A previous post generated many doubts about random sampling, adequate sampling, and induction.

This post, as you might have induced by now, is about induction.

The word induction has many senses – the closest to what I mean here is logical induction: The process of deriving general principles from particular facts or instances.
Now, the important thing to note here is that the induced general principle or hypothesis, might not be deducable.

And this inducing, while seemingly less rational, is far more complicated. An example should put things in perspective –
Say you are teaching your child to recognize a cat.
You point to a cat and tell your child that it’s a cat.
Your child nods, even shakes its rattle.

You point to a pomenarian (a small furry dog), and ask your child what it is.
“Cat” comes the answer. But you correct it. It’s a dog you say.

After a couple more cats and dogs, your child now can recognize a cat. And a dog.

Now, this is human intelligence at work. And what is involved is Induction. Which in this case is far superior to deduction! For poor Artificial Intelligence researchers cannot make even a super-computer distinguish a cat and dog with just a few examples.
And a super-computer is a far superior deducer than a baby.

When the baby sees you point to the cat, it sees so many things – how does it know what pertains to “catness”? It sees your right hand pointing towards the animal, it sees the animal on a rug, it sees gazillion features of the animal – fur,
size, yada.

With these potentially infinite features, a logical deducer should have potentially infinite random samples!! Unfortunately (or fortunately, I hate cats) there
aren’t infinite cats available for your baby’s perusal.
So, the baby induces a general hypothesis of “catness” from specific
examples.

Most of our ideas, our thoughts are inductions – forming stereotypes from specific examples and instances. Thus, the next time somebody tells you that stereotyping is bad, and that only vanilla logical deduction/reason is kosher, you can have a smug chuckle for you’ve induced deduced that he knows little about induction.