Monday, November 2, 2009

When do daffodils bloom?

Daffodils bloom in the spring. Most would view this as an uncontroversial assertion; some would be so bold as to call it a fact. Few would see the statement as it really is: an empty tautology.

For the statement to make sense we need the flower and the season to be separable from each other – object X, a flower with certain characteristics appears at time Y – a temporal concept definable in its own right.

Yet when we delve deeper we find it impossible to define spring as an independent concept. It can only be defined through reference to other concepts. And spring can only be made distinctive from other seasons by thinking about what makes it different to,say, winter. And what makes spring different to winter? Well, spring happens in April not December. And how is April different to December…?

This chain of questioning will continue and before long you will find yourself saying that April is when the daffodils bloom!!

Clearly, there are many different ways of defining spring: height of sun in sky, soil temperature etc. But each of these will in themselves require further definition in the same way that the concept spring does, or the month April. For example, to define spring “as the time of year when the sun is at the height it is at when the daffodil blooms” would not be commonly viewed as erroneous.

But this turns our original statement into:

1) Daffodils bloom when daffodils bloom.

Of course we see the tautology when stated so boldly – and yet this sentence is logically equivalent and provides as much knowledge as these sentences:

2) Daffodils bloom in the spring.
3) Daffodils bloom when the sun is 25°.

Each of them are incomplete statements that requires further definition if they are to gain meaning; and, because they make no sense in their own right they are all equally pre-logical and therefore equivalent. We avoid saying that daffodils bloom when they bloom because it is so obviously tautological. But we are slow to see that “daffodils bloom in the spring” is tautological in exactly the same way.

So when do daffodils bloom? Only the error-prone would even ask such a question!

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