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Background
Background
Democritus was born around 460 BC and died around 370 BC in Thrace. He is most famous for coming up with the idea of atoms.
Nowadays, we have lots of fancy equipment, and methods for finding out about atoms, and we can even (indirectly) ‘see’ them using electron microscopes. Democritus, however, didn’t have any of that equipment when he came up with the idea. He came up with the idea of atoms just by thinking about it.
Democritus’ argument for the existence of atoms
Democritus’ argument for the existence of atoms
Imagine you have a piece of paper, and you tear it in two. Then you take those bits and tear them in two. You can probably tear the piece of paper into many tiny pieces, especially if you have a pair of scissors and maybe some tweezers. The question Democritus asked was this: (if we had the right equipment) could we carry on tearing up this piece of paper (or any stuff) infinitely?
Democritus thought that the answer must be no.
If we could divide a piece of paper up infinitely, how small would the bits of paper be? Well they’d have to be infinitely small! And something that is infinitely small has no size at all. If we could measure them, they’d be 0 metres long!
So, what would happen when you tried to add those bits of paper back together to make the whole piece of paper? If all the bits are 0 metres long, then when you add them together they will add up to… 0 metres! But the piece of paper was obviously not 0 metres long to begin with.
Democritus concluded that stuff cannot be made up of infinitely small parts, and in fact must be made up of parts that have a size, and be indivisible. He called these smallest parts atoms, which comes from the Ancient Greek word for indivisible.
Method: Reductio ad absurdum
Method: Reductio ad absurdum
Democritus’ argument is a reductio ad absurdum. In this kind of argument, you show that one claim is absurd, and so the opposite must be true.
A formal outline of Democritus' argument
A formal outline of Democritus' argument
It is true that either:
A) An object is something that has a length.
or
B) An object is something that can be divided infinitely.
However...
Something that can be divided infinitely is something that is made up of parts that are 0m long.
Something that is made up of parts that are 0m long is something that is 0m long.
Something that is 0m long is something that has no length.
Something that has no length is something that has a length - but this is a contradiction!
∴ Both A and B cannot be true
A is obviously true
∴ B is false…
The symbol ∴ means 'therefore'
Tasks
Tasks
Explain Democritus’ argument as clearly as you can.
How might someone object to Democritus' argument?
Do you agree with Democritus? Do you think we need evidence to support his view or is his argument enough?
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