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 second parameter: argument substance.
Where the argument form tells you how a premise and conclusion are structurally connected, the argument substance digs deeper into what the statements are actually about. In other words: once you know the form, the next step is to ask what kind of content is expressed. This distinction matters because two arguments can share the same form but still differ in type because of their different content.
Importantly, each argument form determines substance in its own way, based on the kinds of meaning relevant to that structure. Let’s go through the four forms and see how the substance is determined.
The substance of alpha form arguments
In arguments of the alpha form – a is X because a is Y – the same subject (a) is given two different predicates (X and Y). Here, the key to substance lies in the type of predicate. Predicates fall into three categories:
- fact (F): about how things are in the world, empirically checkable.
- value (V): expressing a judgment, evaluation, or appraisal.
- policy (P): about what should be done, or which course of action to take.
Substance is coded with two letters: the predicate type of the conclusion, followed by that of the premise. For example: “This movie is great because it was directed by Christopher Nolan”. The conclusion makes a value judgment (V) and is supported by a factual claim (F). So its substance is ‘VF’. This lets us distinguish arguments that look the same structurally but operate in different semantic domains.
The substance of beta form arguments
In arguments of the beta form – a is X because b is X – the reasoning transfers a predicate (X) between two different subjects (a and b). What matters now is the type of subject:
- singular (s): one specific entity.
- particular (p): some members of a group.
- universal (u): all members of a category.
The two-letter code records the subject type in the conclusion and in the premise. In the argument “Mars is inhabited because Earth is also inhabited”, for instance, both conclusion and premise are singular statements, so the substance is ‘ss’. This makes it possible to tell apart, for example, singular-to-singular analogies from singular-to-universal generalizations, even though both share the beta structure.
The substance of gamma form arguments
For arguments in the gamma form – a is X because b is Y – the substance lies in the semantic relationship between the subjects and predicates. The decisive feature is whether these relationships are:
- identical (i): subject a relates to subject b in the same way as predicate X relates to predicate Y.
- different (d): the relationship between subjects a and b differs from that between predicates X and Y.
In the argument “Self-control is good because a hot temper is bad”, for instance, the subjects and predicates relate to one another in the same way, so the substance is i. Substance d has a special status: where the relationship between the subjects differs from the relationship between the predicates, information has often remained implicit. The argument is then read as a “condensed” gamma argument and reconstructed by inserting the missing intermediate statement, after which each resulting argument is characterized in its own right. Only where no suitable insertion can be found does the premise fail to provide the relational support required by this argument form, and the argument is identified as a non sequitur.
The substance of delta form arguments
Arguments in the delta form – q is A/U because q is Z – have a conclusion whose acceptability (A) or unacceptability (U) is supported by a premise that attributes an external predicate to that conclusion. In this case, argument substance is determined by the perspective from which the premise is presented:
- I (first person): the speaker about themselves.
- II (second person): the speaker about the addressee.
- III (third person): the speaker invoking someone else (an expert, institution, authority).
In the argument “The economy has grown because Eurostat says so”, for instance, the substance is III because Eurostat is a third party. The code III identifies the perspective from which the supporting statement is presented. Whether Eurostat is sufficiently epistemically authoritative to support the conclusion is expressed and assessed at the lever level, not the substance level.
