Black-and-White Thinking

HOW LOGIC PUSHES US TO BLACK AND WHITE IF WE'RE NOT CAREFUL

ONE NIGHT DURING MY first term at university another fresher was found in the kitchen just before midnight eating a bowl of cereal. He explained that, according to the best-before date, his milk was about to go off at midnight. I'm afraid we laughed rather heartily at his belief that a best-before date is so precise, or that milk could suddenly go off at midnight like Cinderella's carriage turning into a pumpkin.

Unfortunately many more serious problems arise from our attempts to deal with things that are on a sliding scale. If we're not careful logic pushes us to extremes, so if we want to avoid adopting extreme positions all the time we have to do something more human. A human approach is more nuanced than that. It turns out that our brains are able to process grey areas in subtle ways that don't seem entirely logical but do seem to make sense. Rather than use logic to push out the sense, we should find the logic inside the human nuances. Different logical interpretations offer ways to handle these grey areas; simply drawing a line is only one approach. Allowing for some uncertainty can seem unsettling, but it can avoid both the extremes and the anomalies of drawing a line.

One of my favourite moments in Jane Austen's Pride and Prejudice is when Elizabeth asks Mr Darcy how and when he fell in love with her. He replies,

I cannot fix on the hour, or the spot, or the look, or the words, which laid the foundation. It is too long ago. I was in the middle before I knew that I had begun.

He is unable to draw a line and say that is the exact line in between not being in love with her and being in love with her. Where could such a line possibly be? He can only know that at some point he was not in love with her, and at some later point he definitely was. This is understandable because being in love with someone is a somewhat hazy and nebulous concept that grows gradually (except in cases of love at first sight, if that really exists), with a lot of grey area in between the definite "no" and definite "yes".

Grey areas are an important part of the human experience, but are not very well dealt with by logic. Logic is about getting rid of ambiguity. The law of the excluded middle forces us to put the whole grey area in with black or in with white. That is better than the sort of black and white thinking that pretends the whole grey area doesn't exist, but it can have the same effect as it can push people to think only the black or the white if they try to pursue logic to its rigid conclusion.

The language we use in everyday life seems to be getting pushed further and further to extremes and certainties. People say that something is "the best thing ever" (or the worst). They try to reassure me by saying "Everything is going to be fine", they advertise events to me by saying "You will not want to miss this!" Admittedly, "You might not want to miss this" doesn't sound so good. But I worry about the world turning into certainties that are almost certainly flawed. We should understand different ways of dealing with grey areas and become better at working with their nuance, instead of longing for the false promise of black and white clarity.

CAKE

I am not immune to extreme thinking myself. Here is the kind of reasoning that makes me prone to getting fat:

• It won't hurt to eat one small piece of cake.

• And however much cake I've already eaten, it can't hurt to eat one more mouthful.

Unfortunately, logically this means that it is fine to eat any amount of cake, as long as you go one mouthful at a time. And unfortunately this is what I am prone to do.

It is another example where being strictly logical is not entirely helpful. The only way to avoid thinking it's okay to eat infinite cake is to decide it's not even okay to eat one small piece of cake. I am much better at avoiding cake altogether than eating a small amount and stopping. The trouble is that everyone around me is likely to point out that one small piece by itself is fine.

This is an example where the logic of the situation pushes us to one of two extreme positions, either

• it is not okay to eat any cake at all, or

• it is okay to eat infinite amounts of cake.

The trouble is the grey area. There is no strict line we can draw between a sensible amount of cake and "too much". Parents are liable to try and draw those lines to stop children gorging on cake, but children aren't fooled – they easily see that those lines are arbitrary, and they try to push them by having one more mouthful, and one more. Or they try to push bedtime by an extra two minutes, and then another extra two minutes, by saying they need to go to the toilet, or fetch a toy, or drink some water, or any number of other spurious requests. But really, the bedtime itself is spurious – it is an arbitrary line that has been set in a grey area between "sensible bed time" and "much too late".

One way to get round this logic is just to shrug and say just because something is logically implied, that doesn't mean I'm going to believe it. But that is unsatisfactory as it would allow for all sorts of other illogical thinking, such as believing two things that cause a contradiction.

The idea of believing all the logical implications of your other beliefs is called "deductive closure" – a set of statements is deductively closed if it also contains everything you can deduce from all the statements in the set. So my set of beliefs is only deductively closed if I believe all the implications of my beliefs. I think this is an important part of being a logical human being.

So, if I want to be rational, what can I do about grey areas? I might have to let go of the most obvious logical approach and learn to deal with something more complex.