It is a common misconception that Sherlock Holmes uses deductive reasoning to solve crimes, and the biggest perpetrator of that myth is the Sherlock Holmes series itself. Chapter 2 of A Study in Scarlet (the first of the Sherlock Holmes books) is even called "The Science of Deduction". This is really a misnomer.
What it should be called is abductive reasoning (such is the popularity and ubiquity of this mistake that, even now, my spellcheck is telling me 'abductive' is not a word. Do I mean 'deductive'? NO. NO I DON'T. And technically nor do most other people).
Now, here's where things get a little more muddled, because while Sherlock Holmes says he uses deduction to solve his crimes, what he's actually describing is abduction, but sometimes he also uses induction.
Jesus Christ. Let's break this shit down.
Deductive reasoning is where you reason out something that cannot be challenged. There is no room for you to be incorrect.
So, for example, if I said: "all living organisms need food to survive. That cat is a living organism, so therefore, that cat needs food to survive", this would be an example of deduction.
This is what Sherlock Holmes SAYS he does, but it's not, because all of his 'deductions' have room for interpretation and for another explanation. He could theoretically be wrong. He just never is. And with true deductive reasoning, there is no capacity for a conclusion not to be guaranteed.
Abductive reasoning does not, and cannot guarantee a conclusion. It is a logical inference in which one strives to find the simplest and most likely explanation for the information we have. It usually relies upon observation, and it can be a heavily creative process.
The below example was provided to me by an episode of QI, Series L, episode "Literature":
So, for example , let's say I see my friend Alan, who is crying and wearing a jersey of his favorite sports team. I know that Alan cries every time his favorite sports team loses. I also know that most sports fans wear team memorabilia whenever there is a game on. I can therefor abductively reason that Alan's favorite sports team played a game today and lost.
This is not a guarantee. Maybe he just ran out of clean shirts on the day his wife left him, which would account for him wearing a jersey and crying. But based on what I know and observe and what is the likeliest and simplest explanation, I can assume, with relative certainty, that his team lost a game today.
This is the process Sherlock Holmes uses, albeit with more and more tenuous observations and connections.
Inductive reasoning is when you can predict something based upon patterns of current data, without necessarily an explanation as to why this pattern is repeating.
In a hyper-simplistic example, if you put 50 mice in a maze, and all 50 of them take the first right instead of the first left, you can induce that Mouse No. 51 will turn right instead of turning left, too. Again, this could always be proven wrong, and it doesn't explain why they're all choosing that direction.
On occasion, Sherlock Holmes also uses inductive reasoning--he knows based on what has happened before that someone or something will happen again. The problem is that this often so quickly gets absorbed in his abductive reasoning that we don't see much of it.
Right, so that explains the different types of reasoning. The question is: why does Sir Arthur Conan Doyle call abductive reasoning 'deductive', when it isn't?
The quick, and probably accurate answer, was that Conan Doyle just got the word wrong and never bothered to correct himself, assuming he even knew he was wrong in the first place. I have a friend who is a Holmes scholar, who has verified for me that Conan Doyle was VERY SLOPPY when it came to the Sherlock Holmes canon. He completely contradicts himself at times, or has clearly forgotten things he's written before (so timelines or backstories sometimes don't make sense). He even changes Holmes's and Watson's personalities in some stories to fit with certain behavior he needs them to have in that given moment so his plot will make sense.
He was the king of continuity issues. And, for the most part, that's fine. No one reads Sherlock Holmes stories for the rigorously sculpted and monitored universe--that's not really the draw. But given the HUGE impact of the series and their lasting popularity, this does mean that Conan Doyle's mistake has misinformed generations of people, leading "deductive reasoning" toward becoming what is called a skunked term.
This is my final cool fact of the day, and also one of my favorite academic buzzwords: a skunked term is what happens when a word is misused so much, for so long, by such a majority of the population that speaks that language, that the definition of that word changes culturally, even if not technically. Over time, the definition will officially change, but until that happens, it is called a skunked term. (This does NOT mean that every word which gets misused, even if it has a fairly common misuage, is a skunked term.)
A good example of a skunked term is the word "nauseous". Technically, if you say "I am nauseous", it means that you make someone else sick to his or her stomach. Rough seas are nauseous. Nasty food is nauseous. What you should say is, "I am nauseated", which means you are personally sick to your stomach, i.e., "The nauseous sea made me nauseated".
However, the word "nauseous" has been misused for so long and so consistently, that the definition is actively in the process of changing. Most people would probably interpret "I am nauseous" as "I feel ill", even though the dictionary wouldn't agree with you. In another few decades (if it hasn't already started happening), the definition may officially change, where "I feel ill" replaces "to make one feel ill" as the primary definition, with the latter becoming an archaic usage of the word.
Since deductive/abductive/inductive reasoning are still used very heavily in the maths and sciences, I very much doubt that their meanings will ever properly change. However, at least for deductive reasoning, it is culturally a skunked term in that so many people misuse it that its meaning has shifted in the popular consciousness.
Thanks a lot, Conan Doyle!
Also, my head hurts now.