A Party Political Broadcast by the Chancellor of the Exchequer, Lord Sorites.
These are taxing times for our country. The last government left us with run-down public finances and the need to raise extra revenue. But you, the people, do not want to have to foot the bill. So how can we raise the money we need without making you feel the pain?
The answer is simple. Focus groups, opinion polls and economists have shown that charging an extra 0.01 per cent tax has a negligible effect on personal income. No one who is comfortably off is made to struggle, no one rich is made poor, no one already struggling is made to struggle more, by paying 0.01 per cent extra on their tax bill.
So today we are raising income tax by 0.01 per cent. And logically, since this small amount makes as little difference to the person who earns 0.01 per cent less than you as it does to you, we can repeat the step tomorrow, when you are in the position of that insignificantly poorer person. And so the next day, and the next, for the next 300 days.
Each time we raise taxes, we do so in a way that makes no difference to your quality of life. And so your quality of life will not be affected. Yet, miraculously, the net effect of these measures will be a large increase in government revenue, which we intend to use to cut the national debt and still have enough change left to buy everyone in the country a drink. We hope you will use it to toast our ingenuity.
Source: The ancient Sorites paradox, attributed to Eubulides of Miletus (4th century BCE)
A politician who made a speech like this should not expect to win any votes by so doing. Even if your maths isn’t up to calculating that he is actually proposing a tax rise in excess of 3 per cent, no one would be fooled that 300 tiny tax rises don’t add up to a major hike.
Yet the logic of the Chancellor is hard to fault. It follows that of the ancient Sorites paradox. In the original, we are asked if removing a grain of sand from a heap can ever transform the heap into a non-heap (a small pile, perhaps). The answer seems to be no. But that means you could keep removing a grain of sand, one by one, until you had only one left, and that would still be a heap.
One solution appears to be that somewhere along the line, removing a grain of sand does mean that we no longer have a heap. But that just seems absurd. Hence the paradox: if one grain makes a difference, that is absurd; if it doesn’t, a single grain can be a heap, which is just as absurd.
Our tax example suggests a way out. Could we not argue that each small increment does make a difference, although it is just a small difference? Clearly, if you add up several small differences you can end up with a big one.
This does not, however, get to the heart of the problem. The paradox is that no tiny change in income can be enough to make the difference between someone being well-off or struggling. The paradox is precisely the contrast between what is obvious when we ‘zoom out’ and see the cumulative effect of small changes and when we ‘zoom in’ and see each one having no effect at all.
When confronted by this paradox, most people are convinced it’s just a linguistic trick or there is some other sleight of hand at work. The puzzle should be taken more seriously, however. Many argue that the way out requires us to accept the vagueness of many concepts, such as rich and poor, tall or short, heap or pile. The problem with that solution is that, if we allow too much vagueness into language and logic, reason itself becomes vague. The alternative – that tiny changes really can make the difference between being rich and being poor – preserves the rigour of logic and language, but seemingly at the cost of realism.
See also
| 16. | Racing tortoises |
| 25. | Buridan’s an ass |
| 42. | Take the money and run |
| 70. | An inspector calls |