Here’s a thought for you on a sunny afternoon:
∃x[PKoF(x) & ∀y[PKoF(y) → y=x] & B(x)]
That is the generally accepted way of rendering into predicate logic the sentence: “The present king of France is bald”. Who would want to do this? Bertrand Russell, the British philosopher, and the godfather of modern logic, that’s who. This is the first (and in many cases the only) bit of formal logic that many philosophy undergraduates learn.
The point is that there is no present king of France, so he can’t be bald. The sentence appears to make sense, but on closer inspection doesn’t. Is it true or not? Or meaningless? Does putting it into symbolic logic make it any easier to work out the truth or falsity? And are questions like this the reason philosophy students spend so much time in the pub?
What many people take from this exercise is that language is too subtle, complex and nuanced to be captured in a pseudo-mathematical way. Over time people refined the logical symbols to take into account all sorts of linguistic subtleties until it became clear that they might as well just be using normal language.
There is a point to all this. And it’s that economics is in some ways similar to formal logic. Just as predicate logic tries to simplify language and the world, and ends up stripping out much of the meaning, so mathematized economics tries to describe very complex interactions and behaviour in nice, easily digestible numbers.
Take the recent debate over the so-called Reinhart-Rogoff thesis, the theory proposed by two economists that countries should try to keep debt at 90% of their GDP. This was taken by politicians across Europe to justify austerity. Now another academic has rubbished the 90% thesis (and Reinhart and Rogoff have disowned it). The 90% rule was the latest in a long line of numbers that economists and the politicians who are in thrall to them have become obsessed with.
But the realities that debt levels describe are very complex, and can’t be tidily rendered into numbers. Take another example. In the UK when growth is positive, even at 0.1%, people start cracking open the champagne. When it’s negative, even by 0.1% gloom descends. But why?
These numbers are an agglomeration of a fantastically complex array of events and they are a very crude measure for economic health - whatever that means. There are plenty of other examples. The yen reaching the 100-a-dollar level, dollar-pound parity, the Dow hitting 16,000, the FTSE 6,000, and so on. All seductive numbers, all representing unruly, hard-to-understand behaviour.
The lessons of formal logic would suggest that these numbers are actually meaningless. (Or, more precisely, that they are a proxy for sentiment. They also have a feedback effect, and often create resistance, or momentum. But the momentum is not a feature of some independent entity called “the market” but a stylised description of the actions of a bunch of human beings).
Just because you can create a number, it doesn’t follow that it correlates to anything in reality. Just ask the king of France.