CASE-BY-CASE Argument

1. Definition

Case-by-case argumentation is an investigative technique that develops in several stages, from questions such as “Something happened under such and such circumstances; what could it be?”:

• First, make an exhaustive inventory of possible cases.
• Second, consider each of these cases. Could it have happened under the circumstances considered?
  Eliminate the cases that are incompatible with the circumstances.
• Consider the remaining cases.
  – If there are none, the inventory was not exhaustive.
  – If there are several, they are equally possible at this point.
• If only one remains, take it as the correct answer to the question
  « This is what happened!”

Example:

S1 — All this money either comes from an inheritance, or from your work, or has been stolen. If it’s from your work or from an inheritance, you can easily prove it by showing us the relevant documents. No such documents? Then you stole it.

This argument illustrates the classic law of negation of a disjunction, S. Connectives:

“P or Q or R” is true; but P is false and Q is false; so necessarily, R is true.

Definitions can be given on a case-by-case basis. A crime, such as impiety, might be defined as a lack of respect for either the gods, their priests or their shrines. To accuse someone of impiety (or to exonerate oneself from this crime) one must show that at least one of the three defining conditions has been disrespected (or none) (after Aristotle, Rhet., II, 23, 1399a5; RR p. 367).

Case-by-case argument is a « proof by elimination”, an indirect proof, as opposed to a direct, substantial proof.

2. Argument by division

Perelman (1977, p. 65) gives the following example of an argument by division:

The tire exploded because it was worn out, because there were nails on the road, or because of a manufacturing defect. Now, the tyre had just been bought and there were no nails in it. So, there was poor workmanship. (Perelman, 1977, p. 65)

This shows that the label “argumentation by division” is homonymous: it can refer either to the argumentation by composition or division, or to the case-by-case argument.

3. Refutating the case-by-case argument

A case-by-case argument is perfectly conclusive if all cases have been considered; it can be rejected on the same case-by-case basis by showing that the enumeration of cases is incomplete:

S2 (in response to S1, above): — No Sir, I just won the lottery, here is the winning ticket!

S3 (in reply to Perelman, above) — Well, Sir, here are some other possibilities. The tire could have exploded because it was badly inflated, because there was a pothole in the road, because it hit the curb, because it was overheated (if the driver happened to have just used a torch to loosen a wheel bolt), because the brake was stuck, because it came into contact with an electrical source, because the car was too loaded or too fast… My conclusion is that the investigation must continue.