The Large Language Oracle
Intuitionism, algorithmic authority and the reconstruction of rson in aea digital Dao*
I introduce the Hofman-Chen conjecture:
when a twitter debate goes on long enough,
someone will sooner or later refer to an AI
in support of his/her claims.
In the long, shadow-boxing theatre of online debate, we find a curious, almost whimsical pattern that asserts itself in the invocation of the algorithmic oracle. When a dispute, having exhausted the common wells of citation and rhetoric, stretches towards its inevitable dénouement, one participant will, with a magician’s final flourish, produce a rabbit from a 21st century hat, a transcript. “The model indicates,” they will state, or, more bluntly, “I asked an AI and it agrees with me.” This manoeuvre, let’s term it for now the Oracular Turn, is more than a novel rhetorical tactic. It is a symptom of a profound epistemic shift, a silent tremor in the bedrock of how public reason establishes its claims. When we observe this phenomenon from the particular vantage of a mathematician-philosopher steeped in the tradition of intuitionism whose intellectual heritage is a deliberate synthesis of European systematicity and a Daoist-inflected sensibility for flux and process, we experience a peculiar curiosity, a direct, urgent and deeply ironic provocation to our understanding of truth itself.
The intuitionist project, as initiated in the early 20th century, was itself a radical act of reconstruction. It emerged from a profound discontent with the classical, Platonist tradition of mathematics, which presented its truths as eternal, static objects residing in a perfect, external realm, merely awaiting discovery by the probing intellect. Against this cathedral of pre-existent verities, intuitionism proposed a startlingly different metaphysics: mathematics as a languageless activity of the mind. Truth, in this view, is not unearthed but rather constructed; is brought into being through the disciplined, temporal and supremely personal mental acts of the mathematician. A mathematical object exists only insofar as it can be built, step by finite step, in the intuition. The law of the excluded middle, the idea that a statement must be either true or false, a cornerstone of classical logic, was rejected where it applied to infinite domains. To claim a proposition concerning an infinite set must be either true or false, independent of our ability to demonstrate either, was seen as a metaphysical fiction, an unwarranted projection of finite experience onto the infinite. For the intuitionist, truth is inherently tied to proof and proof is a creative, temporal process.
When we bring this lens to bear upon the Oracular Turn, we immediately perceive a rich and unsettling irony. The Large Language Model as a most linguistic entity, is being positioned as an authority in a tradition that sought to escape the tyranny of language over mathematical thought. The model’s pronouncements, statistical extrapolations from a frozen corpus of human text, devoid of consciousness, intention or temporal lived experience, are presented as oracles from a new kind of external realm: the dataspace. This is a neo-Platonism of the corpus, where truth is not found in a heaven of forms, but in the latent patterns of a training set. The appeal is clear: it offers a simulacrum of objectivity, a deliverance from the messy, partisan and fatiguing labour of human persuasion. It promises an eternal rest to debate by appealing to a source ostensibly beyond human bias, a final arbiter that has processed ‘all’ information.
Yet, from an intuitionist standpoint, this is where the profound epistemological fracture appears. The LLM’s output is the antithesis of a constructive proof. It offers no transparent, traceble sequence of mental acts. Its workings are, by their very architectural nature, opaque and non-syntactic in any humanly comprehensible sense. We are presented with a conclusion, often eloquently and confidently rendered, but we are categorically denied access to the intuition, the construction, that would justify it. We are asked to accept a truth divorced from the process of its becoming. This is precisely the kind of disembodied, process-agnostic claim that intuitionism, in its mathematical context, exists to challenge. The model, in its Delphic black-box obscurity, reifies the very mode of truth-as-external-object that Brouwer’s revolution sought to dismantle.
This is not simply a philosophical parlour game. The intuitionist critique illuminates the practical perils of this new authority. If truth is a constructive process, then its validity is inseparable from the clarity and communicability of that process. The integrity of a mathematical proof lies in its capacity to be scrutinised, challenged and reconstructed in the mind of another. It is a shared journey of the intellect. The AI-generated claim short-circuits this entirely. It presents a finished product, a fait accompli of reasoning, which by its nature resists the kind of dialogic interrogation that is the lifeblood of both Habermasian communicative rationality as well as the scientific method. We cannot, in any meaningful sense, ask the model to justify its steps differently, to explore an alternative line of thinking or to feel its way towards an insight. One can only re-prompt, hoping to tease out a different configuration of its latent statistics. The debate, rather than ascending to a higher plane of reasoned exchange, is flattened into a competition of prompt-craft and screenshot prowess.
Here, the Daoist currents in my background cannot offer a contradiction to the European rigour of intuitionism, but there is a complementary perspective. Daoist thought, with the emphasis on zìrán), usually translated to “self-so-ness” or spontaneous natural order, is deeply suspicious of rigid, artificial categories and the aggressive imposition of a fixed, linguistic “this” against “that.” The Daodejing warns of the dangers of excessive naming and abstraction, which can separate us from the dynamic, flowing processes of reality. The relentless generation of clean, categorical, linguistically perfect output of an AI oracle, can be seen as the ultimate triumph of the named over the nameless, of the fixed category over the flowing process. It provides answers where perhaps the more profound response would be a Socratic silence or a wry observation about the unaskability of the question in its current form. The model, having never lived, cannot embody the wu wei, the effortless action, of understanding that emerges from situated experience. It can only simulate its linguistic residue.
This confluence of intuitions, the mathematical and the Daoist, points towards a shared ethic of epistemic humility and process-orientation. Both traditions, in quite distinct ways, value the journey of understanding over the possessive certainty of a final answer. The current deployment of AI in public discourse incentivises the opposite: the rapid, definitive and decontextualised answer. It risks creating a culture of what we might call ‘epistemic bystanderism,’ where individuals outsource the labour of reasoning to an inscrutable engine, becoming consumers rather than cultivators of judgement. The muscle of constructive thought, the very muscle intuitionism sought to train and honour, atrophies from disuse.
Yet, to dismiss the technology outright would be to succumb to a different kind of rigidity. The challenge, for a thinker standing at this cross-section, is to imagine a reconstruction. Can the intuitive, constructive and process-oriented ethos be brought to bear on our relationship with these digital tools? Perhaps the answer lies in refusing their oracular role and reframing them as something more akin to a dynamic, hyper-engaged interlocutor, a prosthetic for the imagination rather than a replacement for it. The model could be used to not simply settle a debate, but rather to expand it: to generate counterfactuals, to articulate opposing viewpoints with maximal cogency, to reveal the assumptions buried in the framing of a question. Used in this way, it could serve the intuitionist and dialogic ideal by laying bare the possible paths of construction, rather than obscuring them behind a singular, authoritative output.
This would require, of course, a radical shift in digital literacy. It would mean a deviation from teaching how to extract a convincing answer from a model, to methods how to engage with it in a critical, Socratic and co-constructive dialogue. The measure of a good interaction would cease to be the apparent definitiveness of the output and would become instead the fruitfulness of the intellectual pathway it helped to illuminate. The tool would be subordinate to the ongoing, human activity of reasoning, the very activity that intuitionism holds as the sacred ground of truth.
In the end, the Hofman-Chen conjecture, for all its origins in the observation of Twitter’s frivolous trenches, reveals a fault line running through our contemporary epistemology. The appeal to the algorithmic oracle is a desperate lunge for terra firma in a landscape where traditional authorities have eroded. But the ground it promises is, from the perspective outlined here, a mirage. It offers the form of certainty without its substance, the conclusion without the construction, the word without the lived experience that gives it weight. To navigate this new territory, we would be wise to recall the twin insights of the intuitionist and the Daoist: that truth is a verb, not a noun; that it is a path walked, not a treasure found; and that any oracle which obscures the path in order to proclaim the destination is, ultimately, leading us into a labyrinth of its own design. The task ahead is not to find better oracles, but to recover the courage, and cultivate the skill, for the languageless, constructive and deeply human act of thinking, together.
*This is an abbreviated version of a chapter on this subject in an upcoming colection of essays.