Equivocation of Nothing

Theorem
This is a fallacy in the following form.

Consider a universe of discourse $\mathbb U$ whose elements are strictly ordered by a relation, here denoted better.

Let $M \in \mathbb U$ be a maximal element with respect to better.

Let $m \in \mathbb U$ be any other element.

The fallacy of equivocation of nothing goes as follows:


 * $m$ is better than nothing.
 * Nothing is better than $M$.
 * Therefore, $m$ is better than $M$.

As $M$ is maximal, this is a contradiction.

Resolution
This is an example of a falsidical paradox based on the equivocation of the meaning of the word nothing.

In the first statement:
 * $m$ is better than nothing

the word nothing means the element (possibly hypothetical) against which every element of $\mathbb U$ is better.

In the second statement:
 * Nothing is better than $M$

the word nothing means there exist no elements.