This page gives a general introduction to the argument types in the Gamma Quadrant of the Periodic Table of Arguments (PTA). It builds on a basic understanding of its theoretical framework and terminology.
The Periodic Table of Arguments analyzes an argument as consisting of three statements: a conclusion, a premise, and a lever. Each statement has a subject and a predicate. Depending on how these are arranged, an argument takes one of four argument forms. Here we discuss the gamma form, where the conclusion and the premise have different subjects (a and b) and different predicates (X and Y):
a is X because b is Y
Within each quadrant, arguments are further differentiated based on their argument substance. For arguments with a gamma form, this comes down to one simple check: is the semantic relationship between the subjects the same as that between the predicates, or is it different? If it’s the same, the substance is labeled i (for “identical”). If it’s different, the label is d (for “different”).
Identical relationships
When the substance is i, we find arguments such as the argument from synonyms (Sy), the argument from opposites (Op), the argument from converses (Cve), the argument from derivatives (Der), and the argument from integratives (Int). All of these rest on the idea that the link between subjects mirrors the link between predicates. In the argument from converses, for instance, the subjects and the predicates are converse pairs that describe one and the same relation from either end (e.g., “landlord” and “tenant”, “sent” and “received”).
Different relationships
When the substance is d, this usually means that something has been left implicit. In that case, we are dealing with a “condensed” gamma form argument, and the analyst can use a step-by-step procedure to spell out the missing information (see Saadat-Yazdi & Wagemans, 2025). Once the missing statement has been inserted, each of the resulting arguments is characterized in its own right. Only where no suitable insertion can be found does the premise fail to contribute to the acceptability of the conclusion, and the argument is identified as a non sequitur (Non).
