{"query": "Formal logic", "count": 20, "results": [{"id": "card_instr_formal_logic", "title": "Formal logic", "shelf": "codex", "surface": "secular", "snippet": "The Formal logic verifier (src/concordance/verifiers/formal_logic.py). Builds on: Boolean algebra — the base of logic. Found from the code's own imports, never invented; the module keeps the logic, th", "authority_tier": "engine_derived", "source": "verifier: formal_logic", "readable": false, "generated": false}, {"id": "card_src_word_formal_logic", "title": "formal logic", "shelf": "dictionary", "surface": "secular", "snippet": "formal logic: (noun) any logical system that abstracts the form of statements away from their content in order to establish abstract criteria of consistency and validity — syn: symbolic logic, mathema", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_theory_g_del_s_incompleteness_theorems", "title": "Gödel's incompleteness theorems", "shelf": "theories", "surface": "secular", "snippet": "Gödel's incompleteness theorems — an engine domain that can touch it: formal_logic. Calibration: map-only — a meta-theorem about systems, not a sealable computation. FIRST (1931): any consistent forma", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_formal_logic_epistemology", "title": "Formal logic & epistemology (validity, inference)", "shelf": "theories", "surface": "secular", "snippet": "Formal logic & epistemology (validity, inference) — an engine domain that can touch it: philosophy. Calibration: map-only — validity checks compute; epistemology is interpretive. VALIDITY and TRUTH ar", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_zermelo_fraenkel_set_theory_zfc", "title": "Zermelo–Fraenkel set theory (ZFC)", "shelf": "theories", "surface": "secular", "snippet": "Zermelo–Fraenkel set theory (ZFC) — an engine domain that can touch it: formal_logic. Calibration: map-only — an axiomatic foundation, not a computation. Nine or so axioms about sets from which essent", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_income_capitalization", "title": "Income capitalization (V = NOI / cap rate)", "shelf": "theories", "surface": "secular", "snippet": "Income capitalization (V = NOI / cap rate) — an engine domain that can touch it: real_estate. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it, and sea", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_boolean_algebra_propositional_logic", "title": "Boolean algebra / propositional logic", "shelf": "theories", "surface": "secular", "snippet": "Boolean algebra / propositional logic — an engine domain that can touch it: formal_logic. Calibration: seals. Two values and three operations — AND, OR, NOT — with laws of their own (De Morgan's, dist", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_bridge_master_boolean_algebra", "title": "Master equation: (a AND b), (a OR b), NOT a  —  the two-valued algebra", "shelf": "bridges", "surface": "secular", "snippet": "the law of thought made algebra: the same AND/OR/NOT structure is propositional logic, a network of switches, and the algebra of sets. Boole titled it The Laws of Thought; Shannon showed a circuit IS ", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_n_50a5aa72df98", "title": "The three doors the disease framework could escape through — and how they were shut", "shelf": "science", "surface": "secular", "snippet": "The honest part. A framework earns trust by naming where it could be WRONG. The red-team found three\ndoors this one could slip through to avoid ever being falsified — and each was shut, sealed as logi", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-10", "readable": false, "generated": false}, {"id": "card_n_6ca595e0a722", "title": "Cohesion and fracture — the mechanism of holding and breaking", "shelf": "science", "surface": "secular", "snippet": "Some things hold together when every logic says they should break apart; some break apart\nwhen it seems they should hold. Matt saw it in peoples and in words — and there IS an underlying\nmechanism, th", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_bridge_theory_boolean_algebra_propositional_logic__formal_logic_epistemology", "title": "Bridge: Boolean algebra / propositional logic  ↔  Formal logic & epistemology (validity, inference)", "shelf": "bridges", "surface": "secular", "snippet": "Boolean algebra / propositional logic and Formal logic & epistemology (validity, inference) are the same form in different domains. Boole's algebra IS propositional inference in arithmetic dress: AND/", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_n_e7c1d7f721bb", "title": "Gödel — why a calibration tool must point beyond itself", "shelf": "science", "surface": "secular", "snippet": "Kurt Gödel — the deepest logician since Aristotle — proved two things this whole engine rests on,\nand together they are the mathematics of a calibration tool for alignment to source through Jesus Chri", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-10", "readable": false, "generated": false}, {"id": "card_v_f4b827f56b3c", "title": "p ∨ ¬p is a tautology · ¬(p ∧ q) ≡ ¬p ∨ ¬q  (De Morgan)", "shelf": "formal_logic", "surface": "secular", "snippet": "Verdict: HOLDS.\n• formal_logic.tautology: formula 'p | ~p' tautology=True, matches claim\n• formal_logic.equivalence: '~(p & q)' ≡ '~p | ~q' = True, matches claim\nSealed and independently re-checkable:", "authority_tier": "engine", "source": "Verified by the engine — formal_logic", "readable": false, "generated": false}, {"id": "card_alm_bridge_yes_be_yes_is_the_bit", "title": "Almanac: BRIDGE: 'Let your Yes be Yes' (Mt 5:37) IS the bit -- two states, no middle (GF(2) excluded middle)", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  MOAT BRIDGE (two trees, one Author) -- a teaching of Christ bonded to a verified form. WORD FIRST (John 3:12).\nTHE WORD (Tier 1): Matthew 5:37 -- 'Let your Yes be Yes (nai nai), and your N", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_builder_kurt_g_del", "title": "Kurt Gödel", "shelf": "builders", "surface": "secular", "snippet": "Kurt Gödel (1906–1978 AD) — mathematics. The gift: the incompleteness theorems — the proof that any sufficient formal system holds truths it cannot itself prove: no system can be its own complete grou", "authority_tier": "reference", "source": "The builders of the Floor — credited with love, calibrated to the plumb-line", "readable": false, "generated": false}, {"id": "card_calc_v_formal_logic_tautology", "title": "Tautology", "shelf": "calculations", "surface": "secular", "snippet": "Tautology — formal_logic. Formula: phi true under every assignment. Canonical FORM: boolean_logic (phi is SAT / valid / entailed) — engine verifier formal_logic.tautology — the deterministic check the", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_bridge_theory_toulmin_argument__formal_logic_epistemology", "title": "Bridge: The Toulmin model of argumentation  ↔  Formal logic & epistemology (validity, inference)", "shelf": "bridges", "surface": "secular", "snippet": "The Toulmin model of argumentation and Formal logic & epistemology (validity, inference) are the same form in different domains. the warrant is the informal cousin of a logical inference rule — argume", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_n_9d42516b140c", "title": "Quartz at 32,768 Hz — a power of two on the wrist", "shelf": "science", "surface": "secular", "snippet": "Every quartz watch cuts a tuning fork to hum at exactly 2^15 = 32,768 Hz, sealed, and\n32768 / 2^15 = 1: run the signal through fifteen binary flip-flops, each halving the frequency,\nand the last ticks", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_floor_the_instruments", "title": "The instruments — every verifier and validator, and where they join", "shelf": "codex", "surface": "secular", "snippet": "The engine's checking instruments on the one map: the 89 verifiers and the gate that validates them, joined by their real import graph (read from the code at seed time, so it cannot drift). A MEASURE ", "authority_tier": "engine_derived", "source": "Narrow Highway - the instruments on the one map (found from the import graph)", "readable": false, "generated": false}, {"id": "card_domchk_formal_logic_claimed_tautology", "title": "Formal Logic: tautology", "shelf": "formal_logic", "surface": "secular", "snippet": "A worked check in formal logic: tautology.\n\nGIVEN\n  conclusion = q\n  formula = p & q\n\nCLAIMED\n  claimed_tautology = False\n\nTHE ENGINE'S VERDICT\n  formal_logic.tautology: CONFIRMED — formula 'p & q' ta", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_instr_formal_logic"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}