Quodlibet · An instrument of the honest lattice
Build the Argument
A theorem at the base. A reading above it. Follow the links between them, and keep sight of what each link can carry.
An argument that leans on a theorem should be honest about which of its other claims are theorems too — and several of the claims in this collection are not. They come in four kinds, and the differences between them matter.
The honest lattice distinguishes theorem, reduction, framing, and analogy. Choose a framing below; the instrument follows its incoming links from the results beneath it. The links retain their original names. A completed path explains the reading’s support; it does not turn that reading into a theorem.
The arithmetic and reflection claims concern effectively axiomatized theories strong enough for arithmetic; The Endorsement and The Measure state the consistency or soundness assumptions each result needs. The cardinality shorthand for Löwenheim–Skolem concerns a countable language; The Original develops the model-theoretic setting. The diagram follows the collection’s explanatory relations, not a formal derivation of its framings.
The construction, followed
Choose the reading to build
The whole lattice remains in view. Lit claims belong to the path already followed; the ring marks the reading you chose. On a narrow screen, the diagram can be panned; the steps below carry the same account in text.
The path, read closely