A Reconstructive Ontology of Brouwerian Intuitionism

This study reconstructs the ontological foundations of Brouwerian intuitionism, arguing that the rejection of the principle of the excluded middle (PEM) is not a technical choice but a necessary consequence of the ur-intuition of time. Drawing on L.E.J. Brouwer’s primary texts from 1905 to 1948, we demonstrate how the creating subject serves as the sole architect of mathematical truth, positioning language as a secondary, often deceptive, “lifeless superstructure” (Brouwer, 1905). We employ a dual methodological approach, combining genealogical textual analysis with a computational simulation of drifts (choice sequences) to operationalize the subject’s temporal constraints. Our findings reveal a critical distinction between the ideal creating subject of standard theory and the computational subject of our simulation: while the former detects any deviation, the latter is bound by finite resolution, creating a class of undecided states that effectively operationalizes Brouwer’s rejection of PEM in physical systems. These results resolve the paradox of communication by reframing mathematical exchange not as the transmission of objective truth, but as will-synchronization—the sharing of constructive algorithmic protocols.