Equivocation of Nothing
Fallacy
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.
Examples
The classic often-cited argument is:
- Candlelight is brighter than nothing.
- Nothing is brighter than the light from the sun.
- Therefore, candlelight is brighter than the light from the sun.
This version is given in 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.):
- Any soap is better than no soap.
- No soap is better than Wonder-Bubble.
- Therefore, any soap is better than Wonder-Bubble.
This version is given in 2008: David Joyner: Adventures in Group Theory (2nd ed.):
- Time waits for no man.
- No man is an island.
- Therefore, time waits for an island.
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.
$\blacksquare$
Sources
- 1982: P.M. Cohn: Algebra Volume 1 (2nd ed.) ... (previous) ... (next): Chapter $1$: Sets and mappings: $\S 1.1$: The need for logic: Exercise $(9)$