The Instruments Inherited

The documentation is now its own lattice

With this page the set closes. Two distinctions — functional / historical and structure / logic — generate exactly four pages, and each page is legible only against its three counterparts. The documentation has the same shape as the thing it documents: one relation, applied twice, yielding the full space of aspects.

Reading rule, same as everywhere in the house: dark cells are live systems and never reason from light-cell content; light cells credit everything and run nothing.

From a diagram in the mail to a satisfaction relation

The first-order treatment leans on three instruments: binary structure, formal language, and model-theoretic truth. None of them is native to the house. Their construction runs through the sources below — beginning, fittingly, at the one point in history where this archive's two lineages touch.

• [1] The Junction · G. W. Leibniz, Explication de l'arithmétique binaire (1703) — written after Joachim Bouvet mailed Leibniz the xiantian diagram from Beijing. Leibniz recognized the trigram sequence as binary numeration: the single documented moment where the classical lattice and modern formalism are the same object in one mind. Both lineage pages of this archive cite this document; it belongs equally to each.
• [2] G. Boole, An Investigation of the Laws of Thought (1854) — logic as algebra over {0, 1}; the move that makes "power/vacuum as bits" a calculable idea rather than a metaphor.
• [3] G. Frege, Begriffsschrift (1879) — the first full formal language with quantifiers; the invention of the signature-and-formula discipline that the house's decoupling guarantee depends on.
• [4] G. Peano, Arithmetices principia, nova methodo exposita (1889) — axiomatization of arithmetic; the template for "define little, derive everything" that AH₃ imitates at miniature scale.
• [5] J. von Neumann, Zur Einführung der transfiniten Zahlen (1923) — the ordinal construction, 0 = ∅ and 1 = {∅}: existence built from the act of regarding absence. The direct precedent for the house's distinction-as-primitive root, and the source of the working citation on the first-order page.
• [6] A. Tarski, The Concept of Truth in Formalized Languages (1933) — truth as satisfaction in a model. The reason "unsayable beats forbidden" is a theorem-shaped claim and not a slogan.
• [7] G. Spencer-Brown, Laws of Form (1969) — the calculus of indications: one injunction, draw a distinction, from which mark and unmarked space co-arise. The nearest complete ancestor of the house's root; its reception history (embraced by cyberneticians, held at arm's length by logicians) is itself a caution the house accepts knowingly.

The instruments shelf

Public-domain material will be hosted here in reader- and machine-friendly form; works still under copyright receive commentary and guides rather than texts.

• Leibniz, Explication de l'arithmétique binaire — French original with English rendering and the Bouvet correspondence context. Shared shelf with the classical lineage page. md · txt
• Boole, Laws of Thought — selections: the algebra of 0 and 1. md · txt
• Frege, Begriffsschrift — notation guide and selections in public-domain translation. md · txt
• von Neumann (1923) — the ordinal construction, annotated for the lattice-root reading. md · txt
• Tarski (1933/1956) — reader's guide to the satisfaction definition; text where permissions allow. md
• Spencer-Brown, Laws of Form — commentary and correspondence with the house root only; the work remains in copyright. md