In the Periodic Table of Arguments (PTA) framework, each argument type is defined by three key features: its form, substance, and lever. Together, these parameters let you classify and compare arguments systematically. 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 you how its parts are arranged, and the substance tells you 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, people rarely spell out the lever. 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 limits what the lever can be, because it tells us which parts of the premise and conclusion are the same (the common element) and which parts differ (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 the 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 resulting argument is characterized 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 the 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 among the listed options, this lever seems the most suitable: “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”. Standardized, 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 arguments from sign, cause, effect, correlation, motive, and incompatibility, 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 by form and substance. Use them as a heuristic tool for formulating the lever when concrete textual evidence is lacking.
| 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 (W) |
| 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 with respect to X | argument from analogy (A) |
| ss, pp, uu | a is SIMILAR to b with respect to X | argument from similarity (Sim) |
| ss, pp, uu | a is COMPARABLE to b with respect to X | argument from comparison (Cpa) |
| ss, pp, uu | a is EQUAL to b with respect to X | argument from equality (Eq) |
| ss, pp, uu | a is described METAPHORICALLY as b with respect to X | metaphoric argument (Me) |
| ss, pp, uu | a is COMPOSED of b with respect to X | argument from composition (Cpo) |
| ss, pp, uu | a is a PART of b with respect to X | argument from division (Div) |
| ss, pp, uu | a RANKS BELOW b with respect to X | argumentum a maiore (Ma) |
| ss, pp, uu | a RANKS ABOVE b with respect to X | argumentum a minore (Mi) |
| ss, pp, uu | a OWES RECIPROCITY to b with respect to X | argument from reciprocity (R) |
| ps, us, up | b is an EXAMPLE of a with respect to X | argument from example (Exa) |
| ps, us, up | b is a SPECIES of a with respect to X | argument from species (Sp) |
| sp, su, pu | a belongs to the TOTALITY of b with respect to X | argument from totality (To) |
| sp, su, pu | a belongs to the GENUS of b with respect to X | argument from genus (G) |
| Substance | Lever | Name (symbol) |
|---|---|---|
| i | b is SYNONYMOUS with a in an identical way as Y is SYNONYMOUS with X | argument from synonyms (Sy) |
| i | b is the OPPOSITE of a in an identical way as Y is the OPPOSITE of X | argument from opposites (Op) |
| i | b is DERIVATIVE of a in an identical way as Y is DERIVATIVE of X | argument from derivatives (Der) |
| i | b is INTEGRATIVE of a in an identical way as Y is INTEGRATIVE of X | argument from integratives (Int) |
| i | b is the CONVERSE of a in an identical way as 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) |
