The classic formulation of the paradox involves a heap of sand. If I take one grain away, does it stop being a heap? No, of course not — taking away one grain of sand does not transform a heap into a nonheap. But if we extend this logically, I can keep taking away grains one at a time until we have a “heap” consisting of a single grain of sand. That can’t be right, either. So at what point does the heap become a nonheap?
The Equivocation Fallacy, in which a logical error occurs when a word (or phrase) with two meanings is used in a confusing manner:
Margarine is better than nothing.
Nothing is better than butter.
Therefore, margarine is better than butter.
H/t: James Taranto
Here’s a similar one, based on the Fallacy of Four Terms:
Nothing is better than eternal happiness.
A ham sandwich is better than nothing.
Therefore, a ham sandwich is better than eternal happiness.