Bruce Schuman
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Santa Barbara, CA 93121
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Synthetic Dimensionality
Synthetic Dimensionality | Forum on Conceptual Structure
Design for a Transcendental Bridge
Linkage of the universal and the particular

Introduction to the Theory of Concepts
General principles of conceptual structure

The Dimensionality of Concept Structure
Similarities and differences in category formation

The Universal Hierarchy of Abstraction
Framework for a mathematical epistemology

Synthetic Dimsionality
The recursive algebra of semantic space

Foundations of this model

Background and history

Linkage of the Universal and the Particular

"The Bridge Across Consciousness" is based on a design taken from epistemology and the philosophy of mind. The fundamental concept is large-scale, and quite simple.

In essence, it is proposed that all human cognitive activity -- all thoughts, all ideas, all concepts -- can be understood as distributed or organized within one single "transcendent and integral" framework, which takes a hierarchical form, linking "universals" (general principles or concepts) to "particulars" (specific facts or concrete objects), across a series of "descending levels of abstraction".

This linkage across levels of abstraction can be diagrammed as follows:

                         "THE BRIDGE ACROSS CONSCIOUSNESS"
 "Left Brain - Lowest level"                         "Right Brain - Highest level"
             |                                                    |
             |<-Particular/Concrete           Universal/Abstract->|
                              Levels of Abstraction
Across this single distribution of levels, this design organizes all branches of cognitive activity, including all types of academic disciplines. In rough and approximate terms, we can generally position subjects like philosophy and religion near the right pole of this spectrum, and topics like physics and other empirical sciences near the left. Other subjects, such as history or anthropology or sociology, can be understood as occupying positions somewhere in the middle of this array.

In general, the concepts of the various disciplines are assembled from, and defined in terms of, concepts at lower levels of abstraction. Thus, the concepts of a physical science like chemistry are defined in terms of physics, a science defined at a lower level of abstraction. A science like biology can be understood in terms of the concepts of chemistry. Seen this way, there is a clear "hierarchy of concepts" that links the relationship between various academic and scientific disciplines. This hierarchy of abstraction illustrates the relationship between holism and reductionism -- as well as between abstraction and empiricism, and synthesis and analysis.

Given this framework, many of the most challenging problems in philosophy can be understood as involving the linkage across these levels. The problem of "grounding" abstract concepts, and assigning them a precise and unambiguous meaning -- a process that is essential to the scientific method -- can be seen as a "mapping" from high-level abstractions, on the right of this chart, to specific facts or lowest-level empirical particulars on the left. Since many of the concepts of religion and metaphysics involve highly inclusive and holistic abstractions, discussions concerned with "the relationship of science and religion" can be approached through this structure. And psychological models concerned with "the right-brain/left-brain relationship" can be described in these terms. The Universal Hierarchy of Abstraction is a complex and ambitious general theory of cognitive structure, defined in terms of the mathematical concepts of dimensionality. Through this integrated framework, it is possible to define a determinate algebraic linkage between "empirical measurements" defined near the left pole of this spectrum, and "qualitative abstractions", defined near the right pole. This linkage is defined in terms of "ad hoc top-down decomposition" (there is no single decomposition of this form; it is conditional on specific contexts), and is consistent with classical theories of abstraction and measurement.

The Bridge Across Consciousness is thus defined in terms of algebraic connections across levels of abstraction.

This logical principle can be diagrammed in somewhat more detail as follows:

                         "THE BRIDGE ACROSS CONSCIOUSNESS"

 "Left Brain - Lowest level"                             "Right Brain - Highest level"

     zero <--few dimensions              |               many dimensions--> infinite
  <--Lowest level of abstraction         |  Highest level of abstraction-->
     Levels: | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
             |                                                       |
             |<---------------- Main Index of Levels --------------->|
             |                                                       |
             |-->"bottom up"                            "top down"<--|
Concrete     |                                                       |   Abstract
Actuality -->|                                                       |<--Theory,
  Actual     |-->induction                               deduction<--|   Holism,
  Object X   |-->synthesis                                analysis<--|   Metaphysics
             |<--differences                          similarities-->|
For a more complete explanation, see the essays on Universal Hierarchy of Abstraction and Synthetic Dimensionality.