Delta Quadrant

The Periodic Table of Arguments considers an argument as a combination of one conclusion and one premise, both of which are expressed through statements that contain a subject and a predicate. Depending on the constellation of these subjects and predicates, an argument takes one of four possible argument forms. Arguments that share the same form are situated in the same quadrant of the table. [Read more about the theoretical framework and the basic terminology of the PTA.]

The Delta Quadrant pictured above hosts all so-called ‘second-order predicate arguments’. The conclusion and premise of such arguments have the same subject (proposition q) and different predicates (T, meaning ‘true’, and Z), which means they have the argument form:

q is T, because q is Z

An example is We only use 10% of our brain, because Einstein said so, which can be reconstructed as We only use 10% of our brain (q) [is true (T)], because [we only use 10% of our brain (q)] was said by Einstein (Z).

Within each quadrant, arguments are further differentiated based on their argument substance, the specific combination of types of statements. This is done by labelling the conclusion and the premise as a statement of fact (F), value (V), or policy (P). The example just mentioned has a statement of value as its conclusion and a statement of fact as its premise, which means its argument substance is VF.

The working of arguments is based on the presence of a common term – the ‘fulcrum’ of the argument – and the existence of a relationship between the non-common terms – the argument lever. As pictured in Figure 4, second-order predicate arguments have the subject (q) as the fulcrum and the relationship between the predicates (Z and T) as the lever of the argument.

Figure 4. Conceptual representation of a second-order predicate argument

In the case of the above example, the lever is the relationship between was said by Einstein and is true. Since the former is taken to be authoritative of the latter, this argument can be called an argument from authority.

Other examples of arguments within this quadrant are:

the argumentum ad populum, which combines a statement of value (V) with a statement of fact (F)