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 second parameter: argument substance.
Where argument form tells us how a premise and conclusion are structurally connected, argument substance digs deeper into what the statements are actually about. In other words: once we know the form, the next step is to ask what kind of content is being related. This distinction matters because two arguments can share the same form but still differ in type due to their differing content.
Importantly, each argument form has its own way of determining substance, based on the kinds of meaning that are relevant for 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. An example is “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 way, we can distinguish arguments that look the same structurally but operate within 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 the subjects a and b is different from that between the 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: if the relationship between the subjects differs from the relationship between the predicates, no meaningful gamma lever can be formulated. The premise then fails to provide the relational support required by this argument form.
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 level of the lever, not at the level of substance.
PERIODIC TABLE OF ARGUMENTS 