> That quote is an incredibly efficient summarization of the scientific method's core philosophy that (because you can't prove a positive), you falsify wrong hypothesis instead.

I disagree and I'll repeat what I said above: this is the antithesis of the scientific method. It's faith based and it opens the door to accepting hypotheses that have zero evidence to back them up. Follow this reasoning and you can just make things up.

In what way is that faith based? It seems to me that falsifying hypothesis until only one remains seems to be pretty scientific. Especially considering that (with regards to science, not solving a murder mystery) that means the world is forever stuck with whatever hypothesis was left at the end because we just didn't think of something else... the same principle or technique can always be used again...

The problem is that, in practice, there is no way to guarantee that you have actually eliminated every possibility. There are ways to constrain the answer within physics, but that doesn't always mean you have an explanation. Besides, within the scientific method (at least in my field of physics) emphasis is placed more on the predictions the answer can make, rather than the simple explanations. Simply eliminating other answers might give you an explanation for a singular case, but it fails to give you the predictive power we demand from all theories.

>there is no way to guarantee that you >have actually eliminated every possibility

So, what? You just stop once you eliminate the known possibilities?

That last possibility REQUIRES experiment, investigation and thought to verify. If you discover a new possibility then you apply the process again.

The approach is not a one-shot deal, you MUST keep applying it. The current laws of physics are models that we use to explain what we observe and (if the model is good) predict what we might observe.

This by no means implies that that the models describe what's really going on. It is possible to have a model that describes a system that works but is not complete. The deeper we dig, the more we learn.

The fictional quote was meant to describe a deductive approach to investigation, not a rigid method. How often did Holmes dig up new facts and change his mind after eliminating possibilities?

You gotta admit it works with mathematical proofs by contradiction.

Not really. Proof by contradiction means starting with the negation of the hypothesis you're trying to prove and then reach an impossible conclusion, thereby proving your hypothesis was wrong.

It still involves a rigorous logical reasoning, not accepting something because you're running out of ideas.

If you're defining the technique as not using logic, merely running out of ideas, of course its not logical and wouldn't work in practice. I don't see how what you described as not being 'eliminating the impossible', personally.

True, but rarely do mathematical proofs translate into physical proofs.

> emphasis is placed more on the predictions the answer can make

This is still based on falsifying the hypothesis; prediction is one of the useful tools by which a hypothesis can be experimentally tested. If a prediction ends up being incorrect, you're left with the null-hypothesis. It's entirely possible that the null-hypothesis may not be particularly useful, but it - as Holms said - "must be the truth".

At it's core, the scientific method is simply proposing ideas, and testing them. As zombie-Feynman said. "everything else is bookkeeping"[1].

[1] http://xkcd.com/397/

Just because you cannot reject the null hypothesis after an experiment (or 1000), does not mean it is true.