I was wondering if there is any other way of thinking besides deduction and induction, and I want an example.

I understand by “thinking” the action of being able to comprehend smthg, and explain it. I know that by “comprehend” you could think about many things (the same for explaining) but what I want to grasp is if there is any other method besides the ones named above but parallel to them.

Could be an example from mathematics or chemistry or.. well…

There is indeed, namely abduction.

Put simply, the essential features of each are as follows.

Deduction: a conclusion necessarily follows from (is entailed by; is a logical consequence of) the premises. So, if premises are true, conclusion must be true. But deduction tells us nothing new, because the conclusion is implicit in, is already contained in, the premises.

eg  Premise 1.    All Scots are drunks

Premise 2.    Craig is a Scot

Conclusion: Craig is a drunk

Induction:  from “expect more of the same” or “the future will resemble the past” we infer a likely, but not guaranteed conclusion. Unlike deduction this is not logically watertight, it is only probabilistic, but on the other hand it tells us something about the world.

eg   Premise: the sun has risen every morning for as long as we can remember.

Conclusion: the sun will rise tomorrow morning.

Because the world has exhibited regularities for eons, evolution has hardwired induction into sentient species. My dog for instance, is right now looking expectantly for her walk because she has had one around this time of day for years.

Induction notes regularities but doesnt explain them eg why the sun rises.

Abduction: here we infer the best explanation for the facts, so that abduction is also called “inference to the best explanation (IBE)”. It may not always be the right explanation, so that the conclusion, as with induction, and unlike deduction, is not guaranteed. However, unlike deduction and induction, it explains things, and is widely used in everyday life, in science, in medical diagnosis. Most of Sherlock Holmes’s “deductions” are actually abduction eg

Premise 1: the dog didnt bark in the night

Premise 2: dogs dont bark at friends

Best explanation: the intruder was known to the dog

We can update our estimate of the likelihood of our explanation in light of new evidence, and this iterated process can be systematized using Bayesian analysis. Abduction and Bayesian analysis are widely used in the field of Artificial Intelligence.