 We can define a single "closed loop" algebraic form as toplevel container of all sublevel differentiations and distinctions
 All distinctions can be defined by boundary values in abstract dimensions
 This model is based on the idea that "all ideas and concepts are abstract symbolic constructions defined in the continuum across a spectrum of levels created by distinctions"
Models and reality
 Discussions of "what is real" can become misleading or confusing or controversial.
 This project proposes that our most appropriate and useful subject matter involves the discussion of abstract models of reality, where models are defined in symbolic and conceptual terms, and the correlation between that symbolic representation and experience can be tested and confirmed
 Science in general involves establishing a tight correlation between a model  an abstract symbolic representation or idea  and "the reality" or experience that the model describes



Cultural convergence
 Under the influence of many factors, including globalization and semispecialized and interdependent areas of social crisis, there are natural evolutionary forces tending to drive a convergence towards a common foundation for human understanding
 This is a largescale social phenomena, and can be understood in many different ways and at different levels. To some degree we can say "globalization drives universalization".
 The phenomena of "glocalism" illustrates this: replicating the global level at the local level  "as above, so below".
The challenge
 Project is absolutely interdisciplinary and intercultural
 Project trespasses on hundreds of areas of specialized expertise, and for this reason is both highly errorprone in its specifics and likely to be viewed as pretentious or confused nonsense
 Project is difficult and historically unprecedented  it is an unrealized dream of many philosophers throughout history
 Core vision is extremely or absolutely inclusive
 Scale of project may not be feasible in the short term
 Project crosses all disciplines and elements of human experience defined in concepts or symbols
 There are many brilliant people working independently in areas related to this overall agenda; they must be respected and heard
One best interpretation
 We explore this claim
 There is one best way to model and interpret and conceptualize all these diverse elements
 This best way is defined by achieving absolute inclusion of all relevant issues and questions, with a solution defined in the simplest possible set of principles and definitions (Occam's Razor, elegance, inclusion, simplicity, analytic speed of transaction, optimal linearity)
 "All elements are linear, all elements fit together in linear ways into linear structures"  this method creates a smooth fit and map across levels of abstraction. historical failure on this point is a sideeffect of "nonprimitive primitives", inconsistent methodology across levels, and an institutionalized belief that qualitative dimensionality is inherently incomprehensible with no map to the ground
Strategy
 Survey major literature in theory of concepts and be familiar with all common terminology and approaches
 Develop a body of references and citations that links facets of current or recent literature into this model
 Develop a body of general principles governing universal concept formation, grounded in solid academic literature
 Define "convergent" processes in science and technology
 Clarify the common representational ground connecting major disciplines and ways of thinking
 Create a forum for dialogue and critique for any proposal or principle that may be baldy defined or in question
Organizing activism and systematic method
 To unfold the full potential and implications of this model is a grandscale undertaking
 It will require teamwork and institutional support and cooperation
 The project should be "cocreative" and involve many perspectives
Algebraic integration
 we are guessing that we can create a definition of the continuum that supports all these elements
 we can create a single algebraic form that unpacks all these elements as implications of its fundamental construction
 we have initial hypotheses on this subject
"The prime theorem"
 Can we define a single integrated algebraic form that contains all these elements in a highly (absolutely, perfectly) ordered way?
 We are exploring the proposition that the answer might be yes
"One ring to rule them all"
 The world can govern itself through universal standards
 This approach defends local independence and diversity, while preserving global integrity on critical common issues
"Two shall become One"  Moebius Strip Wedding Ring


