The article discusses different types of paradoxes, including veridical, falsidical, and antinomy. Examples are given, such as the adage “It is better to give than to receive” and Zeno’s paradox of motion. Antinomy statements, such as “This statement is false,” have no truth value and lead to contradictory results.
There are several types of paradoxes, including the veridical and falsidical paradoxes and the antinomy. In the first case, a statement that seems contradictory is actually true. A falsidic paradox involves a statement that appears to be true, but leads to a nonsensical conclusion. Antinomy is a statement that has no reasonable answer. Philosopher and logician WV Quine called these different categories.
The adage “It is better to give than to receive” is a real paradox. It seems obvious that the benefits of receiving inevitably outweigh the possible benefits 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 WS Gilbert and Sir Arthur Sullivan. A young man, Frederic, is indentured to a band of pirates until his 21st birthday rather than until the age of 21. Unfortunately for him, his birthday is on leap year day, February 29th. Consequently, although he had lived to be 21 at the time of the operetta action, he was aged – by his birthdays – to just over 5 years and not free from his contract.
A falsidic paradox is a statement of conclusion which, despite an apparently valid argument based on acceptable premises behind it, leads to a nonsensical or fallacious conclusion. Zeno’s paradox of motion is an example of this. Summarizing, the logic of this example is that you cannot reach a given point B from A, because before reaching B you have to go halfway to B, and before reaching halfway B you have to go halfway to halfway B, and then above. Presented as overcoming an infinite number of points to reach a destination, movement is made to seem impossible.
An antinomy is a statement to which no truth value can be assigned; when reason is correctly applied, it reaches a contradictory result. The phrases “This statement is false” and “I am a liar” are examples.
This statement is false. Suppose 1 is true. Contradiction: if it is true that it is false, then it is not false.
This statement is false. Suppose 1 is false. Invoke the opposite of 1: This statement is true. Contradiction: A statement cannot be both true and false.
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