Some Informal Antecedent Indicators

“If” sometimes is replaced informally by such expressions as: “on condition that,” “provided that,” “in case,” and also by “when” or “whenever.” These all indicate a hypothetical (or merely possible, not necessarily actual condition). For example:

When I eat, I’m happy.
Translated: If I eat, then I’m happy.

(Recall that sometimes the "if" or its variant is in the middle of the sentence (see part one).)

Practice Exercise Four

Translation from Categorical Propositions

There are four types of categorical propositions. This discussion is limited to the two universal claims, which have to do with "all" or "no." Translating these two types of categorical propositions into conditional propositions can be very useful. Examples:

Categorical: All horses are animals.
Conditional: If it’s a horse, then it’s an animal.

Categorical: No dogs are cats.
Conditional: If it’s a dog, then it’s not a cat.

Note that in translation of a categorical negative proposition, the denial, “not,” falls into the consequent.

Practice Exercise Five

Contraposition

We can exchange the positions of antecedent and consequent, but only if we deny each.

Example:

If a fire started, then heat was present.
May become: If no heat was present, then no fire started.

There are only two steps. We'll use this example: If I'm rich, then I have money.

Step 1. Switch the clauses:

If I have money, then I'm rich.

Step 2. Deny each clause.

If I don't have money, then I'm not rich.

You're done.

Note that the principle at work is the same as Modus Tollens. In other words, whenever the antecedent is present, the consequent is necessarily present. But if the consequent is NOT present, then the antecedent can't be present.

Practice Exercise Six