Necessary vs Sufficient

Philosophers and mathematicians make a distinction between ‘necessary’ and ‘sufficient’.

Air is necessary for human life, but it’s not sufficient. In other words, if you don’t have air then it’s game over. But if you do have air, you still need some other stuff to survive. So it’s not sufficient for survival.

If you’re a father, you’re definitely male. So being a father is a sufficient condition for being a male. (But you could be a male without being a father, so it’s not necessary.)

By the way, my favourite data science-related example of something being sufficient but not necessary is the Turing Test. If you pass the Turing Test, you’re definitely intelligent. So it’s sufficient. [Hah, reading this a few years later, this sentence has not aged well!]

But you could fail it, and still be intelligent. Perhaps you’re French, and don’t speak English. Or more interestingly, maybe you’re an alien with a different way of thinking. So it’s not necessary.

So passing the Turing Test is a sufficient but not necessary test of intelligence.