The term "scientific method" is itself a philosophical term (as is "method" in this context). Read, or even skim, this and notice how many of the important figures listed were philosophers:
In that case, let me go a step further: although I wouldn't respond the way some other folks have, I get why they would. Many of my most memorable and most intellectually stimulating classes were those that weren't related to my engineering degree. The philosophy classes, though, never even approached "intellectually stimulating" status. I wrote a good 80-100 pages of pseudointellectual drivel about half-baked analogies like the "answering machine paradox," and accrued thousands in debt in the process.
Another thing: The great thing about Philosophy is that there are no wrong answers. But, the bad thing about philosophy classes is there are wrong answers. Open-endedness and free thinking don't scale to 150-seat lecture halls, indifferent TAs, and PhD-candidate "professors" doing the bare minimum to get a diploma.
If there is one space where it shines, sure it’s mathematics. But even there, the most notable mathematicians highly rely on some intuitions far before they manage to prove anything, as well as while selecting/creating their conceptual tools to attempt to build the proof, and rarely go to the point of formalizing their points through Coq/Isabelle or even with meticulous paper craft à la Principia Mathematica from Russel and Whitehead.
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