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’ (see Wagemans, 2019). Arguments that share the same form are situated in the same quadrant of the table.
The Beta Quadrant pictured above hosts all so-called ‘first-order subject arguments’. The conclusion and premise of such arguments have different subjects (a and b) and the same predicate (X), which means their argument form is:
a is X, because b is X
An example is Cycling on the grass is prohibited, because walking on the grass is prohibited, which can be reconstructed as Cycling on the grass (a) is prohibited (X), because walking on the grass (b) is prohibited (X).
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 another statement of value as its premise, which means its argument substance is VV.
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 ‘lever’ of the argument (see Wagemans, 2019). As pictured in Figure 2, first-order subject arguments have the predicate (X) as the fulcrum and the relationship between the subjects (a and b) as the lever of the argument.
Figure 2. Conceptual representation of a first-order subject argument
In the case of the above example, the lever is the relationship between cycling on the grass and walking on the grass. Since the former is taken to be analogous to the latter, this argument can be called an argument from analogy.
Other examples of arguments within this quadrant are:
the argument from similarity, which combines a statement of fact (F) with another statement of fact (F)
the argument from equality, which combines a statement of policy (P) with a statement of fact (F)
the argument from comparison, which combines a statement of policy (P) with another statement of policy (P)