Within the theoretical framework of the Periodic Table of Arguments (PTA), an argument type is conceived as a particular combination of the values of three parameters: form, substance, and lever. Various heuristics are available to determine these values – for a more elaborate description, please see How to identify an argument type? On the hermeneutics of persuasive discourse (Wagemans, 2023).
The third parameter, the ‘argument lever’, is the underlying mechanism of argumentation, which expresses how the premise renders the conclusion (more) acceptable. Since in natural argumentative discourse, the lever usually remains implicit, formulating it can be a real challenge: the reader or listener must add something to the discourse, and in doing so, runs the risk of adding something the author or speaker did not intend to communicate at all or could plausibly deny.
Although the lever can thus often be characterized as a subjective addition to the text, the options for formulating it are still limited as the lever is partially determined by the form and substance of the argument. The form provides us with an abstract formulation of the lever, and the substance helps turn it into a more concrete one.
The abstract lever
The argument form limits the number of candidate formulations of the lever because it reveals the configuration of subjects and predicates in the conclusion and premise. More specifically, the form gives us the common element, the fulcrum (which is either the subject or the predicate), as well as the non-common elements of the argument (the two different predicates or subjects). The abstract lever, then, is defined as the relationship between the non-common elements. For example, if an argument has the alpha form, ‘a is X because a is Y’, the subject (a) is the common element and the predicates (X and Y) are the non-common elements. This means the abstract lever is some kind of relationship between X and Y. In arguments with the beta form, ‘a is X because b is X’, the conclusion and the premise have a common predicate (X) and the subjects (a and b) are the non-common elements. In this case, the abstract lever is some kind of relationship between the subjects a and b.
In argumentation having gamma and delta forms, the formulation of the abstract lever is somewhat more complicated. The abstract lever of argumentation of the gamma form, ‘a is X because b is Y’, expresses that the subjects (a and b) and predicates (X and Y) relate to each other in the same way: a relates to b as X relates to Y. In argumentation of the delta form, ‘q [is A], because q is Z’, the abstract lever expresses the relationship between the acceptability (A) of the conclusion and the property (Z) attributed to the conclusion in the premise.
The concrete lever
But how can we turn these abstract relationships into concrete ones? To do that, we use the argument substance, which further limits the possibilities for formulating the lever. For example, if an argument of the alpha form has substance FF, then we know not only that the lever is some relationship between X and Y, but also that it is a relationship between two factual predicates. Based on our knowledge of the world, we can then give a concrete meaning to the lever. In this case, we use keywords that represent connections between facts, such as ‘cause’, ‘effect’, or ‘sign’. The corresponding levers read ‘Y is a cause of X’, ‘Y is an effect of X’, or ‘Y is a sign of X’.
It sometimes happens that the author or speaker explicitly mentions the lever of an argument. An example is ‘I think she likes Patricia because she is looking at her all the time and that is usually a sign that you like someone’. In this case, we have concrete textual evidence the lever contains the keyword ‘sign’. In practice, however, the reader or listener must choose the best-fitting candidate among the list of levers associated with the form and substance of the argument. In the case of the argumentation ‘He must have been driving too fast because he left a trail of rubber on the road’, which has form alpha and substance FF, that is a choice from the above-mentioned levers with keywords cause, effect, and sign. Of these three possibilities, the lever ‘leaving a trail of rubber on the road is an effect of having driven too fast’ is most consistent with our knowledge of the world. It is therefore probable that this is what the author or speaker intended, which allows us to add it to the discourse.
What’s in a name?
Since in most cases, the names of the argument types are derived from the keyword of the lever, the formulation of the lever usually also gives us a label for identifying the argument type. In the three cases just mentioned, these are the argument from cause, from effect, and from sign, respectively.
List of argument types
The following table lists the levers and names associated with argument types of a specific form and substance. The table can be used as a heuristic tool for formulating the lever in absence of concrete textual evidence.
| Form | Substance | Lever | Name |
| a is X because a is Y (alpha) | FF | Y is the cause of X | argument from cause |
| Y is the effect of X | argument from effect | ||
| Y is a sign of X | argument from sign | ||
| VF | Y is a criterion for X | argument from criterion | |
| Y falls under the definition of X | argument from definition | ||
| VV | Y is a norm for X | argument from norm | |
| PF | Y is a pragmatic justification for X | pragmatic argumentation | |
| PV | Y is a principled justification for X | argument from principle | |
| a is X because b is X (beta) | FF | a is similar to b (in respect to X) | argument from similarity |
| VV | a is analogous to b (in respect to X) | argument from analogy | |
| PF | a is equal to b (in respect to X) | argument from equality | |
| a is X because b is Y (gamma) | [-][-] | a is opposite to b and X is opposite to Y | argument from opposites |
| [-][-] | a means the same as b and X means the same as Y | argument from identicals | |
| q is A/U because q is Z (delta) | [-]F | being said by an expert (Z) renders q acceptable (A) | argument from expert opinion |
| [-]F | being said by many people (Z) renders q acceptable (A) | argument from popularity | |
| [-]F | being said by the arguer (Z) renders q acceptable (A) | ethotic argument | |
| [-]F | being said by an opponent (Z) renders q unacceptable (U) | personal attack | |
| [-]F | the fact that not accepting q has negative consequences (Z) makes that q must be accepted (A) | argument with the stick |
PERIODIC TABLE OF ARGUMENTS 