The theoretical framework of the Periodic Table of Arguments takes an argument to consist of two statements, a premise and a conclusion, both of which contain a subject and a predicate. The Delta Quadrant of the table hosts all so-called ‘second-order predicate arguments’. The conclusion and premise of such arguments have the same subject (proposition q) and a different predicate (T, meaning ‘true’, and Z), giving them the 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 normalized 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 on the basis of an identification of the types of statements involved. By labeling the conclusion and the premise as a statement of fact (F), value (V), or policy (P), every argument can be characterized as a specific combination of statements. The example just mentioned combines a statement of value with a statement of fact.
The working of arguments is based on the presence of a common term – the ‘fulcrum’ of the argument – and the existence of a relation between the non-common terms – the ‘lever’ of the argument (see Wagemans, 2019). As pictured in Figure 4, second-order predicate arguments have subject q as the fulcrum and the relation 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 relation 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)
the argument from commitment, which combines a statement of value (V) with a statement of fact (F)
the argumentum ad baculum, which combines a statement of policy (P) with a statement of fact (F)
the argument from utility, which combines a statement of value (V) with another statement of value (V)
the argument from beauty, which combines a statement of value (V) with another statement of value (V)