Originally Posted by

**Elusive1324** Sorry for the confusion. I think I'm making a point regarding linguistic use of the if-then statement. Perhaps a brief narrative will clarify what I was getting at:

While reading theorems from a math text, I was wondering if the writers used the if-then statement in a colloquial or logical context. Depending on their choice of usage, I figured I would know how to "treat the theorems" (understand & use the theorems).

By colloquial usage I'm referring to the example: Bill, an average guy, might say "If I'm hungry then I eat." and assert that to be true when in reality, there are instances when Bill is hungry but he doesn't eat.

By logical context I'm referring to the usage of if-then statements in the context of mathematics or formal study of logic.

Now if the math text used 'if-then' in a colloquial context to describe a theorem (say the math theorem was 'If A then B'), I would treat the math statement as if it were Bill telling me "If I'm hungry then I eat". That is, I would take *that* if-then statement with a grain of salt -- Bill may or may not eat if he's hungry.

In contrast, if the math text used 'if-then' in the logical context, I would treat their description of theorems as though the rules of inferences applies. For example, if the text asserts 'If A then B', then I would not doubt that 'If not B, then not A' is a true statement.

So to summarize, if the math text used if-then in the logical sense and it included "If Bill is hungry, then he eats", I would have no doubt in reasoning that if Bill doesn't eat, he's not hungry.