3rd3y3

01-16-2011, 05:58 PM

The most baffling of the ancient paradoxes is probably the Sorites Paradox, attributed to Eubulides in the 4th century BC. The word “Sorites” comes from Greek sōros, “heap”, and the riddle is sometimes also called “the paradox of the heap”. The conundrum lies in two assumptions which, by themselves, seem totally reasonable, but combined together, quickly lead to a bizarre conclusion.

Assumption 1. A single grain of sand is not a “heap”;

Assumption 2. If some sand is not a “heap” initially, one more grain won’t make it a heap.

Conclusion: No finite amount of sand qualifies as a heap.

The proof is simple. Let N be any finite number, as big as you like. We claim N grains of sand don’t make a heap. By the first assumption, one grain isn’t a heap. Now apply the second assumption over and over: 2 grains aren’t a heap; nor 3; nor 4… after N-1 steps, we’re forced to agree, N grains of sand do not a heap make. Since we proved this for an arbitrarily large N, that means no finite graincount is high enough!

What can we learn from Eubulides’ puzzle? The most important lesson is that language is inherently vague.

We can apply this to world human population:

One human isn’t overpopulation, and a non-overpopulated world surely has room for one more person. Conclusion: no finite population qualifies as overpopulation. Another exciting breakthrough courtesy of The Riddler!

Do you blindly accept the overpopulation threat?

Do you question things?

Assumption 1. A single grain of sand is not a “heap”;

Assumption 2. If some sand is not a “heap” initially, one more grain won’t make it a heap.

Conclusion: No finite amount of sand qualifies as a heap.

The proof is simple. Let N be any finite number, as big as you like. We claim N grains of sand don’t make a heap. By the first assumption, one grain isn’t a heap. Now apply the second assumption over and over: 2 grains aren’t a heap; nor 3; nor 4… after N-1 steps, we’re forced to agree, N grains of sand do not a heap make. Since we proved this for an arbitrarily large N, that means no finite graincount is high enough!

What can we learn from Eubulides’ puzzle? The most important lesson is that language is inherently vague.

We can apply this to world human population:

One human isn’t overpopulation, and a non-overpopulated world surely has room for one more person. Conclusion: no finite population qualifies as overpopulation. Another exciting breakthrough courtesy of The Riddler!

Do you blindly accept the overpopulation threat?

Do you question things?