The argument runs from the lesser case to the greater one: what holds even of the weaker, the less able, the less likely candidate is taken to hold all the more of the stronger one. The argument works because both cases are placed on one scale, so that whatever is granted lower down must be granted higher up. You can attack it by denying the scale, since without it there is no reason why what holds of the one case should hold of the other.
Example
Einstein can solve this equation because even I can solve it
Standardized form
Einstein (a) can solve this equation (X) because even I (b) can solve this equation (X).
Transformations applied: the pronoun “it” in the premise spelled out as “this equation”, so that both halves show the same predicate.
Classification
The subjects differ and the predicate is the same, so the argument form is beta (a is X because b is X).
The conclusion is about one specific person (s) and the premise about one specific person (s), so the argument substance is ss.
The keyword RANKS ABOVE describes the relationship between subjects a and b: on the scale that underlies the predicate — here, the ability to solve equations — the subject of the conclusion is the greater case and the subject of the premise the lesser one. The argument lever can thus be formulated as “Einstein (a) RANKS ABOVE me (b)”.
Assessment questions
- Can the speaker indeed solve this equation?
- Does Einstein rank above the speaker in the ability to solve equations — is there one scale on which both can be placed?
- Is the speaker’s success enough to conclude that Einstein can solve the equation, or does the greater case not simply inherit what holds of the lesser — for instance if the equation calls for a technique the speaker happens to know and Einstein does not?
Not to be confused with
- Argumentum a maiore — The mirror image: the subject of the conclusion is the lesser case and the subject of the premise the greater one, so the argument runs down the scale instead of up it.
RANKS BELOW - Argument from analogy — The two cases are held to be alike, with no ranking between them.
ANALOGOUS - Argument from example — Substance: the conclusion is about a whole class rather than one further individual.
us
Notes
The argumentum a minore and the argumentum a maiore share their form (beta) and differ only in the direction of the ranking expressed by the lever. In the argumentum a minore the predicate is the positive pole of the underlying scale (being able to solve the equation), so it carries upward from the lesser case to the greater one; in the argumentum a maiore the predicate is the negative pole (not being able to solve the equation, not knowing everything), so it carries downward from the greater case to the lesser one.
Like the argumentum a maiore, one could argue this is an alpha form argument. The reconstruction would then go: “Solving this equation (a) can be done by Einstein (X) because solving this equation (a) can be done by me (Y)”, with the lever “can be done by me (Y) is LESS PROBABLE than can be done by Einstein (X)”.
Source of the example
Source not yet recorded.
