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Paradoxes are apparently self-contradictory statements that lead to logically unacceptable conclusions.

Example 1

What is peculiar about the following statement?

This statement is false

Solution: The meaning of the statement is fluctuating. If the statement is true, it is false, and if it is false, it is true. If the statement is true, then it's not true, and if it's not true, then that's what it says, that it isn't true, so it's true.

Example 2

There are two analog wall clocks with moving hands. One of the clocks loses ten minutes every day and always tells the time ten minutes later than it is. The other clock is broken and always shows the same time. Which of the two clocks is more accurate?

Solution: The broken clock is more accurate, because it is right twice a day, whereas the other clock is hardly ever right.

1. You are at a game show and there are three closed doors. There is a prize hidden behind one of the doors and the game show host knows where it is. You are asked to choose a door. The game show host then opens one of the other two doors showing that it is empty and asks you if you would like to change your selection.

Should you stick to your original selection?

It is better if you select the other door. Since there are three doors then there is a 67% chance that you choose the wrong door with your first selection. If you are wrong the game show host will select the other wrong door since she knows where the prize is hidden. Therefore it is better if you switch to the door which the game show host leaves closed.

2. “All animals are equal, but some animals are more equal than others.” - George Orwell, Animal Farm.

Identify the paradox in the above quotation.

"More equal". By definition something cannot be identical/equal to more of the same thing.

3. Which is an oxymoron and which a paradox?

(A) "It's a definite maybe that Mike will show up at the event."

(B) "No one goes to that mall because it is too crowded."

The first statement is the oxymoron, and the second statement is the paradox.

4. Which is an oxymoron and which a paradox?

(A) The website developer was asked to provide an exact estimate for the project.

(B) "The best advice I can offer is don’t listen to advice."

The first statement is the oxymoron, and the second statement is the paradox.

5. Which quotation is a paradox, and which an oxymoron?

(A) "I can believe anything, provided that it is quite incredible." - Oscar Wilde

(B) "I can resist anything but temptation." - Oscar Wilde

The first quotation is an oxymoron, and the second a paradox.