Island and Lake Paradox
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Paradox
An island is a body of land surrounded entirely by water.
A lake is a body of water surrounded entirely by land.
What if you had a planet whose northern hemisphere was all land, and whose southern hemisphere was all water?
Would you call the northern hemisphere an island, or would you call the southern hemisphere a lake?
Or would you say:
- there is an island in the middle of a lake
- which is in the middle of an island
- which is in the middle of a lake
- which is in the middle of an island
- $\ldots$
?
Resolution
This paradox is an instance of a dialetheia.
Both of the main statements are true, as well as the statement derived from it.
$\blacksquare$
Sources
- 1944: Eugene P. Northrop: Riddles in Mathematics ... (previous) ... (next): Chapter One: What is a Paradox?