# Deductive or Inductive reasoning?

Sherlock Holmes famously said,

“Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.”

Is this Deductive reasoning, Inductive reasoning or something else?

Thanks!
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Commented:
I would say it's Deductive Reasoning because you are deducing at the conclusion by reducing impossibilities but very interesting question.  Hope someone else can join in.
I'm no philosopher, and I know very little about Arthur Conan Doyle quotes, however,

To me in the most simplistic form appears to be a logical statement of causality:

IF you eliminate all the impossible : THEN the truth is returned.

I've spent a few minutes trying to propose a situation where this may not be true.

I'm wondering if one of our physicist, or quantum computing specialists may be able to offer insight into Q-bits or Schrodinger's cat, and whether they might affect the statement?
RetiredCommented:
the statement
“Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.”
is inductive reasoning, i.e. from Wikipedia:
Inductive reasoning (as opposed to deductive reasoning or abductive reasoning) is reasoning in which the premises are viewed as supplying strong evidence for the truth of the conclusion. While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument is probable, based upon the evidence given.
https://en.wikipedia.org/wiki/Inductive_reasoning

however, the process of elimination requires Deductive reasoning, again, from Wikipedia:
Deductive reasoning, also deductive logic, logical deduction is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion. It differs from inductive reasoning and abductive reasoning.

Deductive reasoning links premises with conclusions. If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily true.

Deductive reasoning (top-down logic) contrasts with inductive reasoning (bottom-up logic) in the following way: In deductive reasoning, a conclusion is reached reductively by applying general rules that hold over the entirety of a closed domain of discourse, narrowing the range under consideration until only the conclusion(s) is left. In inductive reasoning, the conclusion is reached by generalizing or extrapolating from specific cases to general rules, i.e., there is epistemic uncertainty. However, the inductive reasoning mentioned here is not the same as induction used in mathematical proofs – mathematical induction is actually a form of deductive reasoning.
https://en.wikipedia.org/wiki/Deductive_reasoning

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