Negation
Negation is how we argue against things, but people often do it badly. Understanding negation helps build logical power by recognizing which statements are equivalent and which constitute true refutations.
THE IDEA
HOW WE ARGUE AGAINST THINGS
THERE ARE ONLY TWO DEBATES I remember from the debating club at school. One was “This house believes that Margaret Thatcher should go”, which was particularly memorable because she actually resigned the morning of the debate. The other one was “This house believes that strawberries are better than raspberries”, a classic pointless and contentless debating topic. It is easy to think that both sides of this debate have an equally impossible task, because how could you ever argue that one kind of berry is better than another? What does “better” mean? However, the key with this type of debate is that the house only decides whether they will support the motion or not. So the proposers have to argue that strawberries are better than raspberries, but the other side only has to argue that the proposers are wrong. There are many ways they could be wrong. One way would be if, in fact, raspberries are better. But they could also be wrong if strawberries and raspberries are equally good. Or if “better” is impossible to define. Or if the entire idea is idiotic.
Most arguments are not like debates, but still consist of someone claiming that something is true, and the other person saying they’re wrong. If they are attempting to be logical, the first person will try to justify what they’re saying by constructing a logical argument to back it up. The second person should then either try to find a flaw in their logical argument, or try to construct their own logical argument to back up their assertion that the person is wrong.
Logic, mathematics and science are all ways of finding out what is true. But they are also ways of finding out what is not true. Admitting the possibility of being wrong and having ways to detect it is an important part of being a rational human being, I am sure. (But I could be wrong.)
Negation is how we argue against things. Unfortunately in normal life we often do it very badly. Arguments degenerate into insults, intimidation or yelling all too quickly, especially in online comments sections. I optimistically think that this is out of frustration at one’s own failure to get a point across, rather than because everyone enjoys insulting, intimidating or yelling at people. My optimism leads me to do things like write books about logic, because I think most people can do better than that, and I even think that most people might want to. Or failing that, could be persuaded to want to.
One reason that arguing against things in normal life doesn’t go very smoothly is that we don’t always properly understand which things are equivalent to each other and therefore which things are true refutations. Once we understand negation, we can start to build logical power; one of the first steps is to understand many different points of view on the same idea, and how they agree or oppose each other.
When to use it
In a debate or discussion, use negation to identify the weakest point of an opponent's argument rather than attacking everything.
When writing a persuasive essay, anticipate likely objections and construct proper negations to strengthen your own position.
In scientific reasoning, use negation to formulate competing hypotheses and design experiments that could falsify them.
During online discussions, pause and structure your rebuttal using logical negation instead of emotional responses.
FROM THEORY TO EVERYDAY LIFE
In practice
Strawberries vs Raspberries Debate
In a school debate, the motion is 'This house believes that strawberries are better than raspberries.' The proposers must argue that strawberries are better, but the opposition only needs to show the proposers are wrong. This can be done by arguing that raspberries are actually better, that both are equally good, that 'better' is undefined, or that the whole idea is absurd.
Thatcher Resignation Debate
In a debate with the motion 'This house believes that Margaret Thatcher should go,' the morning of the debate she actually resigned. External events can render an argument moot, but the logical structure of negation still applies.
A MOMENT TO REFLECT
Put it to work.
Think of a recent argument you had. Did you actively try to negate the other person's claim in a logical way, or did you resort to other tactics?
When someone asserts something, what are the various ways you can argue they are wrong (e.g., their premise is false, their reasoning is flawed, the conclusion doesn't follow)?
Why is understanding equivalence between statements important for effective negation?
CONTINUE THE CONVERSATION
Source texts
- The Art of Logic How to Make Sense in a World that Doesn’t (Eugenia Cheng)