Can argument schemes be organized by formal principles instead of lists?

Argumentation theory has a proliferation problem. Hastings (1962), Schellens (1985), Kienpointner (1992), the pragma-dialectical classification of van Eemeren and Grootendorst (1992), and the new-dialectical classification of Walton, Reed and Macagno (2008) each propose lists of argument schemes — sometimes overlapping, often disagreeing, with no agreed criteria for inclusion. Walton's list alone has more than sixty schemes. Each scheme has its own premise structure and conclusion form, and the boundaries between schemes are negotiable.

The Wagemans diagnosis: the existing classifications proceed by family resemblance. A new scheme is added when an author recognizes a new pattern; consolidation happens when two schemes look similar enough to merge. There is no underlying ordering principle that says where schemes come from or whether the list is complete. The result is unsatisfactory for theoretical, empirical, and computational purposes.

The Periodic Table replaces this with a classification based on formal ordering principles — three orthogonal axes that generate the space of possible argument types. Every existing scheme can be placed in a cell; cells exist whether or not anyone has named the scheme there; and the table is closed in a way the lists are not.

The methodological shift mirrors what the chemical periodic table did for elemental classification: from a contingent list of named substances to a structured space where empty cells are predictions. For computational argumentation — including LLM-based argument analysis — the table provides what the list approach lacked: a finite, well-defined target space for classification, where "argument type" has a definition rather than a custom.