Mathematics as MethodA Conversation with Alexander V. Gheorghiu
Bryan Kam in conversation with Alex, assistant professor and a New Frontiers Fellow in the School of Electronics and Computer Science at the University of Southampton.
As you'll hear in this podcast, my meeting with Alex Gheorghiu was random and fortuitous. In this podcast we discuss whether and how mathematics and logic relate to reality, why Buddhist thought challenges Western categories, and what Gödel's incompleteness theorem might mean for how we understand the world.
Alex traces his intellectual development from teenage mathematical realism—the belief that mathematics describes the fundamental structure of reality—to his current anti-realist position. Through studying algebra and analysis during his degree, he came to the view that these mathematical tools are cultural constructs rather than discoveries about an objective reality "A model is just a model in the way that a map is never the land itself."
Alex is also a Zen practitioner. We explored the famous Zen koan of Master Joshu, to the question of whether a dog has Buddha-nature. He responds "mu"—which neither affirms it nor denies it, but rather rejects the question. This exemplifies a philosophical move that transcends binary thinking, similar to how the Daodejing presents the Dao as preceding both unity and duality. We discuss how Chinese philosophy, lacking the Indo-European grammatical structures that equate existence and predication, developed fundamentally different approaches to how categories work.
Through Michael Dummett's anti-realist philosophy, we explore how meaning emerges from use rather than correspondence to reality. This challenges millennia of Western philosophical assumptions about categories and definitions.
The ancient tension between Parmenides (static being) and Heraclitus (dynamic becoming, which I've written about here) continues to shape philosophy today. We examine how Plato attempted to reconcile these positions through his theory of forms, and why this synthesis may have taken Western philosophy down a particular path—one that privileges nouns over verbs, objects over processes, and abstract categories over lived experience.
Eugene Wigner's famous question—why mathematics works so unusually well in describing nature—dissolves when viewed through an anti-realist lens. If mathematics is a human tool rather than a discovery of reality's structure, its effectiveness becomes less mysterious and more a reflection of how we've shaped our tools to solve our problems.
Alex shares his vision for bringing Gödel's incompleteness theorem into public consciousness the way physics has done with black holes. Having just won the 2025 Graham Hoare Prize for his essay, he argues that this "small technical result" has profound implications for how we understand the limits of formal systems and human knowledge itself.
Alex Gheorghiu is an assistant professor at the University of Southampton and honorary fellow at University College London, working in logic with interests spanning philosophy of mathematics, theories of language, and the relationships between reasoning and reality. He's currently developing a mathematical account of Dummett's philosophy and working to make logic and mathematics accessible to wider audiences.
Bryan Kam hosts the Clerestory podcast and is writing Neither/Nor, exploring how conceptual and experiential ways of knowing can inform both individual flourishing and our approach to philosophical problems.
Recorded at Drake & Morgan, London, where philosophical work happens with "consistently low" productivity but high engagement.
On Thursday 7th August, I walked around Bethnal Green with Christopher Daniel, who organises Long Now London.
We walked through East London, discussing architecture, philosophy, and the importance of long-term thinking. We explored the evolution of our own projects, especially Long Now London and Bryan's discussion group Through a Glass Darkly. We delved into broader themes like societal change, the impact of technology, and embodied experience versus conceptual abstraction. We wandered the streets, thinking about history, our own personal stories, and how to create meaningful and sustainable communities.
The Bertrand Russell quote I butchered:“Work is of two kinds: first, altering the position of matter at or near the earth's surface relatively to other such matter; second, telling other people to do so. The first kind is unpleasant and ill paid; the second is pleasant and highly paid.”
In this podcast, I discuss the draft of the academic paper on Neither/Nor which I wrote about here, with my coauthor, developmental psychologist Dr. Isabela Granic.
This paper has been a lot of work, and we discussed the writing right after finishing a major draft. In the paper and in our discussion, we emphasise the six principles of Neither/Nor. The article currently has an editor at Nature assessing the submission.
Two Modes of Knowing: The first principle identifies the two distinct ways we learn about life — through concepts and experiences. These modes are complementary, and we consider them trainable skills. Neither should be privileged over the other.
Commitment to Oscillation: Rather than selecting a definitive standpoint, we advocate for a dynamic process of oscillating between the conceptual and experiential skills, allowing us to adapt to the strengths of each mode.
Process Over Static Entities: Our understanding should prioritise processes rather than fixed entities, recognising the ever-changing nature of knowledge as it evolves through interaction with the living world. Categories are useful, but we can’t allow them to become too static.
Trial and Error Learning: Engage with the world through continuous experimentation, using trial and error to iteratively refine our understanding and approach — this is at the heart, for us, of adaptive learning.
Social Construction of Knowledge: A recognition that all knowledge is inherently social. Our reason for wanting to know is always social. Knowledge itself is always culturally embedded. This is empowering, and allows to contextual flexibility, not relativism — some ways are more effective than others.
Historicity: Understanding that knowledge and its acquisition grow from historical context gives us a holistic understanding of how changes occur in personal, cultural, and scientific pursuits.
Would you like to read the paper?
If so, you can request a copy of the pre-print here.
Thanks for listening. If you enjoyed the conversation, please share it with someone! Please also consider supporting me on Patreon or Ko-Fi.
Best,
Bryan
The Six Principles of Neither/NorWould you like to read it?
I’m Bryan Kam. I endeavour daily to make philosophy accessible and relevant. To that end I write this newsletter and host a podcast called Clerestory. I’m also writing a book called Neither/Nor and I’m a founding member of Liminal Learning. In London, I host a book club, a writing group, and other events. My work looks at how abstract concepts relate to embodied life, and how to use this understanding to transform experience.
Recently, I had a conversation with Haneen Khan, a sex coach and fellow thinker, about the relationship between abstract thinking and embodied experience.
The Nature of Abstraction and Experience
We began by discussing the academic paper which Isabela Granic and I recently submitted, which describes my philosophy Neither/Nor. The paper and the forthcoming book focus on the relationship between experience and abstraction, or theory and practice. The paper critiques what we term “latent Platonism,” an unconscious tendency to prioritize abstract, theoretical constructs over direct, embodied experience. This can reveal itself in conversation, for example, when sharing about an uncomfortable experience can lead an interlocutor to leap to broad generalizations rather than discussing the experience itself.
The Need for Balance and Awareness
Throughout our conversation, we emphasized the importance of balancing abstract reasoning with experiential knowledge. Haneen and I agree that awareness is key — awareness of when we're gravitating too heavily towards abstraction at the expense of our felt experiences (or, less frequently, vice versa).
Haneen shared valuable insights from her coaching practice, emphasizing the power of grounding practices that help individuals reconnect with their bodies and emotions. This balance, or oscillation as we’ve termed it, is crucial for a holistic understanding of the self.
Abstraction, while powerful, can become a tool of escapism or avoidance if unanchored by embodied awareness. Maintaining a strong connection to one’s felt experience, on the other hand, can enrich not only personal wellbeing but also interpersonal interactions.
Integration: A Path Forward
We concluded by emphasizing integration — a synthesis of experiential and conceptual wisdom — as a winding path forward. This integration offers a potential solution to the pitfalls inherent in each mode of understanding when pursued in isolation. Concepts like Internal Family Systems Therapy illustrate such an integration, offering a framework where conceptual understanding aids emotional and physical awareness.
I’d love to hear your thoughts and experiences on this topic: How do you navigate the balance between abstraction and experience in your daily life? Let me know in the comments.
Bryan
P.S. If this conversation resonated with you, please share it with someone who might benefit from it. Please also like it, subscribe, or support me on Patreon or Ko-Fi!
A photo, not by me, of the place where we recorded the podcast, including the “fake grass” I mention
My friend Pen interviewed me about Type 1 Diabetes, which I've lived with for 38 years.
This is the second episode, in which we focus on my current daily experience living with diabetes. We also discuss how the intensity of managing diabetes relates to the book I'm writing, Neither/Nor, which explores the nuances between conceptual understanding and lived experience. I emphasize the need for a balance between experiential and conceptual knowledge, drawing from my own life to illustrate how these realms relate.
The first episode, in which we covered early diagnosis, is available here.
Clerestory by Bryan Kam • Writing on Substack • Support this podcast at Patreon
My friend Pen interviewed me about Type 1 Diabetes, which I've lived with for 38 years. In this podcast we speak about what diabetes is, and what what it's like to live with.
Clerestory by Bryan Kam • Writing on Substack • Support this podcast at Patreon
I spoke to director, cinematographer, and my good friend Cécile Embleton (instagram) about her work and influences and her new film Mother Vera, which is playing at the London Film Festival next month.
This is a feature documentary about the life of a young orthodox nun from Belarus, I have seen it, and it is spectacular. Cécile and I discuss literature, her influences, and the challenges and joys of making arthouse cinema.
It is also playing at Camden International Film Festival, in Camden, Maine, on Friday 13th September, 1pm @ Journey’s End Cinema.
Other films/shows we mentioned:
This is a cross-post from my friend David Valerio's new podcast, Discern Earth. In it, we speak about what nature is.
Here's David's description:
We discuss the etymology of nature and related terms, whether there is a hard distinction between man and nature, hypostatization and reification, the Christian roots of theories about the inherent value of nature, and the role of embodied experience in facilitating ecological regeneration.
Clerestory by Bryan Kam • Writing on Substack • Support me at Patreon
Delia and I walked along the Parkland Walk in London with Zoom f2 recorders and lapel mics. We cover a bit about Neither/Nor, as well as existentialism versus essentialism.
The biologists I couldn't think of at the end was ecologist Robert MacArthur; see r/K selection theory.
Listen to Delia's podcast, Growing Up with Delia Burgess.
Recorded in June 2024.
In this episode I spoke to Dr. Noah Martin, Director of the College of Modern Anxiety.
We discussed the relationship between phenomenology and existentialism, and the relationship between subjective and objective understanding in philosophy. We cover thinkers like Edmund Husserl, Donna Haraway, Sartre, and de Beauvoir.
Clerestory by Bryan Kam • Infrequent updates at Substack • All my work plus exclusive content at Patreon
I spoke to Kit Tempest-Walters about his new book: Plotinus on Eternity and Time, which includes a translation and commentary of Ennead III.7.
We discuss the challenges of translating, philosophical perspectives on the self, consciousness, and mysticism.
We also talked about some of my perspectives from the book I'm writing, Neither/Nor, including the differences in the organizing assumptions of Eastern and Western approaches to philosophy.
Clerestory by Bryan Kam • Infrequent updates at Substack • All my work plus exclusive content at Patreon
It's been nearly a year since our last episode, in which Maggie Appleton and I discussed why we write.
A year is a long time in AI; has it made much progress in how it writes? Possibly not, but it has made some progress in search.
Discussed:
At the end of 2023, I asked seven people I knew to join me in a WhatsApp group experiment. Read more here.
We set up a schedule by which one of us, each Thursday, would record a (suggested) 5 minute question on a creative or existential quandary we were facing.
The other seven members had committed to responding with a (suggested) 10 minute response, meaning that one person would ask a question, and receive over an hour of perspectives.
Over two months this WhatsApp group supported each other through the trials and tribulations of the holiday period, finishing a documentary film, the meaning of intuition, seasonality, the struggle to re-engage with work, and more.
This episode of Clerestory contains an audio call with seven of the eight participants.
Clerestory by Bryan Kam • Infrequent updates at Substack • All my work plus exclusive content at Patreon
At the end of 2023, I asked seven people I knew to join me in a WhatsApp group experiment. Read more here.
We set up a schedule by which one of us, each Thursday, would record a (suggested) 5 minute question on a creative or existential quandary we were facing.
The other seven members had committed to responding with a (suggested) 10 minute response, meaning that one person would ask a question, and receive over an hour of perspectives.
Over two months this WhatsApp group supported each other through the trials and tribulations of the holiday period, finishing a documentary film, the meaning of intuition, seasonality, the struggle to re-engage with work, and more.
This episode of Clerestory contains asynchronous voicenote reflections from seven of the eight participants on how the experience went.
Stay tuned for an article describing how to set up such a group for yourself, and another synchronous conversation from the participants.
Clerestory by Bryan Kam • Infrequent updates at Substack • All my work plus exclusive content at Patreon
Part 8 in a series of interviews on the book I'm working on, Neither/Nor. In this episode, Isabela Granic and I discuss:
Previous episodes:
Clerestory by Bryan Kam • Infrequent updates at Substack • All my work plus exclusive content at Patreon
Show notes
Part 7 in a series of interviews on the book I'm working on, Neither/Nor. In this episode, Isabela Granic asks about three thinkers that have influenced my thinking: Julian Jaynes (1920–1997), Leo Tolstoy (1828–1910), and Zhuangzi (369–286 BC) sometimes written Zhuang Zhou or Chuang-tzǔ).
Previous episodes:
Clerestory by Bryan Kam • Infrequent updates at Substack • All my work plus exclusive content at Patreon
Show notes
How do you balance your life’s purpose, your creative impulse, or your art, with the realities of life?
Here are the final four responses I received. Thanks to Peter, Olga Yakimenko, Rainbow, and Kevin Bowers.
Clerestory by Bryan Kam • Infrequent updates at Substack • All my work plus exclusive content at Patreon
Principles of Neither/Nor:
How do you balance your life’s purpose, your creative impulse, or your art, with the realities of life?
Here are the next seven responses I've received. Thanks to Shannon, Luiz, Matt Sterett, and Yulia Babanova.
I'm still taking submissions. Please upload your audio response here: https://bryankam.com/record.
Clerestory by Bryan Kam • Infrequent updates at Substack • All my work plus exclusive content at Patreon
How do you balance your life’s purpose, your creative impulse, or your art, with the realities of life?
Here are the next seven responses I've received. Thanks to Patricia, Liv, Ben, Nastasia (@Gryphire), Michael, Maggie (@Mappletons), and Gloria.
I'm still taking submissions. Please upload your audio response here: https://bryankam.com/record.
I will release episodes from responses I receive, aiming for 45 minute episodes after the initial "pilot."