> A simple example is the moment of every episode of House M.D.
House M.D. was based on Sherlock Holmes, who uses inductive, rather than deductive reasoning. e.g. conclusions are not based on analytic reasoning of all the facts, but rather are supplanted by leaps of imagination, which made the series so compelling.
Intuition is inductive reasoning. Because it's not solely analytic, it can also result in answers that are also completely wrong.
Sherlock Holmes used abductive reasoning.
Deduction: cause + deductive rule -> effect
Induction: (cause + effect) x many times -> deductive rule
Abduction: effect + deductive rule -> possible causes
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.
Seems like OP has fallen into that trap.
For whatever it's worth, I don't think Inspector Lestrade would appreciate the difference, so Holmes needn't bother either.
Allow me to rephrase with more detail then: intuition is a mix of strong analytic and strong inductive reasoning running non-stop in the background of consciousness.