There are several types of paradox. On the one hand, a paradox is a statement of conclusion that seems self-contradictory or absurd but is really true. This was classed by philosopher and logician W.V. Quine as a veridical paradox. An example is the adage, “It is better to give than to receive.” It seems obvious that the benefits of receiving inevitably outweigh any possible advantages of giving, but many people find that, contrary to expectations, this is not their experience.

Here is another example. In the operetta The Pirates of Penzance by W.S. Gilbert and Sir Arthur Sullivan, the young man Frederic is indentured to a band of pirates until his 21st birthday. Unfortunately for him, the contract did not say until he was 21 years old, which is only a significant difference when your birthday is on Leap Year’s Day, February 29 – but his was. Consequently, although he had lived 21 years at the point of the action of the operetta, he was aged – by his birthdays – at a bit over 5 and not free of his indenture.

A paradox is also a statement of conclusion that, despite a seemingly valid argument based on acceptable premises behind it, leads to a conclusion that is senseless or fallacious. Zeno’s paradox of motion is an example. Boiled down, the logic of Zeno’s paradox is that you cannot reach a given point B from A, because prior to reaching B you must get halfway to B, and prior to getting halfway to B you must get halfway to halfway to B, and so on. Presented as passing an infinite number of points to reach a destination, movement is made to seem impossible. This is what Quine called a falsidical paradox: one that both appears to be and is, under scrutiny, false.

In addition, a paradox is a statement to which no truth value can be assigned. The sentences, “This statement is false,” and, “I am a liar,” are examples.

1. This statement is false.2a. Suppose 1 is true.Contradiction: If it’s true that it’s false then it isn’t false. 1. This statement is false.2b. Suppose 1 is false.3b. Invoke the opposite of 1: This statement is true.Contradiction: A statement can’t be both true and false.

This type of paradox was called by Quine an antinomy, which is explained as a paradox in which reason properly applied reaches a self-contradictory result.