Having explained the Comprehensive Assessment Procedure for Natural Argumentation (CAPNA), we turn to describe the second framework we use for designing a procedure for assessing the reasoning aspect of natural argument: the argument categorisation framework of the Periodic Table of Arguments (PTA).Footnote 3 Using this framework enables a specification of the Reasoning level analysis of CAPNA. At the same time, while the PTA so far has been mainly used as an analytical tool for argument type identification and annotation (Visser et al. 2018, 2021; Gobbo et al. 2019) its use in specifying parts of the comprehensive assessment procedure articulates how it can also be used as an evaluative tool.
The categorisation framework of the PTA has in common with logical taxonomies of argument that it takes logical form as a defining characteristic of an argument type. However, it also differs from these taxonomies in that logical form is not the only characteristic taken into account. Inspired by the classical dialectical and rhetorical taxonomies of arguments, which define argument types on the basis of their content rather than form, two other characteristics are added to the theoretical framework of the PTA: argument substance and argument lever. Since the PTA defines an argument type as the specific combination of these three parameters (form, substance, and lever), it can be characterized as a ‘combinatorial’ or ‘factorial’ taxonomy of arguments.
Within the theoretical framework of the PTA, an argument is conceptualized as a combination of two statements–a conclusion and a premise. It is further assumed that an arguer puts forward the premise in order to support the conclusion, i.e., to make the conclusion (more) acceptable in the eyes of the addressee. In other words, when viewed from a pragmatic perspective, the arguer aims at changing the epistemic status of the conclusion from ‘doubted’ to ‘accepted’. We refer to this projected change in epistemic status of the conclusion with the term ‘acceptability leverage’.
To explain how the acceptability leverage from the premise to the conclusion works, the PTA assumes the ‘law of the common term’. This law states that the premise, in order to fulfil its pragmatic aim of rendering the conclusion (more) acceptable, should share exactly one common term with the conclusion. While this common term functions as the ‘fulcrum’ of the leverage of acceptability taking place within the argument, the relationship between the non-common terms, which expresses the underlying mechanism of the argument, functions as its ‘lever’.
The law of the common term yields two basic possibilities of argument forms. If the statements share the same subject, the argument has the form ‘a is X, because a is Y’ and is characterised as a ‘predicate argument’ (pre). In this case, the subject (a) functions as the fulcrum and the relationship between the predicates (Y and X) as the lever of the argument. A concrete example is Unauthorized downloading (a) is not theft (X), because unauthorized downloading (a) does not deprive the original owner of the use of an object (Y), which has unauthorized downloading (a) as its fulcrum and the relationship between does not deprive the original owner of the use of an object (Y) and is not theft (X) as its lever.
The other basic possibility is when the common term is the predicate, which means the argument has the form ‘a is X, because b is X’. In this case, the predicate (X) is the fulcrum and the leverage of acceptability can be explained by assuming that there is some kind of relationship between the non-common terms of the premise and the conclusion, namely their subjects (a and b). Within the framework of the PTA, such arguments are called ‘subject arguments’ (sub). An example is Cycling on the grass (a) is prohibited (X), because walking on the grass (b) is prohibited (X), which has is prohibited (X) as its fulcrum and the relationship between cycling on the grass (a) and walking on the grass (b) as its lever.
In natural argumentative discourse, any statement can be expressed as a proposition or as an assertion. The difference between the two modes of expression is that in the latter, the arguer’s doxastic attitude regarding the statement is explicitly present in the discourse. The statement The president is doing a great job, for example, is expressed as a proposition, while the statement I believe that the president is doing a great job is expressed as an assertion. While both statements contain the proposition the president is doing a great job, the assertion additionally contains the doxastic attitude marker I believe that (see Fig. 2).
Within the theoretical framework of the PTA, the distinction between propositions and assertions is used to characterise arguments as ‘first-order arguments’ (1) or ‘second-order arguments’ (2). If the propositions of the statements share a common subject or predicate, as in the examples above, the argument is characterised as a first-order predicate argument (1 pre) or first-order subject argument (1 sub) respectively. If the statements have the proposition of the conclusion as their common term, the argument has the form ‘q is T, because q is Z’–‘T’ standing for ‘true’, a standard formulation of the doxastic attitude marker that may or may not have been expressed in the actual discourse and can be added or substituted by the analyst. Such a ‘second-order predicate argument’ has the shared proposition (q) as its fulcrum, while the leverage of acceptability can be explained by assuming that there is some kind of relationship between the predicate of the premise (Z) and that of the conclusion (T). An example is We only use 10% of our brain (q) is true (T), because we only use 10% of our brain (q) is said by Einstein (Z), which has we only use 10% of our brain (q) as its fulcrum and the relationship between is said by Einstein (Z) and is true (T) as its lever.
If the statements contain different propositions, they have the doxastic attitude marker as their common element and the acceptability leverage is based on a relationship between the propositions. Such arguments are called ‘second-order subject arguments’ and have the form ‘q is T, because r is T’. An example is He must have gone to the pub (q) is true (T), because the interview is cancelled (r) is true (T).
As said above, the theoretical framework of the PTA takes the conclusion and the premise of an argument to be expressed by statements. The third characteristic of arguments that constitutes this framework is the so-called ‘argument substance’, i.e., the specific combination of types of statements. This characteristic is determined on the basis of a widely used typology of statements that is developed in debate theory and distinguishes between statements of fact (F), statements of value (V), and statements of policy (P) (see, e.g., Broda-Bahm et al. (2004), Skorupski (2010), Freeley and Steinberg (2014). An argument can thus be said to substantiate one of nine possible different combinations of types of statements, conventionally starting with the type of statement expressed in the conclusion followed by that in the premise: PP, PV, PF, VP, VV, VF, FP, FV, FF. The government should invest in jobs, because this will lead to economic growth, for instance, can be characterized as a PF argument, since it combines a statement of policy (P) in its conclusion with a statement of fact (F) in its premise.
In sum, in identifying the type of argument, the analyst should classify it as (1) a first-order or second-order argument; (2) a predicate or subject argument; and (3) as one out of nine possible combinations of types of statements. The superposition of these three partial characterizations yields the systematic name of the argument. In order to illustrate this notion, we provide in Table 1 the systematic name of the examples given for each of the four basic argument forms.
In the visual representation of the PTA pictured in Fig. 3, the argument types that substantiate the four basic argument forms are situated in four different quadrants, which are indicated with the Greek letters alpha, beta, gamma, and delta respectively. Within each quadrant, arguments are further differentiated depending on the specific combination of types of statements. As a result, arguments sharing the same form are to be found in the same quadrant, while arguments sharing the same argument substance are to be found in the same column.
Given the respective possibilities of the three partial characterizations of argument, the theoretical framework of the PTA allows for 2 × 2 × 9 = 36 systematic types of arguments. However, not all possible combinations in theory are found in practice. For instance, in the Alpha Quadrant there is no PP element, while in the Beta Quadrant there is no VF element. On the other hand, there can be more than one element corresponding to an argument type, depending on the linguistic formulation of the lever, i.e., the relationship between the non-common terms of the premise and the conclusion. Each element representing the above mentioned systematic types of argument may host a number of ‘isotopes’, which are named in accordance with the existing dialectical and rhetorical traditions of argument classification. We list in Table 2 the formulation of the lever and name of the isotope of the examples mentioned above.