Animals can be divided into Carnivores and Non-Carnivores: A = C + NC. Therefore, if we add some wolves to an island of sheep, the number of animals on that island will increase.

It's easy to see why that argument might not be right. Wolves kill sheep. But if you didn't know that fact about wolves and sheep, the argument looks very appealing. But the equation A = C + NC tells us absolutely nothing about the world; it's an accounting identity that is true by definition. The only thing it tells you is how I have chosen to divide up the world into parts. And I can choose an infinite number of different ways to divide the world up into parts.

Here are two more examples:

1. Y = C + I + G + X - M. Therefore an increase in Government spending will increase GDP.

2. Y = C + S + T. Therefore an increase in Taxes will increase GDP.

My guess is that you are much more uncomfortable with the second of those two examples than the first. You have probably seen the first argument before, but have probably not seen the second. But they are both equally correct accounting identities and are both equally rubbish arguments.

How can a purely arbitrary choice of which accounting identity I write down make any difference at all to how we think about the world?

I call it "The Implicit Theory of Inertia": We assume a thing will keep on doing the same as it would otherwise have done, unless you give me a good reason why it wouldn't. The onus is on you to explain why more wolves would mean fewer sheep, and unless you give me a good reason I will assume that the number of sheep stays the same (or keeps growing or declining at the same rate) regardless of the number of wolves. You need the force of a good argument to overcome the assumed inertia of things. So by choosing one accounting identity over another, I am dividing the world up into one set of things rather than another, and then exploiting your Implicit Theory of Inertia to rig the argument in my favour.

Sadly, we don't just fool other people when we write down accounting identities to divide the world up one way rather than another. We fool ourselves too.

Theorising starts when we write down the variables.