Here's Sherlok Holmes, practicing the science of deduction, in a rather intense scene from the movie.
And here's Inspector Jacques Clouseau locking horns with his rival/partner in Pink Panther 2.
They call it the science of deduction. Yet, there is an interesting technical term to describe what Holmes and Clouseau did in these scenes. It's called abduction or Inference to the Best Explanation. Or simply, educated guess.
It's hard to prove it beyond doubt - like Jean d'Arc realises in this scene.
And yet, everyone resorts to abductive reasoning day in and day out. For example, at your office, you hear that there is a nasty fight between two friends in the sales team. And then a few days later you find them having lunch together, joking about this and that. And you conclude that they have made up with each other. That's abductive reasoning. Or you find the shutters down at one of the eateries you have gone to, almost always, finding yourself to be the only customer - and you guess they have shut shop. That's abduction again - for there could be a few other explanations why it was closed on that particular day. In both these cases, your arguments are not bullet proof. Yet, of all the causes you can attribute to the event you saw, what your conclusion would best explain your observation.
No one talks about abduction without referring to a man named Charles Sanders Peirce. Peirce's contribution to philosophy, maths, logic, statistics, research methodology is huge, and some of is works are considered to be the foundation of pragmatism, that he is referred to as the 'father of pragmatism'. He seems to have lived in a time that didn't care too much about pragmatism. He was kicked out of Johns Hopkins university because he lived and travelled with a person he was not married to. Only, his first wife had left him, and he soon got involved with another woman before getting a divorce. His adversary complained to the university. Starting a sentence with 'for all practical purposes...' probably didn't work in those days. We are digressing. But, let us record the fact that it was Peirce who introduced this term to philosophy, even if the idea had been around already.
And one more thing about abduction, that evokes Bayesian approach to finding things out. Bayesian approach simply states this: keep updating as you get more information. Thus abductive reasoning and Bayesian inference are about forming an hypothesis based on available evidence, and being willing to update as more information come in. Or as Keynes once said: When facts change, I change my mind. What about you, sir?