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 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’), which means they have the argument 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 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 argument lever. 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)