# Appendix D — Bibliography and Intellectual Debts

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## Foundational Works (Technology of Expressions Programme)

- **Ghioni, F.** *Technology of Expressions: A Structural Approach to Meaning.* Ordinative Sciences Press, 2025. — The foundational text. Contains equations 1.1–1.14, the Collapse Function, the Remir, the Semantic Derivative, Pulsation, Vertical Coherence.

- **Ghioni, F.** *Semantic Algebra: Foundations.* Ordinative Sciences Press, 2026. — The SA operators S and π, the 7-layer architecture, the R-vocabulary, the ⟨𝓚⁵⟩ formula, the invariant library (ι₁–ι₁₀), the round-trip test.

- **Ghioni, F.** *Ordinative Set Theory v3.0.* Working paper, 2026. — The ⟨Σ, R, Φ⟩ triple, vertical coherence, semantic inertia, causal inversion, pathological orders.

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## Predecessors and Points of Contact

### General Systems Theory
- **von Bertalanffy, L.** *General System Theory: Foundations, Development, Applications.* George Braziller, 1968. — The aspiration to unify the sciences through organisational principles. Formally vague but directionally correct.

### Category Theory and Applied Category Theory
- **Eilenberg, S. and Mac Lane, S.** "General Theory of Natural Equivalences." *Transactions of the American Mathematical Society*, 58(2):231–294, 1945. — The foundational paper of category theory.

- **Fong, B. and Spivak, D.I.** *An Invitation to Applied Category Theory: Seven Sketches in Compositionality.* Cambridge University Press, 2019. — The closest formal predecessor to the PA in ambition. Demonstrates compositional structure across domains. Semantically silent.

- **Baez, J.C. and Stay, M.** "Physics, Topology, Logic and Computation: A Rosetta Stone." In *New Structures for Physics*, Lecture Notes in Physics 813, Springer, 2011, pp. 95–172. — Cross-domain structural isomorphisms via category theory. Restricted to formal mathematical domains.

### Structural Realism
- **Ladyman, J.** "What Is Structural Realism?" *Studies in History and Philosophy of Science*, 29(3):409–424, 1998. — The philosophical position that relations are ontologically primary. Non-operational.

- **French, S.** *The Structure of the World: Metaphysics and Representation.* Oxford University Press, 2014. — Ontic structural realism: objects are bundles of relations.

### Proportional and Relational Thinking
- **Bridgman, P.W.** *Dimensional Analysis.* Yale University Press, 1922. — The formal framework showing that physical laws are fundamentally about dimensionless ratios.

- **Dirac, P.A.M.** "The Cosmological Constants." *Nature*, 139:323, 1937. — The argument that only dimensionless numbers are physically fundamental.

- **Einstein, A.** "Die Grundlage der allgemeinen Relativitätstheorie." *Annalen der Physik*, 354(7):769–822, 1916. — No absolute space, no absolute time. The physics is in the relations.

### Biological Proportions
- **Thompson, D.W.** *On Growth and Form.* Cambridge University Press, 1917. — The foundational work on proportional relations in biological morphology.

### Musical Proportions
- **Helmholtz, H.** *On the Sensations of Tone.* Dover Publications, 1954 [1863]. — The proportional basis of consonance and dissonance.

### Mathematics of Meaning
- **Yoneda, N.** "On the Homology Theory of Modules." *Journal of the Faculty of Science, University of Tokyo*, 7:193–227, 1954. — The Yoneda Lemma: an object is determined by its relations. The mathematical expression of Axiom 0.

### Philosophy of Proportion
- **Pythagoras / Pythagorean School.** — *All is number*: the proportional relations governing music, geometry, and cosmic motion are one.

- **Goethe, J.W.** *The Metamorphosis of Plants.* 1790. — All botanical forms are variations of a single proportional schema (the Urpflanze).

- **Leibniz, G.W.** — The *characteristica universalis*: the aspiration to a universal formal language for all knowledge. Not achieved, but the aspiration is the PA's direct ancestor.

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## Works Informing Cross-Domain Demonstrations

### Chemistry (Chapter 13)
- **Pauling, L.** *The Nature of the Chemical Bond.* Cornell University Press, 1960.
- **Dalton, J.** *A New System of Chemical Philosophy.* 1808. — The law of multiple proportions.

### Language (Chapter 14)
- **Chomsky, N.** *Syntactic Structures.* Mouton, 1957. — Hierarchical structure in language.
- **Jakobson, R.** "Linguistics and Poetics." In *Style in Language*, ed. T. Sebeok, MIT Press, 1960.

### Emotion (Chapter 15)
- **Damasio, A.** *The Feeling of What Happens.* Harcourt, 1999.
- **Panksepp, J.** *Affective Neuroscience.* Oxford University Press, 1998.

### Medicine (Chapter 16)
- **Engel, G.L.** "The Need for a New Medical Model: A Challenge for Biomedicine." *Science*, 196(4286):129–136, 1977. — The biopsychosocial model.

### Artificial Intelligence (Chapter 17)
- **Vaswani, A. et al.** "Attention Is All You Need." *NeurIPS*, 2017. — The Transformer architecture.

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*This bibliography is necessarily incomplete. The Proportional Algebra draws on work across many disciplines, and any list is a projection — a decoherent expression of a coherent field of intellectual debts. The invariant is gratitude.*

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