Can three axes organize all possible argument schemes?

The Periodic Table of Arguments proposes that any argument can be located along three orthogonal axes. The first distinguishes subject arguments from predicate arguments — derived from formal-linguistic analysis of how the constituents of an argument scheme are structured. The second distinguishes first-order from second-order arguments — in sign argumentation the standpoint is "Y is true of X", whereas in argument-from-authority the speaker's standpoint is just "X" and the acceptability of the whole standpoint becomes itself a subject. The third distinguishes proposition types — every argument has a standpoint proposition and a supporting proposition, each of which is a proposition of policy (P), value (V), or fact (F), generating nine combinations PP, PV, PF, VP, VV, VF, FP, FV, FF.

The structural move is to replace an open-ended list of named schemes (sign, criterion, pragmatic, authority, ad baculum, similarity, equality, tradition, commitment, and dozens more) with coordinates in a three-axis space. Every named scheme in the existing literature maps onto a specific cell in this space. The space is closed; the list is not.

This is a genuine ordering principle rather than a taxonomy. Walton's list of 60+ schemes is a classification by family resemblance: schemes get added when a new pattern is recognized, and the boundaries are negotiable. Wagemans's table is a classification by combinatorics: the cells exist whether anyone has named the scheme in them or not, and every named scheme has exactly one address. The shift matters because the latter supports systematic comparison, computational identification, and the discovery of unfilled cells — claims that were not possible under the list approach.