Susan Stebbing, the UK's first female professor of philosophy, was highly regarded by her contemporaries but remains largely neglected by historians of analytic philosophy. Very little has been written about Stebbing's metaphysics, philosophy of science, and views on common-sense truths. Although recent commentators typically describe Stebbing, as Ayer had done, as "a disciple of Moore", I will ascribe to Stebbing a distinctive view of her own in some respects allied to Moore, in some respects to Whitehead, in some respects wholly original. This becomes clear once we consider, as previous commentators have not done, the connections between Stebbing's views on common sense, metaphysical analysis, philosophy of science, and the refutation of idealism. It is rarely noticed that Moore's anti-idealist "Defence of Common Sense" does not end with a triumph over the idealist, but in aporia. Moore's emphasis on the truth of common-sense claims turned out to leave room for forms of idealism which accept common-sense truths but analyse them in idealist terms. Such analyses were embarrassing to Moore because he considered them "paradoxical". Stebbing, I argue, made a significant advance on Moore by distinguishing between "same-level", language-to-language, analyses, from metaphysical, directional analyses of the facts which account for the truth or falsity of expressions. Metaphysical analyses, Stebbing held, may well sound paradoxical and yet be correct, because they involve significant and possibly surprising assertions about reality, which ultimately settles truth or falsity. Stebbing applied her novel methodology of metaphysics to good effect in her philosophy of science. In Philosophy and the Physicists, Stebbing rebutted Eddington's idealist line, which includes the assertion that every familiar object has a "shadow" object in the world of physics. She argued that the scientific truth "this table is mostly empty space and some subatomic particles" constitutes, despite its "paradoxical" appearance, an admissible directional analysis of "this table is solid", so we need not posit both a solid table and its physical shadow. Thus Stebbing's method might succeed where Moore's failed, providing a new and viable route towards the refutation of idealism.