There are several types of paradox, including veridical and falsidical paradoxes and antinomy. In the first case, a that statement seems contradictory is actually true. A falsidical paradox involves a statement that seems true, but which leads to a senseless conclusion. Antinomy is a statement that has no reasonable answer. Philosopher and logician W.V. Quine named these different categories.
The adage, “It is better to give than to receive,” is a veridical paradox. 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.
Another example is given in the operetta The Pirates of Penzance by W.S. Gilbert and Sir Arthur Sullivan. A young man, Frederic, is indentured to a band of pirates until his 21st birthday rather than until he is 21 years old. Unfortunately for him, his birthday is on Leap Year’s Day, 29 February. 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 falsidical paradox is 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 this example 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.
Antinomy is a statement to which no truth value can be assigned; when reason is properly applied, it reaches a self-contradictory result. The sentences, “This statement is false,” and, “I am a liar,” are examples.
- This statement is false.
- Suppose 1 is true.
- Contradiction: If it’s true that it’s false then it isn’t false.
- This statement is false.
- Suppose 1 is false.
- Invoke the opposite of 1: This statement is true.
- Contradiction: A statement can’t be both true and false.
