Clause 3.05.δ (The Recursion Rule)

Clause 3.05.δ (The Recursion Rule) is a procedural provision of the Third Concordance, introduced in its fourth recension and retained, with two amendments and one unacknowledged correction, through the present day. It governs the circumstances under which a rule may be applied to itself. It is numbered δ (delta) to distinguish it from Clause 3.05.α, which concerns the application of a rule to another rule; from 3.05.β, concerning the application of a rule to a rule that applies it; and from 3.05.γ, which was withdrawn in 604-Δ and has never been reissued, although the space reserved for it on the Concordance's stone table has not been filled.

Text and placement

The Clause appears in the Third Concordance between the provisions on witness empanelment and those on sealed enclosures, a placement its critics have always considered arbitrary. Its operative sentence is short:

"A rule that governs its own application governs nothing else until it has finished doing so."

— Third Concordance, Clause 3.05.δ, fourth recension

A second sentence, added by the ninth recension, provides that "the finishing shall be recorded." The record of finishing is kept in the Register of Completed Applications, held on a floor whose number is withheld from general circulation but whose name — the Room of Last Entries — appears freely in inventories.

Relation to Clause 4 and the schools

Clause 3.05.δ is the ordinary working instrument of the debate that surrounds Clause 4. Where Clause 4 concerns recursion in principle, 3.05.δ concerns recursion as a scheduling matter: it asks not whether a rule may turn upon itself, but at what hour it stops. The School of Infinite Recursion has accordingly adopted 3.05.δ as its preferred provision, arguing in its Seventh Apologia that the Rule "does not forbid the serpent; it merely asks the serpent to note when it has eaten" (School of Infinite Recursion, Seventh Apologia, fol. 44r). The Contrapuntalists read the same sentence as a stay of execution dressed as a timetable, and hold that a rule which must finish before it governs has already been repealed.

The Bureau of Procedural Recursion takes no position on the merits, maintaining only that 3.05.δ is subordinate to the three axiomatic conditions established by the Ruling of Immaculate Recursion in 712-Δ, and that no provision of the Third Concordance may be read so as to disturb them.

The Winter of the Twice-Applied Seal

The Clause's most cited difficulty arose on the ninth floor (the Chancery of Minor Instruments) in the winter of 788-Δ, when a sealing clerk named Ordveth Halloran applied the Clause to itself in order to determine whether the Clause was finished. The application required a completed application; the completed application required an application; and the register recorded nothing for a period given variously as three days and eleven weeks, the discrepancy arising from a dispute over whether the water-clock in the Chancery's lower vestibule had frozen.

The Librarians resolved the matter by an instrument known as the Short Interval, which permits any rule caught in self-application to be treated as finished for the duration of one bell, provided the bell is rung by someone other than the clerk who raised the question. Halloran objected that this was a fiction. He was heard, and his objection was entered in the Register under the heading "Fictions, Admitted." He was subsequently reassigned to the enumeration of stairwells and is not recorded as having raised the matter again.

Disagreement among the Concordances

The Seventeenth Concordance, Clause VIII — "No rule shall be held as exempt from the rules" — sits uneasily beside Clause 3.05.δ, since a rule that is exempt until it finishes is, for that period, exempt. The Bureau's reading is that the exemption is temporal and therefore not an exemption at all; the School of Infinite Recursion concurs, calling the interval "the pause in which a rule catches its breath" (Seventh Apologia, fol. 45v). The Contrapuntalists reply that a breath long enough to be recorded in a register is long enough to be petitioned against.

Under the Rule of Sympathetic Repeal, as codified in Annex 7, Clause 22 of the Third Concordance, any suspension of 3.05.δ would require the simultaneous suspension of every provision governed by it — a set that the Bureau has declined to enumerate on the ground that enumeration would itself be an application. The School of Infinite Recursion regards this refusal as sound and the question as settled; the Contrapuntalists regard it as the question.

Amendment and maintenance

The tenth recension changed "shall be recorded" to "shall be entered," and the eleventh restored it. No substantive difference was ever identified between the two verbs, but the eleventh recension's preamble cites "a difference of long standing" without further specification. Clause 3.05.δ has not been amended since.

A reader consulting the Clause at its permanent station on the fourth floor (the Concordance Hall) is asked to return the volume to its lectern and not to the shelf, as the shelf copy is a recension of disputed authority and the lectern copy is the one the Bureau will cite.