[ceceron]

I don't want to sound nitpicking, but if you're correcting someone, you should be ready to be corrected yourself...

Sherlock Holmes used abductive reasoning.

Deduction: cause + deductive rule -> effect

Induction: (cause + effect) x many times -> deductive rule

Abduction: effect + deductive rule -> possible causes

[ryanjamurphy]

This is a fabulously concise way of explaining the difference between the three. Bookmarking your explanation to share in the future!

A neat thing about reasoning is that we tend to use all three, too. Abduction → Deduction → Induction ... in cycles.

More on topic with the OP: to me, intuition is what happens when we skip through these steps. It's the heuristics we use to make good decisions when we don't have the time to "abduce" possibilities, "deduce" the likely answer(s), and "induce" the evidence of our deductions.

[hinkley]

Isn’t it a common complaint about Doyle that he has Holmes claim he is using one sort of logic when he is in fact using another?

Seems like OP has fallen into that trap.

[revolvingocelot]

It's worth noting that Doyle also has Holmes express ignorance of the Copernican model of the solar system and of popular intellectual figures of the time. Sure, this is probably just lampshading any mistakes Doyle-the-writer might make when Holmes-the-character gets something wrong, but when Watson expresses incredulity at this ignorance, suggesting that Holmes' worldliness surely exposed him to such things, Holmes cheerfully replies that he only ever heeds that information, and that fidelity of information, which helps him solve cases.

For whatever it's worth, I don't think Inspector Lestrade would appreciate the difference, so Holmes needn't bother either.

[chartpath]

Thanks for the breakdown! Abductive reasoning ftw.

[sanp]

Isn't Abduction the same as forming Hypotheses? Not nitpicking or anything. Just asking if it is correct.

[ceceron]

Sure. I've used "possible causes" instead of hypotheses to match other reasoning methods.