Do first-order and second-order arguments unify classical and modern divisions?

This is the conjectural payoff of the Periodic Table that goes beyond classification. Wagemans suggests that the first-order vs second-order distinction — whether the propositional content of the standpoint is "Y is true of X" or whether the entire standpoint "X" is treated as a subject whose acceptability is at issue — may reflect two long-standing dichotomies that argumentation theory has carried separately.

The first is the classical rhetoric / dialectic distinction between internal topoi and external topoi (topoi, loci). Internal topoi derive from the matter of the argument itself; external topoi appeal to authority, witness, tradition, or other sources outside the propositional content. The second is the modern argumentation-theory distinction between reasonable and fallacious arguments — where fallacies are characterized as arguments that systematically substitute appeal for inference.

If both dichotomies map onto the first-order / second-order axis, then a structural feature derivable from formal-linguistic analysis is doing the work that two distinct critical traditions have been doing in parallel. The internal / external divide and the reasonable / fallacious divide would be the same divide, recognized under different framings, and the Periodic Table would expose this with explicit machinery.

The status is conjectural — the paper presents it as a hypothesis worth investigating rather than a proved equivalence. But the move is consequential. If correct, it argues that fallacy theory has been doing structural work disguised as normative work, and that what makes an argument "fallacious" might be specifiable in formal-linguistic terms rather than (only) in dialectical-procedural ones. This is open territory for both philosophical argumentation theory and computational argument analysis.