Expressions.

On occasion, one is tempted to use forms such as (a = a) or (p ⊃ p) and the like. In fact, this happens when discussing prototypes, such as proposition, thing, etc. Thus in Russell's Principles of Mathematics, the phrase 'p is a proposition' or (p ⊃ p) was placed in front of certain propositions as an hypothesis in order to exclude everything but propositions from their arguments. But that makes no sense. A non-proposition as argument does not make the hypothesis false but empty, and the wrong kind of arguments make the proposition itself empty. So it prevents invalid no worse than the empty hypothesis.

The same would apply if one wanted to express 'There are no things' by writing (~(∃x).x =x). But even if this were a proposition, would it not be equally true if in fact 'there were things' but they were not identical with themselves?