7 Puzzles And Paradoxes To Twist Your Brain

6. Sorites Paradox

What is it?

When is a heap not a heap?

In the sorites paradox, we are presented with a heap of sand. When a single grain is removed, can it still be considered a heap? The answer is invariably yes, but imagine that you continue to remove grains until just one remains, is that a heap? The answer is invariably no, but then you have to question at what point the transition was made.

The same principle can be applied for a range of different vague measurements such as "tall", "heavy", "old", "bald" and even "blue".

So, what's the solution?

You can come up with all kinds of arbitrary "rules" to solve this paradox, perhaps by deciding that 20 grains is a heap "just because", but remember that that good logical solutions are supposed to be unassailable.

Another potential solution is to apply the principle of Hysteresis, in which the properties of an object are dependent on how that got that way. For example, a large heap of sand retains its "heap status" for longer as the grains are removed, because it began as an indisputable heap.

You can use this principle to answer the question of whether a glass is half full or half empty. It is the former if it got that way by being filled and it is the latter if it got that way by being emptied.