Indexicality and Learning in the Age of Generative AI

Abstract Generative AI challenges not only educational practice but the epistemological assumptions on which modern education rests. This paper argues that the shift is best understood through Charles Sanders Peirce's semiotics, and specifically through the index. We distinguish two kinds of indexicality that Peirce held apart: causal indexicality, in which a sign is a physical trace of what produced it, and deictic indexicality, in which a sign orients meaning around a here, a now, and a me fixed by the situation of interpretation. This distinction does the central work of the argument. Neural-network-based generative systems are indexical rather than symbolic: their weights are causal sediment of the training corpus, and their outputs are traversals of a learned high-dimensional manifold rather than rule-based manipulations of conventional tokens. We ground this claim in four structural properties of high-dimensional embedding space (concentration of measure, near-orthogonality, exponential directional capacity, and manifold regularity), which together make navigation, not classical computation, the operative mode. Causal indexicality is native to the trained model; deictic indexicality is supplied by the human at each prompt. Reading Seymour Papert's constructionism through these categories shows that its pedagogy was indexical in both senses long before any medium could reciprocate—the turtle's path a causal trace, the learner's situated engagement a deictic act—while its symbolic substrate held it back. Generative AI, for the first time, offers a technological medium rooted in the same indexical paradigm as the pedagogy, distributing the two indices across a human–machine coupling. We argue that mathetics in this age is the discipline of orchestrating that coupling. The traversal of semantic space now transfers to the machine; what remains constitutively human is the deictic origin—the judgment of where to stand, what to point at, and what the journey is for—and this is what education must most deliberately cultivate.