PHI 102 – CRITICAL THINKING
CONDITIONALS
I. Standard Form:
Simply put, a conditional is an "if….then" statement. The standard (or "canonical", if you want to use a big word) form of a conditional statement is "If A, then B." A (what follows the "if" part) is the antecedent, while B (what follows the "then" part) is called the consequent. Since the sentence "If A, then B" means something very different from the sentence "If B, then A." it is crucial that one is able to identify the antecedent and consequent of a conditional. This is complicated by the fact that there are several non-standard ways to express conditional statements in English. Here are a few, along with their translations into "standard form."
If Q, then P
P, if Q.
P, assuming that Q.
P, given that Q.
Provided that Q, P.
Q only if P
If not Q, then P
P unless Q.
Unless Q, P.
Without Q, P.
Exercises: Put the following into standard form:
1. If the cat is away the mice are at play.
2. The cat is away if the mice are at play.
3. Provided the cat is away, the mice are at play.
4. The mice are at play unless the cat is away.
5. If the cat is not away, the mice will not be at play.
6. The cat is away only if the mice are at play.
7. The mice’s being away implies that the cat is away.
8. For the mice to be at play, it is necessary for the cat to be away.
9. It is sufficient for the cat to be away that the mice are at play. (see below)
10. Assuming that the dog is in the pound, the mice are at play only if the cat is away.
11. Unless she manages to escape the house, Lemma will have kittens only if Ickey has not been fixed.
II. Necessary and Sufficient Conditions
To say that a condition A is necessary for another condition B is to say that A must hold (or be the case) if B happens to hold (or to be the case). In other words A is necessary for B just in case the conditional statement, "If B, then A" is true.
To say that a condition A is sufficient for another condition B is to say that A’s holding (or being true) is enough for B to hold (or to be true). So A is sufficient for B just in case the conditional statement "If A, then B" is true.
It might just help to remember that the antecedent of a conditional is the sufficient condition, while the consequent of a conditional is the necessary condition.
Practice: For each of the following pairs of statements, determine whether the first is necessary for the second and also whether it is sufficient for the second. Note that it is possible for a condition to be both necessary and sufficient for another.