Mary Elizabeth
Mary Elizabeth

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.

1. This statement is false.
2. Suppose 1 is true.
3. Contradiction: If it’s true that it’s false then it isn’t false.

1. This statement is false.
2. Suppose 1 is false.
3. Invoke the opposite of 1: This statement is true.
4. Contradiction: A statement can’t be both true and false.
Mary Elizabeth

Mary Elizabeth is passionate about reading, writing, and research, and has a penchant for correcting misinformation on the Internet. In addition to contributing articles to wiseGEEK about art, literature, and music, Mary Elizabeth is a teacher, composer, and author. She has a B.A. from the University of Chicago’s writing program and an M.A. from the University of Vermont, and she has written books, study guides, and teacher materials on language and literature, as well as music composition content for Sibelius Software.

Mary Elizabeth

Mary Elizabeth is passionate about reading, writing, and research, and has a penchant for correcting misinformation on the Internet. In addition to contributing articles to wiseGEEK about art, literature, and music, Mary Elizabeth is a teacher, composer, and author. She has a B.A. from the University of Chicago’s writing program and an M.A. from the University of Vermont, and she has written books, study guides, and teacher materials on language and literature, as well as music composition content for Sibelius Software.

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anon150393

i thought paradox was that if (time traveling was invented) that somehow the past you can't get to the you now because it was trapped or something.

anon134315

Dear jeancastle00: Try to work out this God paradox: If God can do anything, can He make a mountain which is too heavy for Him to lift? Think about it.

PurpleSpark

@snowywinter: Another noted liar paradox is a guarantee to drive a person mad! The following three sentences are written on a card:

1) This sentence contains five words.

2) This sentence contains eight words.

3) Exactly one sentence on this card is true.

dill1971

@snowywinter: The last part of this article is an example of a liar paradox. The roots of the liar paradox go back to the philosopher Epimenides from the sixth century B.C. He was quoted as saying “All Cretans are liars…One of their own poets have said so.”

There have been many variations of the basic liar paradox that have appeared over the years. An English mathematician named Philip Jourdain came up with what is known as “Jourdain’s Card Paradox”. One side of a card reads “the sentence on the other side of this card is true”. The other side reads “The sentence on the other side of this card is false”.

SnowyWinter