Critical Notes — Chapter I: Definition of Pure Mathematics (§§ 1–10)

Primary Text: Read Verbatim Treatise Track (pp. 3–9) · Overview: Analytical Summary · Cross-Corpus Loci: Master Concordance

Historical & Cross-Corpus Commentary

Dialogue with Hoenen (Caput V: On Axiomatics)

In De Noetica Geometriae (Caput V, §3.2.A n. 8 & §4.2.B), Fr. Peter Hoenen, S.J. confronts Russell’s §4 claim directly. Citing G. H. Hardy (Mind 1929) and dissecting Principia Mathematica *2.01, Hoenen argues that substituting tokens into a propositional function already presupposes spatial intuition of linear symbol order and equiformity.

Leibniz’s Anticipation (§5)

Russell notes that Leibniz sought to prove Euclidean axioms logically, failing only because he lacked asymmetric relational logic and assumed Euclidean space categorically necessary.