Thomistic Noetics, Peter Hoenen & the GEOMETOR Symbolic Engine

Why Thirteenth-Century Scholastic Epistemology Illuminates Symbolic Computation

Modern dynamic geometry systems typically split into two disconnected worlds: numerical canvas tools (such as GeoGebra) that approximate coordinates in IEEE-754 floating-point arithmetic, and purely syntactic proof assistants that manipulate symbolic tokens with no native spatial intuition.

GEOMETOR unites both worlds through an architecture remarkably isomorphic to the Aristotelian-Thomistic noetics recovered by Fr. Peter Hoenen, S.J. in geometor-hoenen:

Structural Correspondence Between Thomistic Noetics & GEOMETOR

Thomistic Concept	Classical Locus in geometor-aquinas	Computational Realization in GEOMETOR
Materia intelligibilis (continuous spatial extension free of sensible noise)	Super Boetium De Trinitate q. 5, a. 3; In VII Metaph. lect. 10–11	geometor.model: exact algebraic points, lines, and circles over SymPy polynomial/radical fields ($\sqrt{2}, \sqrt{3}, \phi$)
Conversio ad phantasmata & terminari ad imaginationem	In III De Anima lect. 12 (#777); Super Boetium De Trinitate q. 6, a. 2	geometor.explorer: determinate SVG rendering & interactive visual inspection of exact constructions
Non demonstrat per lineam in pulvere descriptam	In I Anal. Post. lect. 19	Separation between finite screen pixels and the exact symbolic identity verified in geometor.model
Dignitates, suppositiones, & petitiones	In I Anal. Post. lect. 5 & lect. 18–19	geometor.elements: constructive Directed Acyclic Graphs (DAGs) built from Euclid’s Postulates 1–3 and Common Notions
Divisio figurarum in actu (heuristic discovery by dividing continua)	In IX Metaph. lect. 10 (Cathala #1894)	geometor.divine: automated scanning of newly constructed intersections to reveal latent golden sections and harmonic ranges in act