In the Periodic Table of Arguments (PTA) framework, each argument type is defined by three key features: its form, substance, and lever. Together, these parameters let you classify and compare arguments systematically. To see how this works in practice, the Argument Type Identification Procedure (ATIP) (Wagemans 2026) provides detailed heuristics.
On this page, we briefly explain the first of those parameters: argument form.
Argument form refers to the specific configuration of the subjects and predicates in the conclusion and premise of the argument. The PTA distinguishes four basic argument forms, which we denote by the first four letters of the Greek alphabet.
The alpha form – a is X because a is Y
In argumentation of the form “a is X because a is Y”, the conclusion and the premise share the same subject but have different predicates. Such argumentation is based on a connection between the predicates: the fact that something (a) has a certain property (Y) somehow implies that this same something (a) also has another property (X). An example is “This movie is great because it was directed by Christopher Nolan”. In this case, the property of having been directed by Christopher Nolan (Y) points to the property of being great (X). The annotated version of this argument is “This movie (a) is great (X) because it (a) was directed by Christopher Nolan (Y)”. More examples are on the page dedicated to the Alpha Quadrant.
The beta form – a is X because b is X
In argumentation with the form “a is X because b is X”, the conclusion and the premise share the same predicate but have different subjects. The support depends on a specific relationship between the subjects a and b. Similarity is one possible relationship, as in “Mars is inhabited because Earth is also inhabited”, but other beta levers are possible as well. In this example, Mars (a) is attributed the property of being inhabited (X) on the basis of Earth (b), which is attributed the same property. The annotated version is “Mars (a) is inhabited (X) because Earth (b) is also inhabited (X)”. More examples appear on the page dedicated to the Beta Quadrant.
The gamma form – a is X because b is Y
The subjects and predicates of the conclusion and the premise can also both differ. In this case, the argument takes the form “a is X because b is Y”. Determining the gamma form alone does not establish whether the two pairs are meaningfully related. This is decided at the level of substance: the relationship between a and b may be identical to the relationship between X and Y (substance i), or the two relationships may differ in nature (substance d). An example of the first possibility is “Self-control is good because a hot temper is bad”, where self-control and hot temper (a and b) are opposites, just as good and bad (X and Y) are opposites. The annotated version is “Self-control (a) is good (X) because a hot temper (b) is bad (Y)”. More examples can be found on the page dedicated to the Gamma Quadrant.
The delta form – q is A/U because q is Z
The last form distinguished in the PTA is somewhat more complicated. In this case, to establish the acceptability or unacceptability of the conclusion, the arguer assigns a property to the conclusion as a whole. If we indicate that property by Z, the conclusion by q, acceptability by A, and unacceptability by U, the argument form can be reconstructed as “q [is A/U] because q is Z”. The acceptability or unacceptability of the conclusion, which usually remains unexpressed, has been added between square brackets. Delta-form argumentation is based on a relationship between Z and A/U. An example is “The economy has grown because that was said by Eurostat”, reconstructed as “The economy has grown (q) [is acceptable (A)] because that (q) was said by Eurostat (Z)”. More examples are on the page dedicated to the Delta Quadrant.
