Reflections on the Right Use of Artificial Intelligence With a View to the Love of Mathematics

Quentin Meillassoux’s speculative realism, launched with the provocative force of After Finitude, throws down a gauntlet to the pervasive philosophical climate he terms “correlationism.” Correlationism, in its various guises, insists that we only ever access the correlation between thinking and being, never either term in isolation. Thought cannot grasp an object independent of its being-given-to-thought, nor conceive of a subject detached from its relation to an object. Meillassoux’s primary weapon against this enclosure is the arche-fossil: scientific statements, like those dating the accretion of the Earth or the formation of stars, which refer to a reality chronologically anterior to the emergence of life and, consequently, anterior to any thought or consciousness. The arche-fossil presents a profound challenge: how can science meaningfully speak of a time when the correlation itself did not exist? How can a discourse meaningful for us, now, denote a reality radically independent of any us? This is the crux – the arche-fossil signifies a reality definitively not for us in its origin, yet seemingly accessed by us through mathematized science.

Against this backdrop of radical, observer-independent reality, Simone Weil’s reflections offer a different, yet resonant, perspective. In her writings, particularly on the use of studies, intellectual labor, especially the rigors of mathematics, becomes a spiritual exercise. It is the cultivation of attention – a patient, humble, receptive waiting upon truth – that matters most. For Weil, knowledge is not mere data acquisition; it is a transformative process intrinsically valuable for us, leading towards love and a form of prayerful connection to a reality beyond the self. The goal is less the object known, and more the quality of the knowing subject’s engagement.

AI systems, processing vast datasets and navigating complex logical spaces defined by human-created ontologies and knowledge graphs, initially appear as powerful extensions of the for us. They operate within the “house” we build, trained on our data, designed to answer our questions, potentially generating solutions to problems or proofs of propositions within our established mathematical language. In this mode, AI accelerates exploration within the bounds of human-correlated mathematics. Its explanations are for us, limited by the very structures we provide for it.

The crucial speculative question arises when considering AI’s potential to exceed these bounds. Suppose an AI generates a mathematical structure, a proof, entirely alien to our methods, built using tools or logic it has derived autonomously – a structure not built for us, perhaps initially generated for it, for its own operational logic. If this structure remains fundamentally opaque to human understanding, despite its demonstrable validity within the AI’s framework, what have we encountered? Is it still knowledge? Or is it merely information, an artifact pointing towards that ancestral mathematical reality Meillassoux gestures towards? This scenario mirrors the arche-fossil: we have evidence of something real, something structured, yet it resists integration into the meaningful world constituted by human attention. It exists, but perhaps not for us.

This potential disconnect highlights the radicalism of Meillassoux’s position. The existence of an ancestral mathematics, like the existence of the pre-biotic Earth, does not depend on our capacity to comprehend it. AI might become a probe capable of detecting signals from this realm, computational artifacts whose internal consistency points to truths unmoored from human intuition or axiomatics. Such discoveries would challenge the anthropocentric bias inherent in viewing mathematics solely as a human construction or a language for us.

Yet, Weil’s perspective provides a crucial counterpoint regarding meaning and value. Even if AI unveils fragments of an ancestral mathematical truth, their significance for us remains contingent on our ability to bring our attention to bear upon them. The Weilian value lies not in the mere existence of the truth, but in the human act of engaging with it, struggling towards its assimilation, allowing it to shape the attentive mind. An incomprehensible proof, however valid in its own terms, remains outside this transformative circuit. It is like an arche-fossil locked away in a vault – its existence is noted, but it does not participate in the living practice of understanding. The challenge then becomes not just accessing these potential AI-generated structures, but finding ways to translate them, to build bridges, to render them amenable to human attention, lest they remain mere curiosities from a realm definitively not for us. The tension persists: AI pushes against the boundaries of the human-correlated, potentially touching the ancestral, while the very meaning of that touch for us depends on the possibility of Weil’s devoted, difficult attention.

Tags: philosophy , speculative realism , ai