Equivocation of Nothing

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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