Negation vs Opposite

NEGATION VS OPPOSITE

Imagine a debate about education systems in which someone claims, as someone periodically does, that the Asian education system is better than the British or American one. There are two ways to oppose this view:

1. Measured and calm: I don’t think the Asian education system is better.
2. Extreme and excited: No way! The British education system is better!

Emotional tone aside, these are logically two different ways of opposing the original view. The second (extreme) way is what we think of as being the “opposite” in normal language. But it is not the logical opposite. In logic, to make the negation we take the original statement and simply declare that it is not true. This is the first (calm) opposition above: the negation of “the Asian education system is better than the British one” is “It is not true that the Asian education system is better than the British one”. Or, to put it in more natural wording, “The Asian education system is not better than the British one.” There are many ways in which the Asian education system could be “not better”. What does “better” mean, in any case? What are the systems aiming to do? How are we measuring what they achieve? What do we want an education system to achieve? Some people seem to measure everything in terms of maths and science achievement, or other standardised test results, whereas other people want to measure in terms of readiness for the workplace. Is that all we want education to do – train people to score highly in standardised tests and be a good employee?

Here are some more examples showing the difference between logical negation and “opposites” in normal language:

• Original statement: I think the EU is fantastic.

Opposite: I think the EU is terrible.

Negation: I do not think the EU is fantastic. This is not the same as thinking it’s terrible. It is possible to be “not fantastic” without being “terrible”. For example, it could be mostly very good but with some flaws. However there is a tricky issue of language here because with a particular tone of delivery it could sound like a wry understated way of saying it’s terrible. However, this is a quirk of language rather than a logical negation.

• Original statement: Margaret Thatcher was the greatest Prime Minister.

Opposite: Margaret Thatcher was the worst Prime Minister.

Negation: Margaret Thatcher was not the greatest Prime Minister. But perhaps she was not the worst either – she could have been the second worst, or the tenth worst, or something.

• Original statement: Climate change is definitely real.

Opposite: Climate change is definitely fake.

Negation: Climate change is not definitely real. Is anything definite about anything? However, that doesn’t mean it’s definitely fake – it’s highly likely to be real because of a huge quantity of evidence pointing towards it, where here “real” means a scientifically sound theory according to the strict framework of science.

• Original statement: Sugar is good for you.

Opposite: Sugar is bad for you.

Negation: Sugar is not good for you. But it’s also not directly bad for you as a small amount every day probably won’t do you any harm, it’s just that in large quantities it’s probably bad for you.

• Original statement: I am male.

Opposite: I am female.

Negation: I am not male. I still might not be female as I could be one of the estimated 1.7 per cent of the population born intersex.

In general the negation is a broader statement than the opposite. The opposite is the exact opposite extreme, or, as we might say for emphasis, the “polar opposite”. The polar opposite of the North Pole is the South Pole, but there’s an awful lot of world in between those poles.

• Original statement: Barack Obama is black.

Opposite: Barack Obama is white.

Negation: Barack Obama is not black. In fact, his father was black and his mother white, so he is arguably as much black as he is white, or perhaps neither.

Thinking about opposites instead of negations is an extreme and very black-and-white way of looking at things, figuratively or otherwise. In the case of Barack Obama, most people would feel strange calling him white, and he is generally called black although he is in some sense equally both. So why does it seem to make more sense to call him black than white? Does it in fact make any sense? This is part of a question about grey areas.