Categorical Metaphysics
About
What happens when you treat relations, transformations, and coherence—not “things”—as the basic vocabulary of reality?
Book VII brings the Panta Rhei program to its philosophical culmination. Using the categorical framework developed across Books I–VI (τ, τ³, the lemniscate boundary 𝕃, and the guiding idea that global structure arises from gluing local consistency), this volume applies a structural method to the classic domains of philosophy: ontology, phenomenology, aesthetics, language, inference, ethics, social reality, and mind.
The recurring stance is simple but demanding:
- Relations and transformations are primary (objects are what stable relations make them).
- Invariance carries meaning (what survives translation and change is what counts).
- Coherence is a global test (if local stories cannot glue, the “theory of the world” fails).
- Interfaces generate paradox (world/self/social boundaries are where confusion concentrates).
What the book covers (8 parts)
I. Categorical Ontology
A relational ontology rooted in τ: internal domains, truthmakers, boundedness, and the role of τ³ = τ¹ ×₍f₎ τ² as an “arena” with base and fiber playing distinct ontological roles. Boundary and interface are treated explicitly via 𝕃 and bulk–boundary principles.
II. Categorical Phenomenology
Knowledge and justification are reframed as sections over covers and gluing constraints—shifting the focus from “justified true belief” to structural compatibility. Perception is treated as a functorial process rather than a passive imprint.
III. Categorical Aesthetics
Beauty is approached as invariance; elegance as minimal tension; style and motif as structured constraints. Topics range from proportion and self-similarity to music, visual composition, architecture, and creation as iterative refinement.
IV. Categorical Language & Meaning
Language is treated as self-enrichment: what symbols add, what they cost, and how meaning drifts, repairs, and translates. Reference, names, indexicals, pragmatics, and public language (law/justice) are explored. Large language models are discussed as a modern return of the subsymbolic layer.
V. Categorical Logic & Inference
Boolean reasoning is placed at micro-scale, Bayesian reasoning at meso/macro-scale, with internal randomness and representation constraints. Inference is framed as a categorical necessity rather than a purely psychological habit.
VI. Categorical Ethics
Dignity is proposed as a meta-ethical foundation. The categorical imperative is interpreted as a sheaf-like gluing constraint; moral conflict is analyzed through coherence and monodromy; fairness is treated as action protocols, including testable procedures and long-term obligations (animals, future generations).
VII. Categorical Societies
Social reality is modeled structurally: spheres, bubbles, foams; human-scale neighborhoods; cities as connection regulators; architecture as cultural mirroring; lineages and drift; capital and networks; overload and fragmentation; and the mismatch between planetary coordination needs and present institutions.
VIII. Categorical Mind
Mind is treated as an internal topos: the self as a story functor; consciousness as a global section; intentionality and qualia as structured features; metacognition as a self-recognition loop; free will as branching in a category of possible actions; and criteria for comparing minds, machines, and LLMs.
The through-line
Across all parts, Book VII argues that many classic “unsolved” philosophical problems dissolve when reframed structurally: instead of asking what the world is “made of,” it asks what must hold for experience, meaning, ethics, and identity to be globally coherent—and what breaks when local constraints fail to glue.
Book VII is written as a bridge from mathematical structure to lived reality: not “philosophy after mathematics,” but philosophy as structural reconstruction.
“Meaning is what survives translation. Truth is what glues. Mind is what integrates.”
Free reader downloads: To get a fast, high-signal overview of this volume, we provide two PDFs extracted from the original published pages of the book: the Table of Contents (see the full structure at a glance) and the Q&A Appendix (a reader’s guide to key ideas and common questions). Both are free to view and share for review/academic reference.
New to the series? Start with the Q&A Appendix; use the TOC to choose your entry points.