Eric Schmid

Contemporary advances in homotopy type theory and sheaf theory make possible a synthetic transcendentalism that reconciles Husserlian phenomenology with Badiouian ontology—and in doing so, provides a non-moral, non-mythic foundation for AI governance. Gabriel Catren's type-theoretic perspectivalism and Fernando Zalamea's sheaf-theoretic synthetic universality converge in what I have termed "transcendental mathematics'': a compatibilist framework wherein mathematical structures emerge through the interaction of constitutive activity and objective constraints, making them at once perspectival and real. This approach stands opposed to the dominant alternatives. Anna Greenspan's Deleuzean transcendental materialism, with its planes of Chronos and Aeon, dissolves concrete mechanism into poetic abstraction. Nick Land's cybernetic reading of Kant collapses difference into a dogmatic apparatus of control. And the Jungian archetypal worldview, as Padusniak has shown, substitutes counterfeit religiosity for genuine insight. Against all these, I contend that the categorical and type-theoretic structures of mathematics impose a priori constraints on thought and action that are neither arbitrary moral impositions nor mythic projections. These structural constraints, already operative in the planetary techno-social stack, should form the basis of AI governance. The transcendental of AI is not an archetype or a code, but a type, a category, a sheaf.

In the first part of this polemic, I challenged Nick Land’s recasting of Kantian critique as a static apparatus of cybernetic control. Land could have countered with several core arguments drawn from both his early and late philosophy: that Kant really is a philosopher of closure and dominance (as Land insists), that Kant’s own theory of genius in the Third Critique vindicates an inhuman outside which Land merely follows, that Land’s break from Deleuze and Guattari in favor of cybernetic capitalism marks a legitimate embrace of immanence, and that any appeal to navigation or rational agency is futile in the face of self-augmenting techno-capital feedback loops. In this second part, I will explicitly refute Land again and these possible defenses. To do so, I enlist Gabriel Catren’s Pleromatica as a theoretical fulcrum. Catren’s work offers a reconstruction of transcendental philosophy that both criticizes transcendental relativism and articulates a new speculative absolutism. By reconceiving modern science and the immanence of life itself, Catren develops what he calls a phenoumenodelic realism – a view in which the totality of experience and reality (the pleroma) is grasped without positing any transcendent beyond, yet without renouncing the “infinite ideas of reason” (Truth, Beauty, Justice, Love) that oriented the Enlightenment. Through Catren’s concepts of disligation (the modern disconnection or unbinding of meaning) and religation (a re-binding of thought to the absolute immanence of life), I will show that Land’s position – from his Kantian nihilism to his accelerationist fervor – collapses under the weight of its own contradictions. Catren’s speculative absolutism illuminates a path beyond Land’s deterministic cybernetics and supposed ontological nihilism, preserving a space for reason, value, and orientation within an immanent “fullness” of reality.

Nick Land infamously recasts Immanuel Kant as a philosopher of cybernetics-as-control, arguing that the Kantian transcendental subject imposes rigid a priori forms that domesticate all alterity -- much as capitalist exchange imposes commensuration on difference. In this polemic, I contest Land’s reading and propose that Kant, far from inaugurating a closed regime of control, opens the door to a metadisciplinary, porous cybernetics of the transcendental. By revisiting Kant’s critical philosophy through contemporary category theory and sheaf theory, I argue that the transcendental is not a static apparatus of domination but an evolving, self-correcting system of constraints and feedbacks. This transcendental cybernetics synthesizes diversity into provisional unities without totalizing them, thereby offering a recursive, non-totalizing approach to the subject–object relation. To support this view, I draw on my trilogy of works---Prolegomenon to a Treatise (2022), Critique of Transcendental Structure: Toward a Synthetic Unity of Aesthetics and Collective Intelligence (2025), and Dub Langlands: Art Theory Texts on Cybernetics (2025)---which reframe Kantian critique via category-theoretic structures. My Critique of Transcendental Structure}, my magnum opus, demonstrates how a “transversal” or “synthetic” reason armed with sheaf theory can achieve unity-in-diversity without enforcing uniformity. I further incorporate Noah Chrein’s recent distinction between two approaches to "categorical cybernetics''---(1) modeling systems by categories vs. (2) modeling systems in arbitrary formalisms with a categorical metatheory---to clarify how the latter approach fosters an open-ended, reflexive framework. The result is a vision of critique as an open system of knowledge: one that continually revises its own conditions (akin to Fichte’s self-positing I and Novalis’s transdisciplinary "Romantic Encyclopædia'') rather than a final legislator of truth. This approach stands in contrast to both Hegelian absolute closure and speculative realism’s flat ontologies, preserving a space for novelty ("voids'' of indeterminacy) as the very medium through which rational progress occurs.

Johan Georg Granström’s Treatise on Intuitionistic Type Theory represents a landmark contribution to our understanding of the philosophical foundations of Per Martin-Löf’s intuitionistic type theory (ITT). The work is particularly noteworthy for its careful exposition of how ITT emerges as a sophisticated codification of Brouwerian intuitionism while simultaneously advancing a distinctly Kantian program in the philosophy of mathematics. This philosophical grounding, drawing heavily on both Kantian and Husserlian phenomenology, offers valuable insights into the nature of mathematical knowledge and computation. The significance of this work cannot be overstated. At a time when type theory is gaining increasing prominence in both mathematics and computer science, Granström provides a philosophical foundation that helps explain why type-theoretic approaches have proven so successful. By situating ITT within the broader philosophical tradition, particularly in relation to Kant’s views on mathematical knowledge, the book illuminates both the historical development of constructive mathematics and its contemporary relevance. The work comes at a crucial moment in the development of mathematical foundations. The increasing importance of computer-assisted proof and formal verification has led to renewed interest in constructive approaches to mathematics. Granström’s analysis helps explain why type-theoretic foundations are particularly well-suited to meet these contemporary challenges. His careful exposition of the philosophical foundations of ITT provides essential context for understanding both its historical development and its future potential. Moreover, the book represents a significant contribution to our understanding of the relationship between philosophy and mathematics. By showing how deep philosophical insights about the nature of mathematical knowledge inform the development of formal systems, Granström demonstrates the continuing relevance of philosophical reflection for mathematical practice. This is particularly valuable at a time when the relationship between philosophy and mathematics is often questioned.

At the intersection of category theory, cybernetics, and dialectical reasoning lies a profound framework for understanding computation and control. This paper examines how categorical structures—particularly adjoint functors and fixed points—illuminate the nature of feedback and control in both mathematical and philosophical contexts. Through an analysis of Lawvere’s fixed point theorem, Bayesian Open Games, and modern approaches to categorical cybernetics, we develop a unified perspective that bridges computation, control, and dialectical reasoning. We demonstrate the practical implications of this theoretical framework through a compiler pipeline that targets modern GPU architectures.

Andr ́e Weil viewed mathematics as deeply intertwined with metaphysics. In his essay ”From Metaphysics to Mathematics,” he illustrates how mathematical ideas often arise from vague, metaphysical analogies and reflections that guide researchers toward new theories. For instance, Weil discusses how analogies between different areas, such as number theory and algebraic functions, have led to significant breakthroughs. These metaphysical underpinnings provide a fertile ground for mathematical creativity, eventually transforming into rigorous mathematical structures. Alexander Grothendieck’s work, particularly in ”R ́ecoltes et Semailles,” resonates with Weil’s ideas by emphasizing the organic and generative aspects of mathematical creation. Grothendieck sees mathematical work as akin to cultivating a garden, where ideas grow and develop in a nurturing environment. He describes the process of mathematical discovery as a deeply personal and creative journey, involving both solitary reflection and collaborative effort. Grothendieck’s concept of creating mathematical ”houses” aligns with his broader philosophical view that mathematics provides structures within which new ideas can flourish. His work in category theory and algebraic geometry exemplifies this approach, where he developed vast, interconnected frameworks that have become foundational in modern mathematics. Grothendieck’s analogy of constructing houses for others to live in highlights the mathematician’s role in creating abstract frameworks that others can inhabit and explore. This metaphor emphasizes the constructive nature of mathematics, where researchers build theoretical structures that form the basis for further exploration and application by the mathematical community.

Due to the wide scope of (in particular linear) homotopy type theory (using quantum natural language processing), a metatheory can be applied not just to theorizing the metatheory of scientific progress, but ordinary language or any public language defined by sociality/social agents as the precondition for the realizability of (general) intelligence via an inferential network from which judgement can be made. How this metatheory of science generalizes to public language is through the recent advances of quantum natural language processing, but the traditional metalogical encodings (of Tarski) is relatively comparable through universes such as the type of types or type of types of types found in the inherent inferentialism of UF/HoTT via infinity-groupoids. The "computational trinity" of proofs=programs=algebra in HoTT also means reason is defined functionally as "what it does" by what it computes (proofs are programs). Following Reza Negarestani's recent book, through the self's self-realizability, achieving self-consciousness and consciousness beyond selfhood, "geistig manifestation" is achieved in the form of general intelligence, but only through an inferential network of social agents intrinsically encoded through computation.