Recursive Definitions

Recursive Definitions

Recursive Definitions are a class of definitional instrument in which a term is specified by reference to itself, either directly or through a chain of intermediate terms that returns to the point of origin. Within the Tower they are recognised as a distinct documentary species under Article I: Definitions, and, where a recursive definition is used to establish the validity of the instrument containing it, the resulting document is classified as a Scroll of Recursive Definitions. Lesser recursive definitions — those that define a term without thereby settling any question of their own force — are termed open by the Courts of Definition and are catalogued separately.

The distinction is not idle. Open recursive definitions are in routine use throughout the archive and excite no comment; it is the closed sort, and the procedural consequences attending it, that have occupied the Tower for the greater part of a century.

Origin and the Font

The drafting of recursive definitions is administered jointly by the Font of Unwritten Definitions, which produces the draft text, and the Custodial Spire for Recursive Amendments, which revises it. The arrangement is described in the concordance governing both bodies as one of "mutual revision without precedence" (Third Concordance, Annex 4), and in practice neither office will date its own contribution first. Drafts bearing the seal of one office and the correction marks of the other are held to be complete; drafts bearing only one are held to be pending, sometimes for decades.

The Font's name records a genuine curiosity of its work: recursive definitions are conventionally drafted with the defining term left blank, the blank being filled at revision by the Custodial Spire. The Font's archivists maintain that a recursive definition written out in full at the first sitting has never once survived revision unaltered, and so the blank is now considered a technical requirement rather than a convenience.

Instability and the Unfurled Scroll

Recursive definitions have a documented tendency to generate instability in the calendar systems of the floors on which they are deposited. The Scroll of Recursive Definitions formally documented this instability in the Year of the Unfurled Scroll, and its Annex C, the 'Prologue of the Unaffixed Seal', remains the standard account of a definition that could not be closed because the clause closing it required a definition that could not be closed. The Year of the Unfurled Scroll ran to fourteen months while the matter was unresolved.

Since that episode, the Bureau of Referential Integrity has been the office of first recourse in conflicts arising from citation loops, and the Post of Recursive Oversight is required to countersign any recursive definition entering The Wing of Recursive Application. Countersignatures of the Post are frequently deferred, a circumstance the Post attributes to workload and other offices attribute to the Post.

Disputed Jurisdictions

Scholars disagree sharply over whether an open recursive definition becomes closed upon citation by a document that is itself recursive. The Courts of Definition hold that the closure is effected at the moment of citation, in the matter of the Third Descant of the Rota, and the Bureau of Referential Integrity holds that it is effected only at the moment of seal. Since the two offices seal citation amendments differently, a definition can be simultaneously open and closed for the whole of a session of the Courts.

"A term defined by reference to a document that defines itself is not thereby defined twice, but once in two places."

— Marginalia of Lantern-Keeper Osveil, at Part I: Definitions of Litigation, folio 61

The position of the Font of Unwritten Definitions is that the question is improperly framed, since the blank in an unrevised recursive definition makes the matter moot until revision, and revision is precisely what the question presupposes. This view has the merit of being unanswerable and the drawback of having been offered by every officer of the Font since the dispute began.

Cataloguing and Loss

Recursive definitions are catalogued by Recursive Folios and, where a large body of them has accumulated, protected by the machinery described in The Recursive Certification Loop. The principal hazard of the species is not contradiction but circular loss: a definition that cannot be closed cannot be shelved, and a definition that cannot be shelved cannot be closed. Sections of the archive known to hold such material are marked with an affixed pausal tab, and no member of the public is to be admitted to an open section while a tab is disturbed.

A surviving inventory from the winter termination of a recursive definition on a floor since renumberd records the ordinary measures taken:

• four scrapers of horn, unreturned, charged to the Custodial Spire;
• eleven damp cloths;
• one ladder, borrowed from the floor below, of a length that floor disputes;
• the seals of both offices, held against signature pending a second sitting;
• a note that the draught was from the eastern stair and the door had not been found.

Adjacency

The Atrium of Recursive Truth and The Atrium of Recursive Truth are commonly taken to be two names for one place, and the clerical error that produced the duplicate entry has been permitted to stand on the grounds that correcting it would require a recursive definition of the correction, invoking the very office that caused it. The Atrium of Recursive Truth remains the only holding in the archive whose two entries cite each other without remainder.

Definitions of the open sort are indexed under Definitions. Recursive definitions outside the Tower's walls are not contemplated; the question is treated as a category error and, per Article I: Definitions, is not entered in the register.