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 sub-units 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 one-to-one correspondence with") the structure of any other categorical taxonomy.
• The "space" between lowest-level terminating decimal numbers is the real actuality of "the continuum", and takes the form of "pure uncertainty". "The continuum is the space between lowest-level 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 high-level composite abstractions into specific lower-level 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 two-sided two-edged 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 top-down/bottom-up 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 special-case 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.

• 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 (finite-state, 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

• 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 finite-state 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 large-scale 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 special-case 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

• 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 all-containing 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 micro-fragments of an undefined super-context, going over and over the same or similar subjects, but in fragmentary ways. This does not makes the alternative micro-theories 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 well-aware 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 brand-new as of July 2019

• 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, "non-linear" ("multi-dimensional")
• 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 computer-consistent 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 "non-primitive 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 "n-dimensional 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 symbolically-encoded 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 top-down stipulation, the meaning of words can be defined precisely in terms of dimensionality across levels of abstraction
• human intention and stipulation context-specific cascades across levels of intentional/intended boundary values

Compositional semantics

• bottom-up definitions grounded in bit and distinction as the fundamental primitive
• top-down definitions grounded in the undifferentiated continuum
• bottom-up and top-down 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

• Induction
• Deduction
• Bias

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 context-specific 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 - upper-level ontology
• Taxonomy
• Abstraction
• Top-down / bottom-up 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 context-specific 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 top-level container of all sub-level 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

• Under the influence of many factors, including globalization and semi-specialized 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 large-scale 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 error-prone 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 side-effect of "non-primitive 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 grand-scale undertaking
• It will require teamwork and institutional support and cooperation
• The project should be "co-creative" 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