Logic as Illumination

LOGIC AS ILLUMINATION

Our aim throughout all of this is to shed light on the world. If we push our use of logic too far we risk overstepping that aim, and we will open ourselves to accusations of pedantry. Unfortunately mathematicians and extremely logical types of people are often accused of being pedantic by non-mathematicians or less logical people. Here, at the risk of sounding pedantic myself (and becoming very self-referential), I’m trying to shed light on the difference between pedantry and precision. I think the difference is illumination. I would characterise pedantry as precision that has gone further than necessary to shed light on a situation. There is plenty of precision that is there to clear things up, just like getting definitions right before trying to construct arguments with them. However, when extra precision does not help, I would call that pedantry.

Thus, self-referentially, I think that my distinction between pedantry and precision is itself a case of precision, not pedantry, because I think it sheds light on the situation.

Of course, people may disagree on where the lines are. One person’s precision may well be another person’s pedantry. It depends how much someone is seeking precision, and how much tolerance they have for ambiguity.

One of the difficulties that children have in learning about the world is dealing with the ambiguities of language. They are liable to take things rather literally because they haven’t yet learnt to use context to interpret the ambiguities. They haven’t yet developed a tolerance for (or understanding of) subtle shades of nuance. A friend of mine recounted an incident when her small son was eating a bag of crisps and said he’d had enough. “You can just leave them on the table,” she said, whereupon he obediently tipped them out onto the table.

As adults we develop the ability to become more relaxed about figurative language, and more relaxed about how precise we need things to be in order to get on with our lives. This is a bit like how accurately you need to measure things. When I’m weighing sugar to make a cake, I know it doesn’t matter all that much if I’m off by 10g or so. However, when I’m weighing sugar to make macarons I know it matters an awful lot so I’ll try to weigh to the nearest gram according to my digital scales. If someone is measuring the amount of anaesthetic to use to put someone under general anaesthetic I rather hope they’ll measure extremely accurately. Indeed I was rather put out the one time I did go under general anaesthetic, for a knee operation, when the anaesthetist discovered I was a mathematician and said in that cheerful way people do, “Oh, I’m terrible at maths!” I did not feel heartened.

I admit that I often find myself seeking more precision than some other people, and I do get accused of pedantry. But I’m convinced that I’m honestly just trying to shed light on situations. Actually, I tend to like more light in situations physically as well. I have bright lights on my desk, and I love bright sunshine because I like seeing everything more clearly. I like this in my thought processes as well. Achieving the illuminating precision sometimes takes longer – more thought, more words of explanation, more groundwork – and this is often unacceptable in today’s world of soundbites, memes, and so-called mic-drops. It turns out that saying something with impact is often more important than saying something true. But there should be a way to show truth without sacrificing impact, and of having an impact without sacrificing truth. That is the best way to use logic in this complex world of unpredictable, emotional, beautiful humans.

I imagine shining a bright light to illuminate the things we are trying to understand. If we hold it close, the light will be bright but will illuminate only a small spot. If we move it further up, we illuminate a wider area but the light will be less bright. Eventually if we hold it too far out the light will become so diffuse that we won’t see anything at all. But if we put it right on top of the things we’re studying, we also won’t see much.

Logic and abstraction are like shining a light at things. As we get more abstract, it’s like raising the light off the ground. We see a broader context, but with less fierce detail; however, understanding the broad context helps us understand the detail later. In all cases the aim should be illumination of some kind. First we need some light, and then we can decide where, and how, to shine it.