When one thing is enough to make another thing happen, we could say that the first is a sufficient condition for the second. An example is running out of gas and having a car stop.

Since formal logic is about truth-functional relationships and not about cause-and-effect, we are better off thinking about a sufficient condition as telling us that knowing the truth of the first (called the antecedent) is enough for us to be sure of the truth of the second (called the consequent). For instance, in a sentence such as “If Jane passed then she studied” we are in no way saying that passing caused the study (presumably it was the other way around) but instead that knowing it is true that Jane passed allows us to be sure that she did study.

Sentences which can be symbolized as conditionals (using the signal C) can be expressed many ways. For instance, if we have a code in which P represents the thought that Jane passes and Q the thought that she studies, the sentence “If Jane passed then she studied” would be symbolized PQC. So would these sentences:
“The fact that Jane passed leads us to say she studied.”
“Jane’s passing calls for her to have studied.”
It would also be the case that we can think of Q as the necessary condition for P,as in
“Jane passes only if she studies.”
“Jane’s passing requires study.”
“Jane must study in order to pass.”

The key rule of formal logic involves saying that when the antecedent is true, the consequent will be true also (P, therefore Q; traditionally this is called modus ponens). The corresponding fallacy or logical error is affirming the consequent (Q, therefore P).

For additional practice, run the interactive program STDFORM supplied on your disk.

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