Inductive Logic

Written on 26 December 2022.

Suggested by Eric from the book Plato and a Platypus Walk into a Bar

Inductive logic reasons from particular instances to general theories and is the method used to confirm scientific theories. If you observe enough apples falling from trees, you will conclude that apples always fall down, instead of up or sideways. You might then form a more general hypothesis that includes other falling bodies, like pears. Thus is the progress of science.

In the annals of literature, no character is as renowned for his powers of “deduction” as the intrepid Sherlock Holmes, but the way Holmes operates is not generally by using deductive logic at all. He really uses inductive logic. First, he carefully observes the situation, then he generalizes from his prior experience, using analogy and probability, as he does in the following story:

Holmes and Watson are on a camping trip. In the middle of the night Holmes wakes upand gives Dr. Watson a nudge. “Watson,” he says,

“look up in the sky and tell me whatyou see.”

“I see millions of stars, Holmes,” says Watson.

“And what do you conclude from that, Watson?

Watson thinks for a moment. “Well,” he says, “astronomically, it tells me that there are millions of galaxies and potentially billions of planets. Astrologically, I observe that Saturn is in Leo. Horologically, I deduce that the time is approximately a quarterpast three. Meteorologically, I suspect that we will have a beautiful day tomorrow. Theologically, I see that God is all-powerful, and we are small and insignificant. Uh, what does it tell you, Holmes?”

“Watson, you idiot! Someone has stolen our tent!

We don’t know exactly how Holmes arrived at his conclusion, but perhaps it was somethinglike this:

I went to sleep in a tent, but now I can see the stars.
My intuitive working hypothesis, based on analogies to similar experiences I havehad in the past, is that someone has stolen our tent.
In testing that hypothesis, let’s rule out alternative hypotheses
:
1. Perhaps the tent is still here, but someone is projecting a picture of stars on the roof of the tent. This is unlikely, based on my past experience of human behavior and the equipment that experience tells me would have to be present in the tent and obviously isn’t.
2. Perhaps the tent blew away. This is unlikely, as my past experiences lead me to conclude that that amount of wind would have awakened me, though perhaps not Watson.
3. Etc., etc., etc.
No, I think my original hypothesis is probably correct. Someone has stolen our tent.

Induction. All these years we’ve been calling Holmes’ skill by the wrong term.