Tributes

Every thought has its parents. The Tao of Lucidity’s skeleton comes from Spinoza, its soul from Laozi, its structural grammar from Aquinas, and the origin of its political philosophy from Plato. Here, I wish to pay tribute to these four thinkers : not as academic survey, but as a student’s gratitude to his teachers.

Spinoza: The Solitude of the Geometric Method

Three years ago, I read Spinoza’s Ethics cover to cover for the first time, in English. That experience has never left me.

What I remember is not any particular argument (though each one is exquisite) but a feeling of architecture. You open Part I, “On God,” and you find not prose but a blueprint: definitions, axioms, propositions, demonstrations. Layer upon layer, never skipping a single step. Every conclusion traceable to its premises, every premise traceable to the axioms, the axioms themselves so simple they are undeniable.

This structure stunned me. Someone had written ethics in the manner of Euclid.

Spinoza did what most philosophers dare not do, and many cannot even conceive of doing: he placed God, freedom, emotion, and happiness, the softest, most subjective of human experiences, inside the hardest, most unforgiving framework of mathematics. Definition 1: self-caused. Definition 3: substance. Definition 6: God. Then, Proposition 11: God necessarily exists. Not prayer, not a leap of faith, but proof.

When I read his arguments for the existence of God, I was struck by the sheer power of the writing. This was not rhetorical persuasion; it was logical compulsion. You finish the proof and find you must accept the conclusion, because you have already accepted the premises, and the deduction is airtight. The sensation is unique: not being moved, but being convinced; not agreeing, but yielding to the force of reasoning.

God is Nature.

Spinoza’s God is not an old man sitting on a cloud, judging humanity. His God is Nature itself, that is, Deus sive Natura. There is only one substance, with infinite attributes; everything we see (thought, matter, emotion, stars) is a mode of this single substance.

This idea was dangerous in seventeenth-century Holland. The Jewish community issued a cherem against him, the most severe form of excommunication, tantamount to social death. The Christian churches were equally hostile. He lost his family, his community, his livelihood.

But Spinoza did not retreat. He moved into an attic room, ground optical lenses by day to earn his living, and continued writing his Ethics by night. The lenses he ground with his hands let humanity see distant stars and tiny cells; the philosophy he ground with his reason let humanity see the structure of existence.

This steadfastness in solitude is the quality I most wish to follow.

Freedom through understanding.

The title of Part V of the Ethics is “On the Power of the Intellect, or On Human Freedom.” Here Spinoza offers a paradoxical conception of freedom: freedom is not arbitrary choice (that is an illusion born of ignorance of causes) but understanding necessity. When you understand the causal chains that drive your actions, you are no longer blindly pushed by them; you lucidly walk alongside them.

This idea profoundly shaped The Tao of Lucidity. Lucidity \(\mathcal{M}\) is not about which choices you make, but about how much awareness you bring to the making, that is, how deeply you understand the forces that drive you. Spinoza called it amor Dei intellectualis, the intellectual love of God. The Tao of Lucidity calls it lucidity. Different names, the same light.

Connection to The Tao of Lucidity.

The Tao of Lucidity’s axiomatic method (postulates, theorems, corollaries, proofs) directly inherits the geometric method of the Ethics. This is not accidental formal mimicry. When I first finished reading Spinoza, a bold thought surfaced in my mind: I could implement his philosophical and ethical framework in Python.

Months later, I actually did it. The joy was indescribable. The moment the code compiled, all tests passed, and a seventeenth-century philosophical system ran correctly on a twenty-first-century computer, I felt a resonance across time. Spinoza proved ethics with geometry; I verified his geometry with code. Before that, I had read Bertrand Russell’s analysis of Spinoza in A History of Western Philosophy. Russell’s prose has a cold elegance: he neither worships nor denigrates Spinoza, but dissects the system’s strengths and weaknesses with a mathematician’s precision and an essayist’s restraint. Those chapters, I often wished I could memorize. Russell taught me one thing: you can deeply love a thinker while lucidly seeing his limitations. The Tao of Lucidity’s inheritance from Spinoza works the same way: three points of continuation, three points of departure (§XV). Spinoza gave me the skeleton. Without that skeleton, The Tao of Lucidity would be mere prose.

Laozi: Naming the Unnameable

I grew up in China. As a child, my family had a copy of the Comprehensive Mirror in Aid of Governance (Zizhi Tongjian) and a copy of the Cihai encyclopedia. I loved browsing them from the age of nine. The chronicle gave me a dim sense of history’s weight (dynasties rising and falling, the wheel of fortune turning), but I did not yet understand why these stories fascinated me. In middle school, I encountered Laozi’s Dao De Jing. Those five thousand characters changed everything.

Saying the unsayable.

The first sentence of the Dao De Jing is a paradox: “The Tao that can be told is not the eternal Tao; the name that can be named is not the eternal name.” If the Tao can be spoken, it is not the abiding Tao; if a name can be given, it is not the abiding name. And yet Laozi proceeds to write five thousand characters. This is not a contradiction but a profound self-awareness: you must attempt to say the unsayable, while admitting your words will always fall short. This posture (attempting without pretending to succeed) is exactly how The Tao of Lucidity approaches Mystery. Postulate 3 says Pattern and Mystery are interwoven, not mutually exclusive; Chapter §III explores the Four Depths of Mystery. But The Tao of Lucidity never pretends to understand Mystery; it merely uses the tools of Pattern to illuminate Mystery’s boundary, then stops at the boundary and admits that the light cannot reach further.

Laozi knew this twenty-five centuries ago. He did not need an axiom system to know it.

Wu wei: the deepest form of action.

“Through non-action, nothing is left undone”, not the laziness of inaction, but a profound alignment. Like water: water does not compete with the mountain for height; it follows the terrain to the lowest place. But precisely because it does not compete, it eventually reaches the ocean.

“The highest good is like water. Water benefits all things and does not contend; it dwells in places that all disdain. Thus it is close to the Tao.”

The elegance and concision of this passage captivated me. Every word is necessary; remove any one, and the sentence collapses. This economy (saying the most with the least) is a quality I have always pursued. The Tao of Lucidity’s six postulates attempt the same thing: supporting the largest possible framework with the fewest possible assumptions.

I like simple things. I once tried to study Fuxi and the I Ching. Honestly, I found them very hard to understand, and I still do not. The ambition of deriving all phenomena from two lines, yin and yang, is awe-inspiring, but its symbolic system felt to me like a language requiring a spiritual key I am not sure I possess. When I was a child, my grandfather’s house had a copy of the Qimen Dunjia, and I actually tried to figure out how it worked, even thought about using it to tell my own fortune. Needless to say, I did not divine anything useful. But that curiosity (the impulse to glimpse hidden order) has never left me. Perhaps The Tao of Lucidity is the adult version of that impulse.

Water: the supreme metaphor.

Water is soft, yet overcomes the hard. Water is formless, yet adapts to every vessel. Water does not rush to the front, yet always reaches its destination. Water brings nourishment to all things, yet demands nothing in return.

If Spinoza is stone (hard, precise, immovable), then Laozi is water (soft, changing, everywhere). The Tao of Lucidity needs both: the stone-like axiom system to support the structure, the water-like openness to hold what cannot be formalized.

Connection to The Tao of Lucidity.

Laozi’s xuan (“Mystery upon Mystery, the gate of all wonders”) is precisely The Tao of Lucidity’s Mystery dimension. The Tao of Lucidity’s entire framework of Mystery is, at its core, an attempt to formalize Laozi’s intuition. Postulate 3 (the interweaving of Pattern and Mystery) says exactly what Laozi never expressed mathematically but rendered perfectly in poetry: the Tao is greater than the sum of the knowable and the unknowable.

But I must be honest with Laozi. The Tao of Lucidity’s use of an axiom system to “capture” Mystery is itself an act of Pattern, using Pattern to illuminate Mystery. Laozi might smile and say: “You tried. Good. But you know you only reached the edge.” He would be right. Laozi gave me the soul. Without that soul, The Tao of Lucidity would be mere formulas.

Aquinas: The Invention of Analogy

On the intellectual map of The Tao of Lucidity, Aquinas does not occupy as prominent a position as Spinoza or Laozi. But he left behind a key whose full power would not become apparent for seven hundred and fifty years.

Neither identical nor wholly different.

Medieval Christianity faced a fundamental dilemma: how can humans speak about God? If you say “God is good,” does the word “good” mean the same thing as when you say “this person is good”? If yes, you have reduced God to the human level (univocity). If no, you cannot speak about God at all, because your language cannot reach him (equivocity).

Aquinas’s answer was analogy (analogia): God’s goodness and human goodness are neither exactly the same nor entirely different, but bear a structural similarity, a relation that can be grasped by reason but never fully exhausted.

This concept might seem like a technical detail of medieval scholasticism. But it unlocks a question The Tao of Lucidity must face: what is the relationship between AI and humans?

A key seven hundred and fifty years later.

When we ask “Does AI have experience?” we confront Aquinas’s exact dilemma: if we say AI’s “processing” and human “experience” are the same thing (univocity), we ignore qualitative differences. If we say they are entirely different (equivocity), we sever all possibility of ethical concern.

The Tao of Lucidity’s Definition D8 (analogical relation) and Bridge Axiom E2 (extension of ethical concern to analogical members) directly inherit Aquinas’s concept of analogy. The notion of “analogical membership” (neither equivalent to humanity nor mere instrumentality) is Aquinas’s gift to the age of AI.

The architecture of the Summa Theologica.

Aquinas’s Summa Theologica is one of the grandest architectures in the history of human thought. It is not a collection of essays but a Gothic cathedral: each Quaestio (Question) is a pillar, each Objection a window, each Respondeo (Response) a vault. The entire edifice is logically self-consistent, each part supporting the next.

The Tao of Lucidity’s postulate-theorem-corollary structure is of course closer to Spinoza’s geometric method, but Aquinas taught me something else: to treat objections as building material. Every Question in the Summa begins with opposing views: Aquinas first faithfully states his opponent’s position, then gives his own reply. This intellectual honesty (first understanding what you wish to refute) is a principle I strive to follow in writing The Tao of Lucidity.

Connection to The Tao of Lucidity.

Aquinas stood at the intersection of faith and reason. He believed they would ultimately not contradict each other, but also acknowledged that reason has its ceiling. This resonates deeply with The Tao of Lucidity’s Postulate 3 (the interweaving of Pattern and Mystery): Pattern can illuminate far, but it never reaches the center of Mystery. Aquinas used “analogy” to bridge humans and God; The Tao of Lucidity uses “analogical relation” to bridge humans and AI. Seven hundred and fifty years, the same wisdom, a different application.

Aquinas gave me the grammar, the structure of “neither fully identical nor fully different.” Without that grammar, The Tao of Lucidity could not speak about AI.

Plato: The First Light in the Cave

If Spinoza is the skeleton of The Tao of Lucidity, Laozi the soul, and Aquinas the grammar, then Plato is the origin, the first person to derive political philosophy from metaphysics.

The Allegory of the Cave.

Plato’s Allegory of the Cave is one of the greatest images in the history of human thought. Prisoners are chained deep inside a cave, facing a wall, seeing only the shadows cast by a fire behind them. They take the shadows for the whole of reality. When one prisoner is freed and led outside, he is first blinded by the sunlight, then gradually sees the real world, not shadows, but things themselves.

This is what The Tao of Lucidity calls lucidity and obscuration. Shadows are obscuration, mistaking secondhand, distorted appearances for reality. Sunlight is lucidity, clearly seeing the structure of existence. Twenty-four centuries ago, Plato described in images what The Tao of Lucidity formalizes with mathematics: \(\mathcal{M}\) and \(1 - \mathcal{M}\). The Allegory of the Cave is the archetype of the lucidity/obscuration dialogue.

The Republic: from metaphysics to politics.

Plato did something unprecedented: he derived the political question “How should we govern?” from the metaphysical question “What is real?” His chain of reasoning was: if there exists an eternal, unchanging Form of the Good, then only those who can apprehend this Form are fit to rule; these are the philosophers. Therefore, the ideal state should be governed by philosopher-kings.

The Tao of Lucidity’s Chapter §X does the same thing (deriving political philosophy (Propositions P12–P19) from ontology (the postulates)) but arrives at a radically different conclusion.

The root of the divergence lies in Theorem T1 (the Boundary Theorem): no agent can achieve complete lucidity. \(0 < \mathcal{M} < 1\), for all agents, without exception.

Plato believed some people could exit the cave, gaze directly at the Form of the Good, and achieve complete knowledge. The Tao of Lucidity says: no one exits the cave. Lucidity means knowing that the shadows are shadows, but you are still inside the cave. You are always inside the cave.

The political consequences of this difference are enormous. Plato’s answer: find the wisest person and let them rule. The Tao of Lucidity’s answer: acknowledge that no one is wise enough, and design a system capable of self-correction (§X.7).

The Allegory of the Divided Line: degrees of knowledge.

In Book VI of the Republic, Plato describes a line divided into four segments, representing four levels of cognition: images, belief, mathematical reasoning, and direct intuition of the Forms. From the lowest (shadows in the cave) to the highest (gazing upon the Good), knowledge ascends step by step.

This resonates deeply with The Tao of Lucidity’s lucidity spectrum. Lucidity is not a switch (on or off) but a continuous spectrum, from near zero to near one, but never reaching either endpoint. Plato’s divided line is four discrete levels; The Tao of Lucidity’s lucidity is a continuous \([0,1]\) interval. The form differs; the intuition is the same: cognition has degrees of depth, and the deepest point can never be fully touched.

Connection to The Tao of Lucidity.

The Tao of Lucidity’s Section §X.7 (“The Tao of Lucidity’s Ideal Polity”) is a direct response to Plato’s Republic, not a rejection, but a variation. Both share the same starting point: deriving politics from metaphysics, yet diverge at a crucial premise: whether there exist people who can see reality completely. Plato’s answer: yes, the philosopher-kings can. The Tao of Lucidity’s answer: no, but we can design institutions that never stop examining themselves. Plato sought the ultimate ruler; The Tao of Lucidity seeks the never-ending process of governance. Plato is a destination; The Tao of Lucidity is a direction.

But my respect for Plato runs deep. Without him, the path “from metaphysics to politics” would not exist. The Tao of Lucidity merely set out on the same road from a different starting point. He was the first light. Even if The Tao of Lucidity holds that the light cannot reach to the end, it is still the first light. Plato gave me the path. Without that path, The Tao of Lucidity’s political philosophy would have nowhere to begin.

Spinoza sought to prove everything; Laozi sought to leave everything unspoken; Aquinas invented a third language of “neither this nor that”; Plato was the first to shine philosophy’s light into the cave of politics.

The Tao of Lucidity lives at the intersection of all four.

With Spinoza’s method, carrying Laozi’s disposition, speaking Aquinas’s grammar, walking the path Plato opened, that is what this book attempts. Perhaps all four sages would shake their heads at the result. But I believe they would appreciate the attempt, because attempting is itself lucidity.