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 Gamma Quadrant pictured above hosts all so-called ‘second-order subject arguments’. The conclusion and premise of such arguments have different subjects (propositions q and r) and the same predicate (T, meaning ‘true’), giving them the form:
q is T, because r is T
An example is He must have gone to the pub, because the interview is cancelled, which can be reconstructed as He must have gone to the pub (q) [is true (T)], because the interview is cancelled (r) [is true (T)].
Within each quadrant, arguments are further differentiated based on 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 has a statement of value as its conclusion and another statement of value as its premise, which means its systematic type indicator is ‘2 sub VV’ (second-order subject argument combining value and value).
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 3, second-order subject arguments have the predicate (T) as the fulcrum and the relationship between subjects (q and r) as the lever of the argument.
Figure 3. Conceptual representation of a second-order subject argument
In the case of the above example, the lever is the relationship between he must have gone to the pub and the interview is cancelled. Since the former proposition is taken to be disjunctive with the negation of the latter, this argument can be called an argument from disjuncts.
Other examples of arguments within this quadrant are:
the argument from opposites, which combines a statement of value (V) with another statement of value (V)