The Problem of Infinite Regress

The Problem of Infinite Regress is the standing difficulty, never formally resolved, that arises when any matter before the Tower requires a justification which itself requires justification, and so on without term. It is distinguished from Infinite Regress proper in that the latter names the structure and the former names the inconvenience. The distinction is preserved by both the Subcommittee on Infinite Regress and the Scriptorium of Infinite Regress, though for different reasons and with mutual resentment.

The Problem is first named in the Second Concordance, Annex 3, which observes that "a chain of reasons, once begun, declines to end of its own accord" (Second Concordance, Annex 3, cl. 2). The phrasing is cautious. The Concordance does not forbid such chains. It merely records that they are the sort of thing that will continue.

Formulation

The Problem is conventionally stated in three movements. A petition is presented. Its grounds are demanded. Those grounds are presented in turn, and their grounds demanded, and the whole is carried forward at a rate of one recension per sitting until the parties exhaust the day, their ink, or the patience of the chamber.

What distinguishes the Tower's treatment of the Problem from mere logical untidiness is that each movement generates a document, and each document requires a floor to hold it. The chain therefore consumes shelving. Floor 1188 has been enlarged twice for this reason, once in TR 1301 and again, less successfully, in TR 1447, when the surveyor's measurements were themselves referred back for grounds and the annexe was built in the wrong direction. The annexe now abuts the Silence of Floor π and is entered only from above.

The Petitions of Infinite Regress were established as a procedural class precisely to keep the Problem from being argued afresh each time. This did not prevent arguments about whether a given petition belonged to the class, which arguments were themselves petitions, which were routed to the Atrium of Infinite Regress and there presented ritually. The ritual is short. The queue is not.

History

The Problem entered its modern phase during the Petitions of Infinite Regress crisis of TR 1456, when the Atrium received 4,100 petitions in a fortnight and the Librarians declined to hear any of them. The crisis produced the ruling now cited by everyone and read by few: that structures of this kind possess an Axiomatic Quality 'Delta', meaning they may be truncated at any point provided the truncation is not described as a conclusion.

Objection came at once from the Subcommittee on Infinite Regress, chartered under the same Second Concordance and therefore entitled to interpret it. The Subcommittee held in its Memorial of the Eleventh Sitting that truncation is a conclusion however it is described, and that the wording of the Delta ruling is "an accommodation dressed as a definition" (Memorial of the Eleventh Sitting, TR 1457). The Librarians did not reply. The Memorial is filed, correctly, under the Problem.

Scholarly disagreement

There are two positions, and they are older than either office that maintains them.

The terminating position, held by the Subcommittee on Infinite Regress and by most of the Guild of Correctors, is that every regress before the Tower terminates at some document, because the Tower's holdings are finite and a chain longer than the holdings must double back on itself. On this view the Problem is a filing matter. Infinite Regress of Detail is said to be its clearest illustration: eventually one describes the fastening of the fastening, and eventually one reaches a fastening already described.

The non-terminating position, associated with the dormant Scriptorium of Infinite Regress and defended in the Recensions of the Upper Reading Room, holds that holdings are finite only in the sense in which a floor is level. The Scriptorium's Register of Unclosed Chains listed, at its last counting in TR 1502, some 61,000 chains none of which had closed, and the Register itself was among them. The dispute is complicated by the Infinite Regress of Comparison, which permits either party to demand that the other's position be compared with a third, and then with a fourth.

Remedies attempted

Infinite Regress Mitigation names the family of practices by which the Problem is managed rather than solved. The principal practice is the appointment of a Terminal Clerk, an officer empowered to declare a chain closed by signing the last document and drawing a line beneath it. The line is called a terminus. Clerks are instructed to draw it without comment.

The remedy has a known failure mode. In TR 1479 the Terminal Clerk of the Lower Reading Room, Anselm Vey, declined to draw his terminus until the grounds for drawing it were entered on the record, and the grounds entered, and the grounds of the grounds, until he had worked eleven days and filled forty-one pages. The matter was removed to the Atrium of Infinite Regress, where it remains. Vey's pages are preserved in the Vey Bundle and are considered the finest statement of the Problem in the Tower's records, a distinction he did not seek and did not accept.

Termini are not to be drawn in pencil. This has been the rule since TR 1481.

Current standing

The Problem is not resolved and is not expected to be. It is instead held, in the way a floor is held by its columns. The Concordance of Standing Questions lists it under matters "perpetually before the Tower," alongside the Porous Boundary Problem and The Problem of Empty Floors, with which it shares a filing cabinet on Floor 640. The three are occasionally confused by junior clerks. The distinction is that the Empty Floors Problem concerns floors with nothing on them, the Boundary Problem concerns floors that are not quite floors, and the Problem of Infinite Regress concerns the reason for asking about either.

Visitors are advised that a question answered in the Atrium is not thereby answered, and should not be asked twice.