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Ars combinatoria

ars_combinatoria · permutation · catalogued

A text generated by systematically combining terms drawn from fixed sets, the sets and their order being the whole of the method.

Provenance

  • Source: Ramon Llull, Ars Generalis Ultima (1305); named as such by Leibniz (1666)
  • Attribution: primary — a named author, work and year this catalogue stands behind
  • Checkability: none — no computable acceptance criterion exists
  • Attested: author-stated — the originator set this rule down

Details

  • Kind: constructive
  • Languages: en
  • Requires: tokens
  • Deterministic: yes
  • Also known as: combinatory art
  • In other languages: Kombinatorische Kunst (de), Art combinatoire (fr)

Notes

This names a tradition rather than a single procedure: what counts as a valid combination is whatever the particular device specifies, so there is no criterion to check at this level. Its instances are checkable and are catalogued separately — llull_figure, denckring, cent_mille_milliards, wechselsatz.

Prompt hint

Combine one term from each set, in order, and write out what the combination asserts.

Why this has no checker

This procedure has no computable acceptance criterion, so it will never be implemented. It is catalogued because the form belongs in an honest survey of the field, and denckring status counts it separately rather than reporting a gap that cannot close.