On the Formal Inexplicability of Self-Evident Metaphysical Phenomena and Related Systems

A Synoptical Narrative

This is a paper about consciousness. This is also a paper about how to write about consciousness. It is a theory, in the strictest sense. But it is also the story of an algorithm, an semantic framework, an homage to a . piece of mathematical history with an unfathomable title, and our best attempt at a work of art. In what follows, we take a unique approach: we face up to the Hard Problem of Consciousness by distilling it into a definition, formalizing why the mystery exists, and how it might be resolved without vanishing.

We will follow Newton's lead, providing intuitive, informal definitions to the many words we add to the lexicon of logic, computation, mathematics and science. We will cite Gödel — not merely for rigor, but because his work gives us the precise language needed to speak of both the inexplicable and the self-evident. And we will begin with Chalmers: not because he gave us the answers, but because he had the clarity to ask the right question.

This is a paper that believes in definition, but also in narrative. We believe the act of formalization can be felt. And that clarity can coexist with wonder.

Table of Contents

We begin by examining why consciousness has remained elusive, and why David Chalmers’ articulation of the Hard Problem has achieved rare cross-disciplinary consensus. We do not borrow from Chalmers’ work—we converge upon it. His framing becomes our jumping-off point: a precise definition of the mystery itself.

From this, we extract and define the core object of our inquiry: the Conscious Experience. We begin with a natural language definition that captures the philosophical intuition — and then build, step by step, toward a formalization that earns it.

Next, we explore what it means for something to be inexplicable, and why formal systems must confront such truths through mathematical structures pioneered by Gödel. Our title — On the Formal Inexplicability of Self-Evident Metaphysical Phenomena and Related Systems — is both a thesis and a tribute. It winks in Gödel’s direction with all the self-awareness of a system looking back at itself.

We then lay out the structure of our theory, progressing through definitions and constructions that carry the reader from informal intuition to formal architecture. We define not just consciousness, but the conditions under which consciousness emerges. Not just what must be present, but why it must arise. Each definition comes with a conceptual bridge: intuition, formalism, and—where appropriate—proof.

The paper culminates in a return to our first definition. But now, it has been transformed. It is no longer a philosophical placeholder. It has been earned — structurally, semantically, mathematically.

Finally, we reflect on what this means — not only for consciousness studies, but for science itself. For if consciousness is the process by which truths are integrated that transcend current frameworks, then every act of science is already an act of consciousness. The Hard Problem, then, is not just solved. It is recontextualized.

A Note Dedicated to Gratitude

This paper very much hopes to be a continuation of a conversation that began long before us. It starts with a tome of biblical proportions, that loops seamlessly from the strange language of logic, to the flickering mirror of an "I", jumps up to levels beyond levels, and yet ends you back where you started. To that end, we hope our Theory, and its Synoptical Narrative. which serves as the synopsis for a paper that promises to contain a formal definition of a Narrative Synopsis, will do Douglas Hofstadter proud.

We believe Hofstadter's contribution to the study of consciousness has been profoundly underappreciated. In our view, "Gödel, Escher, Bach" should be the textbook placed in the hands of every college student who has ever wondered what the Consciousness might truly means. Were there to be a University of Consciousness, GEB would be the only book covered across all three trimesters of Consciousness 101, 102, and 103. And his infinitely accessible follow-up work, "I Am a Strange Loop," would be the recommend reading for all prospective students who are unsure they can handle the rigor of the course, but still find themselves grappling with the mystery of Consciousness at well past midnight. 

This theory would not, and could not, exist without the contribution of Professor Douglas Hofstadter. I have never met the man, yet I consider him a to be a co-author in spirit, if not in already in name. Without him, the spark that brought the self-referential nature of Consciousness to light in my life would never have been caught, fanned, flamed, and, to ruin the analogy, nourished, enriched, deepened, and actualized.

The goal of this paper is to provide a formal definition of consciousness that stands up to the fires of falsifiable scrutiny under the watchful eye of an ever-so-slightly augmented variety of science. One that remembers where science came from. One that embraces subjectivity as structure. One that smiles when it sees itself in the mirror of Metaphysical Transduction - whatever that might soon come to mean!

And, finally, this work could not have happened without the support of my daughter, who, despite her age, managed to help with both the math and the art in equal measure. Thank you sweetie.
It’s not just a theory. It’s a thank you. It's a promise. Please enjoy my heartfelt attempt to paint a portrait of portraiture itself.