 Logically valid inferences are those that are guaranteed to be valid by their form. And above we spelled this out as follows: an inference is valid by its form if as long as we fix the meaning of certain special expressions, the logical constants, we can ignore the meaning of the other expressions in the statements involved in the inference, and we are always guaranteed that the inference is valid, no matter what the meaning of the other expressions is, as long as the whole is meaningful. A logical truth can be understood as a statement whose truth is guaranteed as long as the meanings of the logical constants are fixed, no matter what the meaning of the other expressions is. Alternatively, a logical truth is one that is a logical consequence from no assumptions, i.e. an empty set of premises.