Simulating Student Success in the Age of GenAI: A Kantian-Axiomatic Perspective

Abstract: This study reinterprets a Monte Carlo simulation of students' perceived success with generative AI (GenAI) through a Kantian-axiomatic lens. Building on prior work, theme-level survey statistics Ease of Use and Learnability, System Efficiency and Learning Burden, and Perceived Complexity and Integration from a representative dataset are used to generate 10,000 synthetic scores per theme on the [1,5] Likert scale. The simulated outputs are evaluated against the axioms of dense linear order without endpoints (DLO): irreflexivity, transitivity, total comparability (connectedness), no endpoints (no greatest and no least; A4-A5), and density (A6). At the data level, the basic ordering axioms (A1-A3) are satisfied, whereas no-endpoints (A4-A5) and density (A6) fail as expected. Likert clipping introduces minimum and maximum observed values, and a finite, discretized sample need not contain a value strictly between any two distinct scores. These patterns are read not as methodological defects but as markers of an epistemological boundary. Following Kant and Friedman, the findings suggest that what simulations capture finite, quantized observations cannot instantiate the ideal properties of an unbounded, dense continuum. Such properties belong to constructive intuition rather than to finite sampling alone. A complementary visualization contrasts the empirical histogram with a sine-curve proxy to clarify this divide. The contribution is interpretive rather than data-expansive: it reframes an existing simulation as a probe of the synthetic a priori structure underlying students' perceptions, showing how formal order-theoretic coherence coexists with principled failures of endpoint-freeness and density in finite empirical models.