"I agree that there is a difficulty; it is the difficulty of the gap between conscious processes and physical events." Stebbing, Philosophy and the Physicists Chapter 9, 164 (in my 1944 edition [in other editions p. 217]).
"There is an urgent need to-day for the citizens of a democracy to think well. It is not enough to have freedom of the Press and parliamentary institutions." Stebbing, Thinking to Some Purpose
Readers may recall my exchange with Mohan about the enduring significance of L. Susan Stebbing. I argued that among the pre-eminent (and largely anti-metaphysical) founders of analytical philosophy she was the most significant theorist of the nature of analysis and the metaphysical turn it could take (I also argued she gives us a good glimpse of why Spinozism is the main alternative to analytical metaphysics). Mohan responded by criticizing Stebbing's command of the analytical tools available to her. I defended Stebbing by claiming that Mohan misunderstood the way in which Stebbing is thinking about reference. We left it there in public. Mike Beaney gives a nice treatment of the issues here, although (and I say this with trepidation) Beaney mistakenly follows Max Black in understanding Stebbing-style metaphysical analysis as uncovering facts rather than the structure of facts!
Here, I focus on another enduring, largely overlooked significance of Stebbing's philosophizing: her willingness to challenge the way the authority of science is used in irresponsible, public speech (recall the moving closing lines of her (1937) Philosophy and the Physicists). Now we are all indebted to Abe Stone for reminding us that the Carnap-Heidegger split centered on what the nature of responsible speech by philosophers is (see Jeff's post and mine), but Stebbing reminds us that the authority of science has displaced philosophy (and theology) not just to settle questions within philosophy [I call this "Newton's Challenge to Philosophy"], but also among the educated public, but in doing so the need for a certain philosophical expertise remains (recall David Albert's criticism of Krauss). Stebbing's Philosophy and the Physicist ought to be a model for us as we think about the public role of philosophy.
"the former ["the world of physics"] is to be found only in physics; it is the work of scientists; its forms changes as fashions of thinking change and in accordance with the discoveries of experimentalists. The latter, the physical world or Nature, is that which physics is about, and other sciences also are concerned with it. This does not change; there is no reason to suppose that this is created by physicists." (208; emphasis in original) 
As the last sentence reveals, Stebbing is (despite talk of "fashions") not some kind of skeptic or even a constructivist. She is a common-sense realist. (She underestimates the ways in which sciences do create the environment they study, but about that some other time.) Scientists should not conflate their model-world(s) with reality. (To do so often leads to expert overconfidence of the sort familiar from recent economics.) Beyond substantive issues in philosophy of physics and issues pertaining to freedom-of-will, there are three related (let's call them meta-philosophical) issues her book illuminates:
First, not unlike Schlick, who contrasts his “true” empiricism (which grants considerable authority to first-person experience) with the (presumably false) empiricism he associated with Hempel (who relies on the authority of text-book experience), Stebbing is a friendly critic of science. She allows that science can teach us a lot about the physical world and show that common sense can be wrong in serious ways. But she believes that then-existing science had not properly tacked the problem of consciousness (see the first epigraph to this post above). In failing to do so, "The methods of physical science are not adequate, and not intended to be adequate, to the description of all that is experience." (93; ) Second, she thinks that when science tries to re-describe ordinary experience it is very likely (a) to conflate "the world of physics" and "the physical world;" this often happens in the context of (b) taking metaphors, which are needed for articulating the content of esoteric mathematical physical theory in ordinary speech, too literally (for example here).
Third (and this is related to the previous two), in show-casing her analytical skills in conceptual analysis, she is diagnosing a problem due to intellectual division of labor (a common interest among scientific philosophers in the 1930s): scientists are trained as specialized experts not as sophisticated philosophical, public intellectuals. (I am not claiming that contemporary training in philosophical expertise makes one good at being a public intellectual!) Her criticism of Eddington, who was (of course) not just a fantastic physicist, but also had very serious and insightful philosophical acumen, is all the more sobering given that he is about as good as it gets in mixing science, philosophy, and writing for a public audience. (Nearly as good as Feynman w/o the dismissiveness toward philosophy!) Much of Stebbing's work can be understood in trying to help us all (scientists, philosophers, citizens, etc) speak responsibly to the public (see the second epigraph above). [A topic of recent interest to me.]
Now in response to an earlier post, the distinguished philosopher of physics, Steven French, wrote, "Stebbing also exemplifies analytic philosophy's failure to grasp the huge changes in physics represented by quantum mechanics and general relativity. Her famous critique of Eddington - Stebbing, S., (1937), Philosophy and the Physicists, Methuen and Co. - fails on so many levels to grasp both his structuralist agenda and the relevant physics it was motivated by." When asked to clarify, French followed up with:
Let's leave aside tone and eliminativism, and let's grant French that Stebbing is uncharitable to Eddington's philosophical project and does not emphasize fruitful features in it. But French misses the point when he claims that she does not appreciate the implications of the relevant science. She does not claim to do so. Her book is not about the philosophical promise of Eddington. It is about his tendency to promote a world-view that goes well beyond the scientific evidence he could have marshaled. Having said that I find her pretty sensitive to both her lack of expertise in some areas as well as scientists' tendency of misunderstanding the philosophical implications of science. (I also think Stebbing forced Eddington to clarify his claims in non-trivial fashion.) We need a lot more philosophers that are willing to engage in critical and informed fashion with the public authority of science; we can all learn from the debates that will follow.
"What irritates me is that she took an uncharitable analytic axe to Eddington's popular works - so she comes across as rather sneering, as certain philosophers are/were wont to do - but fails to appreciate either the implications of the relevant science (perhaps because she was relying on help from a minor and rather staid physicist) or the nature of E's project (which is flawed in all sorts of ways of course but has virtues that she entirely misses). And of course part of the reason for my irritation is that she represents an early form of the anti-eliminativist tendency!" [See here for more on French's favorable opinion of Edington, and treatment of some of the disagreement between Stebbing and Eddington]