The complete collection.

The construction and its foundations.

• The Diagonalone theorem at the foundations
• The KernelLawvere's theorem, in full
• The Mechanismhow a system learns to name itself
• The Ceilingthe limit that has no top
• The Floorrecursion, built from the bottom up
• The Knotparadox, and the thread that ties it
• The Silencewhere the diagonal goes quiet
• The Lawone construction, four fates, conserved
• The Multitudethe models a theory cannot tell apart
• The Keystonewhere proof and truth coincide
• The Barrierwhere the diagonal meets its limit

Self-reference as a source of recursion.

• The Enginethe generative face of self-reference
• The Combinatorsthe fixed point, in plural
• The Pluralthe fixed-point combinator as a syntactic object
• The Clockthe tempo that tells the combinators apart
• The Tollwhat types exact for taming the fixed point
• The Operatorthe fixed point as a mathematical object

Proof, reflection, and the climb through theories.

• The Ascentwhy the diagonal cannot be escaped
• The Measurethe reflection ladder and its ordinal
• The Lawthe logic of provability
• The Recurrencethe diagonal turned on itself
• The Summitreflection becomes an axiom
• The Gapproof, truth, and the wall between them
• The Endorsementtruth, the Liar, and the soundness a system cannot give itself
• The Jumpthe halting problem relativized, and the tower it builds
• The Orderevaluation strategy, and how a fixed point computes
• The GroundKripke's fixed point, revision, and the truth a language can hold of itself
• The Continuumthe size of the reals, and why ZFC cannot fix it
• The Quinethe recursion theorem, and a program that holds its own code
• The TowerGirard's paradox, and why no universe contains itself

Models, meaning, and the search for a foundation.

• The Descentwhy the ground recedes
• The Originalthe model that maps into all the rest
• The Impostorsthe anatomy of the nonstandard
• The Relativitythe size that is not absolute
• The Regressgrounding is ascent, and the ascent conserves the obstruction
• The Confluenceone distance, two forces, four descents

The theorem and its six movements.

• The Mirrorthe one theorem beneath the corpus
• The TheoremThe Mirror, I of VI — Quodlibet
• The ProofThe Mirror, II of VI — Quodlibet
• Where It LandsThe Mirror, III of VI — Quodlibet
• What Grants ItThe Mirror, IV of VI — Quodlibet
• The DialThe Mirror, V of VI — Quodlibet
• The CostumesThe Mirror, VI of VI — Quodlibet

The apparatus of the argument.

• Scholiathe formal apparatus of the corpus
• The Keystonea guide to the apparatus, opened up
• The Substratethe categorical setting, in depth
• The FulcrumLawvere's theorem, proved in full
• The Fatesthe instances of Lawvere's construction, worked
• The Boxprovability logic, and the unique fixed point
• The Bridgesthe formal theory of reduction, and what makes an instance
• The Horizonwhere the construction's reach ends
• The Recurrencethe epistemology of multiple discovery
• The Forgethe constructive face, where the fixed point builds
• The Loomthe coinductive face, where the infinite is woven
• The Prismone construction, refracted into three modes
• The Correspondencepropositions, types, and the proof that Y is falsity

The history and the figures behind the construction.

• The Annalsa history of the discovery
• The Thresholdwhat it takes for a paradox to become a theorem
• The Recurrencemultiple discovery and the one forced object
• The Obversethe diagonal’s two faces, and why one came so late
• The Tribunalwhere the likeness stops being a proof
• The Calculusprovability as a modal operator, and the fixed point made explicit
• The Correspondenceprograms are proofs, and the fixed point is the price of both
• The Replicatorthe recursion theorem, and the diagonal as the logic of self-reproduction
• The Jumpthe diagonal relativized, and the endless hierarchy of the unsolvable
• The Stagesthe iterative conception, and how the universe escapes the diagonal

The collected edition, with its frontispiece and shorter studies.

• Quodlibetthe fixed point and its consequences
• Scholiathe apparatus
• The Anatomythe one construction, dissected
• The Annalsa history of the discovery
• The Ascentwhy the diagonal cannot be escaped
• The Atlasthe universe of the diagonal
• The Boxprovability as its own logic
• The Coilthe benign face of circularity
• The Collationthe corpus checked against its own standard
• The Descentno floor
• The Diagonalone theorem at the foundations
• The Enginethe diagonal read forwards
• The Horizonincompleteness as an information bound
• The Knotthe object that holds its own maps
• The Latitudethe second root of mathematical limitation
• The Mirrorthe keystone
• The Provenancewhere a fixed point comes from
• The Recurrencewhy one construction, six times
• The Staircaseincompleteness, measured in ordinals
• The Wallthe diagonal's own boundary
• The Webthe shape of self-reference

The original frontispiece and studies, retained as a distinct earlier edition.

• The Diagonal
• The Atlas
• The Ascent
• The Descent
• The Mirror
• Quodlibet · original frontispiece
• The Engine
• Scholia
• The Annals
• The Lathe

The Line and The One Number: wage-law instruments from the original collection.

• The One Number
• The Line

A separately written frontispiece with its own design and reading paths.

• Quodlibet · rewritten introduction

The five named editions, from the original three-movement essay to the final refinement. The three intermediate releases were reconstructed in the original authoring session.

• The Descent · 1.0.0
• The Descent · 1.1.0
• The Descent · 2.0.0
• The Descent · 2.1.0
• The Descent · 3.0.0

About the five releasesRelease notes

The distinct project frontispiece and its eight readings. This preserves that edition’s organization.

• Quodlibet · project frontispiece
• The Diagonal
• The Atlas
• The Engine
• The Ascent
• The Descent
• The Mirror
• Scholia
• The Annals

Continuations of the original collection’s unfinished interactive work.

• Build the ArgumentFollow the honest lattice, one link at a time

The original PDFs and their illustrated editions. Images retain their native files and dimensions; each reader includes a link to the full-size original.

• One ConstructionOriginal eight-page PDF
• The Fixed PointOriginal five-study broadside · PDF
• One Construction · Illustrated ReaderEight page images and searchable text
• The Fixed Point · Six-Study BroadsideThe distinct later broadside, including The Engine
• The Fixed Point · Original ImageNative 1500 × 2000 PNG
• One Construction · Original PreviewNative PNG