The Recursive Hierarchy of the Abstract and the Concrete
All knowledge and perception oscillate between the hierarchies of the abstract and the concrete. Without this movement, applying knowledge to reality would be nearly impossible. Here, the concrete refers to that which is perceptible via the five senses, while the abstract refers to that which cannot be directly sensed and is instead indicated through symbols. A symbol is a sensory expressive medium used for description and sharing.
Abstraction and concretion can also be framed as the polysemic vs. the univocal, or the whole vs. the part. This relationship is not fixed; it shifts depending on the perspective. By switching perspectives, the concrete becomes abstract, the univocal becomes polysemic, and the part becomes the whole. The concrete is univocal and partial, manageable through bodily manipulation. When a series of such manipulations are linked, they manifest a single, abstract, and polysemic whole. Knowledge is the methodological system of these bodily manipulations, while perception is the foundation upon which this methodology is formed and executed.
Inference, therefore, is the means of constructing this methodology of bodily manipulation, executable only upon the foundation of perception.
The Kinematic Basis of Univocity
The core of these concepts lies in two definitions: first, that the “concrete” is what is perceptible through the five senses; and second, that what is “bodily manipulable” is univocal—meaning it is kinematically unique. The definition of the concrete relies on human experience or intuition—whether felt in daily life or believed to be felt—essentially rooted in sensory reception.
The idea that bodily manipulable objects are univocal represents the limit of human physical operation. Anything that can be operated upon at once is, within that operation, kinematically unique. This univocity depends on a [Time Window Δt, Reference Frame R]. Even if an operation appears polysemic, it is a complex of univocal operations. This complex of univocal operations is a composite of concretions, an abstraction, and a structure formed by synthesis. The reason this abstraction can only be described or shared through symbols via the senses is that bodily manipulable actions are kinematically unique. At this juncture, semantics emerges as a chain of these operations.
Definitions & Formalization
- Five Senses: Sensory reception in a broad sense.
- Symbol: A medium with conventional mapping.
- Shift in Perspective: Formalized as a change in 「Δt, R」.
- Δt: The minimum time window required to uniquely determine an action.
- R: The reference frame, including the body and embodied tools (extended body).
Rules of Scaling:
- Expanding Δt or R: Tends to shift the focus from the univocal to the polysemic and from the part to the whole.
- Narrowing Δt or R: Tends to shift the focus from the polysemic to the univocal and from the whole to the part.
