If pigs can fly then my name is Midas

Economists speak a lot about something being a necessary condition or a sufficient condition for something else. So, for example, someone might claim that

a high growth rate is a necessary condition for eradicating poverty

How do we verify such a claim? One can imagine a diligent economist checking the data to see if every year in which poverty fell was also a year in which growth was indeed high. Only if she can find some year in which poverty fell and growth wasn't high that the claim is disproved.

[Of course, a real economist would have to use statistical inference here since there would be other factors assumed constant while making the claim but which would actually vary while making the observations. But let's ignore that for the moment.]

Now suppose I make the claim,

Pigs being able to fly is a necessary condition for my being able to turn lead into gold.

Our diligent economist once again gets ready, clipboard in hand, to check this claim. But day after day pigs don't fly and I can't turn lead into gold. If we use the same criteria as before, this claim can never be disproved.

We seem to have opened up a huge hole in our system of reasoning. We can claim "Pigs being able to fly" as a necessary condition for anything at all and our claim would never be disproved. In fact this property of the standard logical system is well known to logicians and mathematicians: one can prove anything starting from a contradiction. To put it in our terms, 'nothing' is a necessary condition for everything and anything is a sufficient condition for 'nothing'.

Is this really a hole? Suppose we were investigating the claim that "high growth is a necessary condition for poverty eradication". Imagine an economy where growth is low in some years and high is others but poverty decreases only in those years when growth is high. We would consider our claim to be true in such an economy. Since we did not demand to know the proportion of years in which growth is high while making this judgment, our conclusion should remain the same in the corner case where this proportion is zero and all years are low growth years.

So, if we were to meet an economist who prefaced all his predictions with "If pigs can fly then ...", it would be more consistent to think of him not as wrong but as irrelevant to our world where pigs don't really fly. To avoid falling into such irrelevance ourselves, we must be convinced that the conditions in which our predictions hold occur at least some of the time. Hence the importance of existence proofs in economics.

Of course sometimes economists who are in a hurry forget to establish the existence of objects that they are talking about. And then they can turn lead into gold.