Ok all you planetbrains out there, help me with this one.
The other night we were all stuck in a traffic jam on the M40 and conversation turned, as it always does, to the problems of philosophical logic.
The seven year old and the ten year old were savouring the paradox of the barber – you remember, the famous hairdresser in the Cretan mountain village of Agios Giorgios who shaves all the men in the village who do not shave themselves.
Does the barber shave himself? the seven year old asked the ten year old.
If he does, he doesn’t, said the ten year old.
And if he doesn’t, he does! said the seven year old. Paradox!
This is a variant of the set-of-all-sets-that-do-not-include-themselves paradox that – I seem to remember – sent Russell round the bend and caused him to tear up ten years of work.
Then I thought of a snappier variant.
“All generalisations are wrong,” I announced to the car.
Now is that statement true?
If it is, it isn’t, said the seven year old.
And if it isn’t, it is! said the ten year old.
Am I right?