So far we have developed concepts that apply to whole arguments (validity, soundness) and one concept applying to a pair of sentences (logical equivalence.) Be careful here: we will not say that an argument is, or that two arguments are, logically equivalent. Nor will we say that the members of a pair of sentences are valid. Such claims don't make sense: logical equivalence applies only to sentence pairs and validity applies only to arguments.

Now, let's consider concepts that apply only to single sentences. Consider the following fact about me:

Halpin is either male or he's not.

Is this true (it's about the author of the Logic Cafe)? Well of course it is. One doesn't have to know me to see that I'm male or I'm not. Roughly, we might say that this sentence is true because of the logic or meaning of the words "or" and "not".

Similarly,

No women are bachelors.

is true, surely, because of the meaning of the words involved. (You didn't have to do a survey to see that it's true!)

The idea, here, is that certain sentences must be true in virtue of their logic. This brings up the notion of logical possibility again. And we can give the following definition.

A sentence is logically true if and only if it could not possibly be false.

Now, think about a different sort of example:

No women are women.

There is something wrong with this sentence, of course. We will call it logically false. This time, you provide the definition.

Erase the three question marks, fill in the correct word, then press the SUBMIT button.