In the framework of the Periodic Table of Arguments (PTA), each argument type is defined by three key features: its form, its substance, and its lever. Together, these parameters make it possible to classify and compare arguments systematically. If you want to see how this works in practice, the Argument Type Identification Procedure (ATIP) (Wagemans 2026) provides detailed heuristics.
On this page, we provide a short explanation of the third parameter: the argument lever.
What do we mean by “argument lever”?
If the form of an argument tells us how its parts are arranged, and the substance tells us what those parts are about, then the lever is what actually makes the argument work. The lever is the underlying mechanism of the argument. It explains why the premise should make the conclusion more acceptable.
In everyday conversations, the lever is rarely spelled out. When an argument consists only of an explicit premise and conclusion while the connecting principle remains implicit, it is traditionally called an enthymeme. The reader or listener must then reconstruct the missing link. This can be tricky: an analyst may interpret the connection incorrectly or attribute reasoning to the speaker that they did not intend and might even deny. Still, the lever is not entirely open-ended. The form of the argument provides its skeleton (the abstract lever), while its substance, together with contextual information and background knowledge, helps the analyst formulate the concrete lever.
The abstract lever: finding the hidden connection
Every argument form sets limits on what the lever can be, because it tells us what parts of the premise and conclusion are the same (the common element) and what parts are different (the non-common elements). The lever always boils down to: what kind of relationship is there between the non-common elements?
- Alpha form: a is X because a is Y
The common element is the subject (a), and the non-common elements are the predicates (X and Y). The lever is therefore a relationship between Y and X. - Beta form: a is X because b is X
The common element is the predicate (X), and the non-common elements are the subjects (a and b). The lever is therefore a relationship between a and b. - Gamma form: a is X because b is Y
Both the subjects (a and b) and the predicates (X and Y) differ. The abstract lever compares the relationship between a and b with the relationship between X and Y. If those relationships are identical, the substance is i and a meaningful gamma lever can be formulated. If they differ, the substance is d. This often means that information has remained implicit: the argument is then read as a “condensed” gamma argument and reconstructed by inserting the missing intermediate statement, after which each of the resulting arguments is characterised in its own right. Only where no suitable insertion can be found does the premise fail to contribute to the acceptability of the conclusion, and no lever can be formulated. - Delta form: q is A/U because q is Z
The conclusion q recurs as the subject of the premise, which attributes an external predicate Z to it. The lever is therefore a relationship between Z and the acceptability (A) or unacceptability (U) of q.
So at the abstract level, the lever is just a pattern of relationships.
The concrete lever: making it meaningful
Of course, abstract patterns aren’t enough. To understand an actual argument, we need to know what kind of content is involved. That’s where argument substance comes in. Take an alpha form argument with substance FF (both conclusion and premise are factual claims). Then we know the lever is some relationship between two facts. Our everyday knowledge suggests typical options:
- Y is a SIGN of X.
- Y is a CAUSE of X.
- Y is an EFFECT of X.
- Y is CORRELATED with X.
- Y is a MOTIVE for X.
- Y EXCLUDES X.
Consider this example: “He must have been driving too fast because he left a trail of rubber on the road”. Here, the form is alpha, the substance is FF, and the lever is best read as: “Leaving a trail of rubber is an EFFECT of driving too fast”. In other words, the lever is the hidden reasoning that makes the premise support the conclusion.
When the lever is spelled out
Occasionally, the speaker makes the lever explicit. Take, for instance, the following example: “I think she admires Patricia because she’s looking at her all the time and that’s usually a sign that you admire someone”. Standardised, this reads: “She (a) must admire Patricia (X) because she (a) is looking at her all the time (Y) and that (Y) is a SIGN of admiring her (X)”. Here, the word “sign” openly states the lever. But in most cases, we have to reconstruct it ourselves from the context.
What’s in a name?
The lever is more than just a hidden piece of reasoning. In many cases, it also gives us the name of the argument type. In the cases just mentioned, these are the arguments from sign, from cause, from effect, from correlation, and from motive, respectively. So the lever not only explains how the argument works but also tells us what kind of argument it is. Isn’t it funny that arguments are named after what usually remains unexpressed?
List of argument types distinguished in PTA 3.1
The following four tables list the levers and names associated with argument types of a specific form and substance. They can be used as a heuristic tool for formulating the lever in the absence of concrete textual evidence.
| Substance | Lever | Name (symbol) |
|---|---|---|
| FF | Y is a SIGN of X | argument from sign (Sig) |
| FF | Y is a CAUSE of X | argument from cause (Cau) |
| FF | Y is an EFFECT of X | argument from effect (Ef) |
| FF | Y is CORRELATED with X | argument from correlation (Cor) |
| FF | Y is a MOTIVE for X | argument from motive (Mot) |
| FF | Y EXCLUDES X | argument from incompatibility (Inc) |
| VF | Y is a CRITERION for X | argument from criterion (Cr) |
| VF | Y is the DEFINITION of X | argument from definition (Def) |
| VF | Y can be SUBSUMED under X | argument from subsumption (Su) |
| VV | Y is a NORM for X | argument from norm (Nor) |
| VV | Y is an INSTANTIATION of X | argument from instantiation (Ins) |
| VV | Y is a DISQUALIFIER of X | argument from disqualifier (Dis) |
| PF | Y is a PRAGMATIC MOTIVATION for X | pragmatic argument (Pra) |
| PF | Y is a PRIOR INVESTMENT in X | argument from waste  |
| PF | Y is the FEASIBILITY of X | argument from possibility (Pos) |
| PV | Y is a PRINCIPLED MOTIVATION for X | argument from principle (Pri) |
| PV | Y is an EVALUATIVE MOTIVATION for X | argument from evaluation (Ev) |
| PP | Y is a DEONTIC MOTIVATION for X | deontic argument (Deo) |
| PP | Y is a TELEOLOGIC MOTIVATION for X | teleologic argument (Tel) |
| Substance | Lever | Name (symbol) |
|---|---|---|
| ss, pp, uu | a is ANALOGOUS to b | argument from analogy (A) |
| ss, pp, uu | a is SIMILAR to b | argument from similarity (Sim) |
| ss, pp, uu | a is COMPARABLE to b | argument from comparison (Cpa) |
| ss, pp, uu | a is EQUAL to b | argument from equality (Eq) |
| ss, pp, uu | a is described METAPHORICALLY as b | metaphoric argument (Me) |
| ss, pp, uu | a is COMPOSED of b | argument from composition (Cpo) |
| ss, pp, uu | a is a PART of b | argument from division (Div) |
| ss, pp, uu | a RANKS BELOW b | argumentum a maiore (Ma) |
| ss, pp, uu | a RANKS ABOVE b | argumentum a minore (Mi) |
| ss, pp, uu | a OWES RECIPROCITY to b | argument from reciprocity (R) |
| ps, us, up | b is an EXAMPLE of a | argument from example (Exa) |
| ps, us, up | b is a SPECIES of a | argument from species (Sp) |
| sp, su, pu | a belongs to the TOTALITY of b | argument from totality (To) |
| sp, su, pu | a belongs to the GENUS of b | argument from genus (G) |
| Substance | Lever | Name (symbol) |
|---|---|---|
| i | b is SYNONYMOUS to a and Y is SYNONYMOUS to X | argument from synonyms (Sy) |
| i | b is the OPPOSITE of a and Y is the OPPOSITE of X | argument from opposites (Op) |
| i | b is DERIVATIVE of a and Y is DERIVATIVE of X | argument from derivatives (Der) |
| i | b is INTEGRATIVE of a and Y is INTEGRATIVE of X | argument from integratives (Int) |
| i | b is the CONVERSE of a and Y is the CONVERSE of X | argument from converses (Cve) |
| d | — | non sequitur (Non) |
| Substance | Lever | Name (symbol) |
|---|---|---|
| I | Z is ETHOTICALLY AUTHORITATIVE for A | ethotic argument (Eth) |
| II | Z is CHARACTERALLY AUTHORITATIVE for U | argumentum ad hominem (H) |
| II | Z is a NEGATIVE MOTIVATION for A | argumentum ad baculum (B) |
| II | Z is an OFFERED REWARD for A | argumentum ad carotam (Car) |
| II | Z COMMITS the addressee to A | argument from concession (Cce) |
| II | Z is an UNDESIRABLE IMPLICATION supporting U | argumentum ad consequentiam (Cse) |
| III | Z is EPISTEMICALLY AUTHORITATIVE for A | argument from expert opinion (Exp) |
| III | Z is MORALLY AUTHORITATIVE for A | argument from moral authority (Mor) |
| III | Z is TESTIMONIALLY AUTHORITATIVE for A | argument from testimony (Tes) |
| III | Z is POPULARLY AUTHORITATIVE for A | argumentum ad populum (Pop) |
| III | Z is a PRESUMPTION in favor of A | argumentum ad ignorantiam (Ig) |
PERIODIC TABLE OF ARGUMENTS 