How to make a logical paradox - �鶹��ҳ�� Bitesize

A paradox is a seemingly untrue or contradictory statement that, when investigated further, may prove to be true.
Paradoxes can also take the form of philosophical riddles or images that appear to show something impossible.

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A video explaining how to make a Möbius strip logical paradox.

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Click to see a step-by-step slideshow.
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WHAT YOU NEED - An A4 sheet of paper, a pair of scissors, sticky tape and a pen.
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STEP 1 - Fold a piece of paper to create a narrow strip.
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STEP 2 - Cut the strip of paper using scissors.
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STEP 3 - Write "The statement on the other side is true" on one side.
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STEP 4 - Write "The statement on the other side is false" on the other side. These two statements do not work together as neither can be true/false at the same time.
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STEP 5 - But if you twist the paper and tape the two ends together it creates a Möbius strip. The statements now make sense when you flip over the Möbius strip!

What is a logical paradox?

Paradoxes are often statements that need to be thought about as opposites or contradictions of each other. For example:

This sentence is a lie

Is the sentence true or false? Could it be both true and false? When thinking about this question your thoughts seem to go around in a circle. This is because the sentence is referring to itself. We can call this self-referential.

Philosophical paradoxes

A famous example of a philosophical paradox is Theseus' ship.

Theseus' ship is kept in a harbour. As the pieces of the wooden ship decay they are replaced by new pieces. If no original pieces are left, is it the same ship?

If your answer is no, consider the questions: at what point does it stop being the original ship? Surely replacing one plank doesn't make it a different ship?

Image of a Penrose Triangle, an impossible illusion that appears to loop round and round

Visual paradoxes

This is a Penrose triangle.

It is an example of an impossible object or a visual paradox.

It appears to depict a contradictory object that cannot exist.

Some artists in the 20th century (notably M.C. Escher) were fascinated by visual paradoxes.

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Shape, space and measures

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What is a logical paradox?

Philosophical paradoxes

Visual paradoxes

Where next?

More on Shape, space and measures

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