In the framework of the Periodic Table of Arguments (PTA), each argument type is defined by three key features: its form, its substance, and its lever. Together, these parameters make it possible to classify and compare arguments systematically. If you want to see how this works in practice, the Argument Type Identification Procedure (ATIP) (Wagemans 2025) provides detailed heuristics.
On this page, we provide a short explanation of the first of those parameters: argument form.
The argument form refers to the specific configuration of the subjects and predicates contained in the conclusion and the 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 with the form “a is X because a is Y”, the conclusion and the premise have the same subject and a different predicate. 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 book is great because it was written by Javier Marías”. In this case, the property of being written by Javier Marías (Y) points to the property of being great (X). The annotated version of this argument is “This book (a) is great (X) because it (a) was written by Javier Marías (Y)”. More examples can be found 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 have the same predicate but 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 can be found 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 be different. 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 (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 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 in its entirety. 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 the Prime Minister”, reconstructed as “The economy has grown (q) [is acceptable (A)] because that (q) was said by the Prime Minister (Z)”. More examples can be found on the page dedicated to the Delta Quadrant.
PERIODIC TABLE OF ARGUMENTS 