Pedantic Issues with Sherlock Holmes

I have always had an issue with Sherlock Holmes. Not because I dislike the character or anything like that, but because of his misuse of terms.

Holmes frequently claims that he has arrived at his various astounding conclusions via deduction. Yet, it is clear to anyone familiar with types of inferences that deduction plays a relatively minor role in his reasoning. His keen observations and abductive inferences are what play the larger role in his inferences.

Deductive reasoning is when, given a certain set of assumptions, your conclusion must (logically) be true. There is no possible way that it is not true. So, if your assumptions are:
1. P implies Q
2. P
Then you can deductively conclude: Q
So, for example:
If I am sitting, I am not standing
I am sitting
Therefore, I am not standing

Deductive reasoning is very strong - the only way a valid deductive inference can be incorrect is if one of your assumptions is incorrect.

Abductive reasoning is different. You have some thing(s) to explain, and you do so by reasoning about what could have caused those things.
1. Q
2. P implies Q
Therefore, P (maybe)
For example, my friend is late for our scheduled meeting. If the bus was running late, this would cause her to be late. Therefore, it is reasonable to assume the bus is running late. This is an abductive inference. Even if the assumptions are true, it may be the case that the conclusion is false. However, this is still an invaluable reasoning tool which we all use frequently throughout the day.

The other main form of inferential reasoning is inductive reasoning, where you reach a conclusion based on repeated observations. Just like abductive reasoning, an inductive inference is not as airtight as deductive, and can be incorrect

So, let's look at what Holmes does. I will take the example Wikipedia uses.

1. If leather on the side of a shoe is scored by several parallel cuts, it was caused by someone who scraped around the edges of the sole in order to remove crusted mud.
2. If a London doctor's shoes are scraped to remove crusted mud, the person who so scraped them is the doctor's servant girl.
3. If someone cuts a shoe while scraping it to remove encrusted mud, that person is clumsy and careless.
4. If someone's shoes had encrusted mud on them, that person has been very wet lately and has been out in vile weather.
5. Watson's shoes are cut
Therefore, Watson has been out in vile weather and has a clumsy servant girl.

Note that the first 4 premises must not have been deduced - it is possible for any one of them to be false in certain circumstances, and therefore at least part of the justification for them will be inductive or abductive. Yet, given these premises, there is no big surprise about the conclusion. Nearly anyone who is given these premises could come to the conclusion which Holmes comes to. The deductive inference is not the interesting part. This story of how Holmes did this inference is also very questionable. Did his mind really first come up with all of those disjointed premises, and then realize they all fit together in this nice deductive pattern to a specific conclusion? I find it much more likely that Holmes has really done is made the observation of the cut shoes (an observation), and then realized that the best explanation for the cuts in the shoe is a clumsy servant girl scraping mud off of the shoes (he likely abduced that they were cut while scraping mud off his shoes, and knew from an inductive inference that doctors usually have their servant girls scrape the mud off his shoes). He then realized that this implies that Watson has been muddy and that Watson has a clumsy servant girl. The deduction of these conclusions is secondary to the inference to the best explanation (inference to the best explanation is just abductive reasoning) of the shoe cuts.

A second pedantic issue that I have with Holmes' reasoning is when he claims, about possible explanations "When you have eliminated the impossible, whatever remains, however improbable, must be the truth." While I must admit that this is, technically, true, it is very hard to ever know that you have all of the possible explanations, so you never know exactly what "remains". Simply, this never applies to any of Holmes' situations. He never proves that the various crimes he is investigating could not have been caused by aliens, who used their superior technology to plant evidence. This is extremely improbable, but it has not been shown to be impossible. What Holmes' does do, is inference to the best explanation, not the only remaining possible explanation.