How to Solve a Paradox

A paradox is a set of statements that are apparently true but, when compared with each other, indicate a contradiction that is intuitively untrue. For years, philosophers, logicians and mathematicians have struggled with paradoxes that seem to indicate that things like motion and aging are impossible. If you have discovered or confronted a paradox, follow these steps to solve it.

Instructions

Difficulty: Challenging

1. Digest the paradox. The first step in solving a paradox is to understand it. This means understanding each of the statements and where any contradiction arises. If the paradox is stated in terms of first order logic (or other logical systems), find a hypothetical example that illustrates it.
2. Makes sure that what you are calling a paradox is actually a paradox. The word is often misused to mean a simple contradiction or tricky statement, neither of which are truly paradoxes. Remember that something is a paradox only if a set of true statements creates a contradiction when combined.
3. Translate the paradox into other systems or languages. Once you have understood the paradox and made sure that it actually is a paradox, one good first step to digging into the logical mechanics of the paradox is to translate it. If the paradox is stated in a natural language (in regular terms), try translate it into first order logic or mathematical terms. If you can manage to do this, you will go a long way in understanding the paradox and be closer to being able to solve it.
4. Challenge the premises. Paradoxes are interesting because they seem to challenge the logic of the universe. So, start out assuming that the universe and the laws which govern it are valid and sound, and the premises or statements of the paradox are wrong. Use new information to help you do this. Many people have used Einstein's relatively new idea that space and time form a continuum to challenge and solve Zeno's paradox, one of the oldest and most difficult in the world.

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