Paradox

Paradoxes in

What’s a paradox?a statement or proposition that seems self-

contradictory or absurdIt makes the situation impossiblea self-contradictory and false proposition.

Examples of famous paradoxes in historyCan an God create a rock too heavy to lift?You will never reach point B from point A as you

must always get half-way there, and half of the half, and half of that half, and so on... (This is also a paradox of the infinite)

A man travels back in time to discover the cause of a famous fire. While in the building where the fire started, he accidentally knocks over a kerosene lantern and causes a fire, the same fire that would inspire him, years later, to travel back in time. It would seem that as a result of time travel, he appears to have no beginning.

The Liar Paradox is among the simplest of paradoxes. It can be traced back at least as far as Eubulides of Miletus, a fourth-century B.C. Greek philosopher.

Eubulides’ version of the paradox is this: A man says that he is lying; is what he says true or false?

However we answer this question, difficulties arise.

If we suggest that what the man says is true, then we end in contradiction: if the man’s claim that he is lying is true, then he is lying, in which case what he says is false.

If we suggest that what the man says is false, then we are no better off: if the man’s claim that he is lying is false, then he is not lying, in which case what he says is true.

Both answers are logical contradictions; it cannot be the case either that what the man says is true or that what the man says is false.

Sentences can be constructed that cannot consistently be assigned a truth value even though they are completely in accord with grammar and semantic rules.

This statement is false. (A) If the statement is true, everything asserted

in it must be true. However, because the statement asserts that it is itself false, it must be false. So the hypothesis that it is true leads to the contradiction that it is false. Yet the sentence cannot be false for that hypothesis also leads to contradiction. If the statement is false, then what it says about itself is not true. It says that it is false, so that must not be true. Hence, it is true.

Under either hypothesis, the statement is both true and false. This cannot be. This is a logical paradox.

Three Laws of Thought (Aristotle)

1. An object is what it is. (Law of identity)

2. A cannot be both A and B . (Law of contradiction or no proposition can be both true and not true.)

3. Every statement is either true or false; there is nothing in between. (Law of the excluded middle.)

Is this a paradox?