A PARI argument
Lat. a pari, or a pari ratione, “for the same reason”: par, “equal, same” ratio, “reason”.
There are two kinds of a pari arguments, depending on whether they deal with individuals or classes of individuals.
1. When the argument concerns individuals, the a pari argument includes an individual x in a category C. The individual becomes (is identified as) a member of the category, in logical symbols < x ∈ C >, S. Categorization.
2. When the argument concerns classes of individuals, the a pari argument reorganizes the category system (classification, taxonomy). It reduces two formerly distinct categories (class, species) to one, on the basis that they belong to the same super-category (genus). This entry is about this second definition.
The vocabulary of analogy and the label “argument a comparatione” are sometimes used to refer to the argument a pari, in both its forms, S. Taxonomies and Categories.
The a pari argument “[applies] to another species of the same genus what can be said about some particular species.” (Perelman, Olbrechts-Tyteca [1958], p. 241);
A pari reasons by equality of the cases if a parricide deserves death, so does the matricide. (Chenique 1975, p. 358)
The a pari argument transfers a property (a quality, a right, a duty…) (here “— deserves death”) originally attached to a species A (here: “— is a parricide”) to another species B (here: “— is a matricide”), arguing that they belong to the same genus (here: “— is a murderer of a parent”). The reasoning is as follows:
The tendency is towards severity
The penalty for matricide is life imprisonment.
Let’s increase the penalty of matricide!
The penalty for parricide is death.
Parricide and matricide are crimes of the same genus (type, genre, kind…).
The penalty for matricide should be death!
For the discussion of a pari, two different situations should be distinguished.
— Situations of complete knowledge, where the truth is fully known and can be fully considered; then, syllogistic reasoning applies.
— Situations in which the truth is debatable and a concrete decision must be made, i.e., argumentative situations.
1. Syllogistic a pari
From the point of view of absolute knowledge, the a pari argument is either a truism or a paralogism, depending on whether or not the property under consideration is generic or not, see Taxonomies and Categories.
If the property is generic, then it is true for all species belonging to the genus, and especially for the two species involved in the a pari argument. The syllogism is as follows:
Having a constant body temperature is a generic property of mammals.
Whales, humans… are mammals
So whales, humans… have a constant body temperature.
The corresponding a pari argument is:
Both humans and whales are mammals (“belong to the same genus”, here mammals)
Humans have a constant body temperature (“what is true of a species”, here humans)
So whales (must) have a constant body temperature (“applies to another species”, here whales).
If the property is not generic, then, the conclusion is a paralogism:
Labradors, poodles… are dogs
Labradors are gun dogs
So, poodles are / must be gun dogs.
The corresponding a pari argument is:
Both Labradors and Poodles are dogs (“belong to the same genus” here dogs)
Labradors are gun dogs (“what is true of a species”, here Labradors)
So poodles are gun dogs (“applies to another species”, here gun dogs).
But poodles are not gun dogs. The property “— is a gun dog” is not a generic property, it belongs to the Labrador as a species, not to the genus “dogs”. It follows that this characteristic cannot be safely transferred to poodles.
In short, a trait can be transferred from one species to another species belonging to the same genus only if the trait on which it is based is a generic trait. The validity of the argument depends on the quality of the taxonomy on which it is based, and the argument will be considered persuasive only if people agree on the classification, see the cases below.
2. The apparent deadlocks a pari vs. a contrario
and a pari vs. a pari
Two paradoxes are attributed to a pari argument. In the same situation:
- a contrario and a pari cancel each other out;
- a pari can destroy a pari.
2.1 A contrario versus a pari
(i) A pari extends to the As the treatment given to the Bs, arguing that both belong to a common super-category:
(1) the As are like the Bs! they should be treated like the Bs!
(ii) A contrario, the argument from the opposite, justifies the different treatment of the As and Bs, by arguing that they are indeed opposites:
(2) The As and Bs are different, so they are rightly treated as such!
In both cases, the question is whether a difference between A and B should be preserved: a contrario answers “yes”, a pari answers “no”.
2.2 A pari against a pari
A pari argument extends to B a property of A, or to A a property of B. It can be objected to (i):
(3) If A’s are like the B’s, then the B’s are like As’; the B’s are the ones who should be treated like A’s!
Here, the proponent and the opponent refer to the same data and use the same rule to support opposing claims. They agree on the need to recategorize A’s and B’s into a single category, but they disagree on which category should prevail.
Hence one can conclude that all this maneuvering is pointless (in the following quote, “analogy” means a pari):
That the argumentum a contrario and analogy as means of interpretation are utterly worthless can be seen from the fact that both lead to opposite results, and that there is no criterion for deciding when the one and when the other should be applied.
(Kelsen 1967, p. 352).
This is the case for an abstract, syllogistic situation, where:
— A contrario is actually logically invalid, S. Opposites – A contrario.
— A contrario can be systematically opposed to a pari.
— As a “bidirectional” argument scheme, a pari can always be opposed to a pari.
3. Argumentative a pari and the situated condition of argumentation
Let us schematize a situation in which Gs and Bs are treated differently. A pari can be used to support the claims “All Gs!” or “All Bs!” and a contrario, to rebut both.
Current situation | Revendication |
All Gs! | |
G ≠ B and G and B are treated differently | |
All Bs! |
— A contrario is the status quo argument, that can be used against both a pari alignments. Those who argue for a status quo do not support the burden of proof, they can simply reformulate and amplify the current “doxical” discourse, to maximize the opposition between As and Bs, and thus a contrario justify the difference in treatment:
It is no accident that As and Bs are called A and B, precisely because they are A and B, and not something else!
— The proponent of either a pari alignments of categories must undermine this discourse, showing that the difference previously considered as essential should now be considered a mere coincidence. These minimizing strategies that accompany a pari depend on the characteristics of the specific situations.
In a more complex move, the person making an a pari argument may try to show that it is possible to construct a super-category that includes both A and B. This solution implies that the previous definitions of both categories must be modified
The problem with the a priori syllogistic approach is that it does not take into account the argumentative situation, whereas in every such situation there are embedded preferences and impossibilities. These contextual conditions systematically exclude one or the other application of a pari. A pari is logically bidirectional and contextually monodirectional, as can be seen in the following cases.
3.1 Military service: girls / boys
Context: a country in which boys, but not girls, perform compulsory military service. Applying a pari to boys, i.e. to claim that they should not do their military service, is tantamount to calling for the dissolution of the army, its professionalization, or the like. That would be the real issue, not the equal treatment of boys and girls.
Thus, the a pari argument can only be made by the girls, or by the military administration that is willing to integrate girls. The relevant argumentative question can only be “Should girls also do military service?”, and a pari supports a positive answer very well.
3.2 Murder: Patricide / Matricide
Context: A social situation in which a “civilizing process” is taking place; there is a clear effort being made to eliminate all forms of violence. In such a situation, an a pari generalization of the death penalty is “out of the question”. The only relevant question can be “Should we reduce the penalty for patricide?”, with a pari being used to support a positive answer.
If the social climate tends to increase penalties, the situation is the same, with a pari serving to justify the positive answer to the question “Should we increase the penalty for matricide?”.
3.3 Employment: temporary / permanent contract
Context: Some workers have a permanent contract (PC), while others have a fixed-term contract (FTC), the former being considered better than the latter from the worker’s point of view. In a period of prosperity and full employment, the PC is the golden standard, and a pari alignment of FTCs with PCs is on the agenda. The question of a possible alignment of PCs with FTCs is irrelevant. The difference will be denied by arguments such as:
People with FTCs are exploited, we are all workers, everyone should be able to get a PC!
In less favorable economic conditions, FTCs become the norm, and equalizing them with PCs is not on the agenda. The difference is denied with arguments like:
People with PCs are privileged, privileges should be ended, everyone should be put on an FTC!
3.4 Going out at night: girls / boys
Consider a traditional family of consisting of both teenage boys and teenage girls, two species of the same genus. The boys are allowed to go out at night,but the girls are not. Suppose the girls resent this prohibition. They can argue their case in many ways. They could, for example refer to the positive effects that going out at night will have on their social awareness, S. Pragmatic argument; they could also point out that their brothers go out at night, in an elliptical a pari:
G — But the boys do go out at night!
Not surprisingly, the parents argue a contrario:
P — Yes but you are a girl …
To strengthen their case and eliminate the difference, girls could emphasize the similarities that characterize the new catc-hall category « like the boys »:
Boys and girls receive the same education; they have access to the same media; they practice judo; they follow the same courses with the same requirements; they share the same responsibilities at home …
and minimize the gender gap:
Dad, you gave us an excellent education, we are mature, we know how to stay out of trouble.