I do understand that some people may consider the philosophy of science intrinsically valuable.
I do understand that some people may consider the philosophy of science intrinsically valuable.
Also, philosophy of science is not necessarily about producing useful stuff for the practice of science, but usually helps better understand the relationship between humans and knowledge. It allows scientists to take a step back and see the big picture before diving back into their practice. As such, it shapes the way we think of and do science, and allows for better questions to be asked, and gives better ways to frame those questions.
At this level, mathematics is a discipline that's entirely unlike science, in that (at least if you believe it's philosophers) science doesn't prove anything true, it just has a bunch of competing theories some of which get disproved by experiments.
Also, the second paragraph of my first comment is not about logic.
Karl Popper was a major study of this problem and wrote about probably the most common and universally acceptable notion of scientific truth in the mid 1900s. Before then this notion of truth was in practice used, but it may have been difficult to have a clear conversation about it. Worse, without a clear understanding of the properties which give rise to processes with generate "truth" (i.e. the "scientific method" which, even being really generous, is better thought of as a menagerie of related methods) it may have been a little hard to determine whether someone's scientific program would be effective or agreeable.
So Popper clarified the notion of "Science as Falsification", of "Truth as what weathers evidence". For Popper, nothing was science unless it was vulnerable to falsification and nothing was true unless it was both science and withstood all attempts to falsify it.
This has a major effect on modern statistics. Statistics can be regarded, not entirely incorrectly, as the quantification of the pursuit of truth. It seems to give mechanism to the idea of models relating to evidence and the pruning out of falsified models. It's difficult to ask questions about why statistics is a meaningful tool for scientific pursuits without invoking Popper.
The scientific method comes to mind.
http://en.wikipedia.org/wiki/Novum_Organum
Full text here: http://www.constitution.org/bacon/nov_org.htm
So its not like nothing has ever come from philosophy as a hypothesis successfully validated as a useful predictive model, its that it happens all the time and we do NOT talk about it, just like Fight Club.
(edit to add another way to phrase it is if a hypothesis is dredged out of one individuals unconscious random internal noise source, we call its source Science. If it comes from a rational and reasoned conscious debate between thinkers, we don't talk about it at all, or at best we call it common knowledge. Perhaps its an attempt not to appear vain or conceited?)