domain 32 / 55 · λογική · the proof rises
LOGIKĒ
the algebra of thought.
63 gates in the lattice · sealed & live
⊢ THE PROOF LATTICE · 63 gates · the proof rises ⊥→⊤
⊥ axioms
⊤ theorems
hover a gate · click to enter its sphere
⊢ the lattice
every gate, ordered & enterableBALANCED BASE-5 — THE HELD CENTER CLIMBS THE O · BASBalanced base-5 — the held center climbs the odd ladder→[V{-+6}] · THE BOX · BOX[V{-+6}] · the box→THE TERNARY SIERPIŃSKI — PASCAL MOD 3, AND ITS · SIEThe ternary Sierpiński — Pascal mod 3, and its time-twin→THE STANDING WAVE — STACK TWO HOURGLASSES · STAThe Standing Wave — Stack Two Hourglasses→TERNARY LATTICE — THE 27 BECOMES THE RULE · TERTernary lattice — the 27 becomes the rule→KARSA CONTROL PLANE 14 PAGES DEEP · KARKarsa Control Plane 14 Pages Deep→KARSA CONTROL PLANE 13 PAGES DEEP · KARKarsa Control Plane 13 Pages Deep→11+1 MOBIUS KERNEL · MOB11+1 Mobius Kernel→TRUTH / UNTRUTH MOBIUS 531 · MOBTruth / Untruth Mobius 531→OCTET HOLONOMY CALCULATOR FROM MY WORLD · OCTOctet Holonomy Calculator from my world→TRUTH / UNTRUTH MOBIUS 531 · POETruth / Untruth Mobius 531→3 BODY / 12 BODY // BINARY-4 HARMONIC LATTICE · TER3 Body / 12 Body // Binary-4 Harmonic Lattice→UNITY TENSOR SEED SYSTEM · UNIUnity Tensor Seed System→EUCLID — THE CARVED STOCK · EUCLOGIKE · Bridge-Burners LLC / Fiddler · Euclid IX.20, live-c→EIGHT DOMAINS, ONE SINK · PHSLOGIKE · Bridge-Burners LLC / Fiddler · real Wikipedia subca→EIGHT DOMAINS, SATURATED · EDSLOGIKE · Bridge-Burners LLC / Fiddler · 8 knowledge domains →THE ELECTRON PROBE · ELPLOGIKE · Bridge-Burners LLC / Fiddler · firing a particle th→TWO ENTANGLED CLOUDS · TECLOGIKE · Bridge-Burners LLC / Fiddler · Philosophy and Ethic→THALES OF MILETUS · Ithe first to PROVE — a truth that must follow by argument, n→PYTHAGORAS & THE BROTHERHOODthe front (c. 570 BCE) — number as reality, and the first pr→PARMENIDES OF ELEAthe front (c. 515 BCE) — reason over the senses; the first r→ZENO OF ELEAthe front (c. 490 BCE) — the paradoxes of motion; the first →ARISTOTLE · IIthe first SYSTEM of valid inference — the syllogism + the th→EUCLID · IIIthe first complete deductive EDIFICE — from 10 axioms, all o→CHRYSIPPUS & THE STOICS · IVpropositional logic — the truth table & the gate, ~2000 →RAMON LLULL · Vthe first machine of thought — rotating wheels that generate→WILLIAM OF OCKHAMthe medieval root (c. 1320) — Ockham's razor, suppositi→LEIBNIZ · VIthe hinge — 'Calculemus!' · reasoning reduced to c→GEORGE BOOLE · VIIthe destination — logic becomes an algebra of 0 and 1; AND i→AUGUSTUS DE MORGAN · VIIIthe duality — negation swaps ∧ and ∨; why one NAND gate buil→WILLIAM STANLEY JEVONSthe Boolean cleanup (1866) — the LOGIC PIANO, the first mach→JOHN VENNthe visual logic (1880) — the Venn diagram: a logical statem→ERNST SCHRÖDERthe Boolean cleanup (1890–1905) — the canonical Algebra of L→GOTTLOB FREGE · IXthe greatest leap since Aristotle — quantifiers ∀/∃, relatio→KURT GÖDEL · Xthe limits — true statements no system can prove; numbering →ALAN TURING · XIthe machine — computation defined, the universal computer, t→GIUSEPPE PEANOlogike · arithmetic from a zero, a successor, and induction →MOSES SCHÖNFINKELlogike · combinatory logic — functions with no variables (19→WILHELM ACKERMANNlogike · the first computable-but-not-primitive-recursive fu→W. V. O. QUINElogike · Quine–McCluskey — the smallest expression for a tru→RICHARD DEDEKINDlogike · the cut — an irrational built from nothing but frac→N. G. DE BRUIJNlogike · the shortest loop that contains every string once (→CLAUDE SHANNON · XII · THE CLOSERthe gate — Boolean algebra IS the algebra of switches (1937)→CHARLES SANDERS PEIRCE · XIIIthe foundations rank — one sign builds all logic (NOR, the a→GEORG CANTOR · XIVthe foundations rank — the infinite has sizes; the diagonal →BERTRAND RUSSELL · XVthe foundations rank — the paradox that broke Frege (1902); →ALONZO CHURCH · XVIthe foundations rank — the λ-calculus: computation as pure s→DAVID HILBERT · XVIIthe foundations rank — the program the whole crisis answered→JAN ŁUKASIEWICZ · XVIIIthe foundations rank — a THIRD truth value (many-valued logi→ALFRED TARSKI · XIXthe foundations rank — the definition of TRUTH (model theory→ADA LOVELACE · XXthe other half — the first algorithm (Note G, 1843); the lea→CHRISTINE LADD-FRANKLIN · XXIthe other half — the antilogism: one test for every syllogis→RÓZSA PÉTER · XXIIthe other half — founder of recursion theory; a function tha→JULIA ROBINSON · XXIIIthe other half — Hilbert's 10th: no algorithm decides i→RUTH BARCAN MARCUS · XXIV · THE OTHER HALF CLOSESthe other half — the first quantified modal logic (1946) &am→EMMY NOETHER · XXVthe other half — the algebra of STRUCTURE (groups/rings/idea→STEPHEN KLEENE · XXVIthe other half (men) — regular expressions = finite automata→GERHARD GENTZEN · XXVIIthe other half (men) — natural deduction & the sequent c→SAUL KRIPKE · XXVIIIthe other half (men) — possible-worlds semantics: the meanin→HASKELL CURRYthe modern foundations — combinatory logic (compute with NO →EMIL POSTthe modern foundations — production systems; the Post Corres→LUDWIG WITTGENSTEINthe modern foundations — the Tractatus (1921): the truth tab→GEORGE BOOLOSthe modern foundations — provability logic (GL): Gödel'→