Many calls for a feminist science have ended with the disclaimer that there is no way to imagine such a science from within an androcentric society. Making the attempt requires dealing with two broad questions: “Is all or some of science socially constructed?” and “By what features is science recognized?” The strategy used here involves defining the components as we know them, asking if they are socially constructed, and, if they are, how they could be changed to be less androcentric. The conclusion is that all of science may be androcentric, and the approach to attaining feminist science may need to be radical, a total replacement of the scientific enterprise with one not based on the scientific method. Alternatively, we may accept a modification of current science, a “feminized” science (defined as doing the same science differently), as consistent with the political goal for feminist scientists.