Aikins's two page-cited engagements with Jevons both land inside the traditional-syllogism block of Elementary Lessons in Logic; the Logic Piano sits two thematic blocks later, under a heading Jevons himself calls "recent"

william-stanley-jevonsherbert-austin-aikinslogic-pianohistory-of-logicbibliographyargument-from-silence

Jevons's own table of contents divides Elementary Lessons in Logic into named thematic blocks: "TERMS," "PROPOSITIONS," "SYLLOGISM" (Lessons XIV–XIX, including Lesson XV, "The Rules of the Syllogism," p.126), "FALLACIES" (XX–XXI), "RECENT LOGICAL VIEWS" (XXII–XXIII, including Lesson XXIII, "Boole's System of Logic," p.191 — where the Logic Piano appears; see claim-jevons-elementary-lessons-lesson-xxiii-describes-logic-piano-and-its-royal-society-debut), "METHOD," "INDUCTION," and "SUBSIDIARIES OF INDUCTION." Aikins's two documented page-cited engagements with Jevons's stated rules — conversion in his own Ch. XI (keyed to Lesson X, under "PROPOSITIONS"; see claim-jevons-elementary-lessons-lesson-x-source-of-aikins-conversion-rule-citations) and the syllogism rules in his Ch. XVI footnote (keyed to Lesson XV, under "SYLLOGISM"; see claim-jevons-elementary-lessons-lesson-xv-source-of-aikins-eight-syllogism-rules) — both land inside the traditional-logic core of Jevons's book.

Lesson XXIII sits two thematic blocks later, under a heading Jevons himself labels "recent" rather than traditional. At the close of that lesson (p.201), what Jevons declines to introduce "into an elementary work like the present," "on account of their speculative character," is narrower than an earlier draft of this finding had it: "certain views as to the real nature of the process of inference" contained in his own The Substitution of Similars (1869) — not the Boole-derived material itself, which the same closing passage presents as "so clearly proved to be true by its reduction to a mechanical form" that he does "not hesitate to bring it to the reader's notice." The broader reservation about Boole sits in the Preface instead: the "recent logical discoveries" of Hamilton, Thomson, De Morgan, "and especially the late Prof. Boole, cannot yet be fully adopted in an elementary work."

This gives a structural account, independent of intent, for why demonstrably close engagement with one part of this book — close enough to cite it to the page — does not imply engagement with another: Aikins's quarrel, textually, is with the traditional rule-stating lessons specifically (claim-aikins-1902-preface-states-program-of-replacing-jevons-style-syllogism-rules-with-principles), and his citations never leave that block.