19. A figure is an alphabet read at several levels

Context

Llull's ternary Ars letters nine principles B to K, skipping J. The same letter names a dignity, a relation, a question, a subject, a virtue or a vice, depending on which table it is read against — and that multiple assignment is the device, not a convenience of notation. Turning three concentric wheels produces chambers of letters; what a chamber says depends on the level.

The existing Device does not fit. Its slots are different sets and a reading is a product across them. A figure draws every position from one alphabet, and a chamber is a combination rather than a product.

Decision

Figure sits beside Device: an alphabet, a set of levels mapping each letter to a name, and chambers(arity) giving the combinations. llull_figure accepts a chamber written either as letters or spelled out at any level, and if no level is named it asks whether some level reads — the satisfiability question this package keeps arriving at.

Kircher's Ars Magna Sciendi becomes a preset rather than an implementation, because it is the same mechanism with a different stock.

Consequences

Counts are computed, never quoted: 84 ternary chambers and 36 pairs for Figura A fall out of nine letters, and the number of entries in the printed tabula stays unchecked until someone reads a facsimile. That follows the rule the expansion research set — recomputing beats citing, in a field where the headline numbers are often wrong.

Matching spelled-out principles needed the Denckring's segmentation rather than a word split, because some names are several words long: the ninth question is Quomodo et cum quo, and splitting on whitespace would never find it.

Two things stay in notes rather than being smoothed away. The wheels do not freely generate new truths — the stock is fixed and heterodox combinations are excluded elsewhere in the Ars, which is Eco's point and cuts against how the device is usually described. And the reading of the figure as a first computer is reception, not a finding about the object.

ars_combinatoria moved to checkability: none. It names a tradition, not a procedure: what counts as a valid combination is whatever the particular device specifies, and its instances — this figure, the Denckring, Queneau's sonnets, Kuhlmann's Wechselsatz — are catalogued and checkable separately.