[2] After receiving her doctorate, she accepted an appointment as assistant professor of philosophy at the City College of New York.
[3] Besides for her academic and editorial appointments, she also served as a fellow of Lichtenberg-Kolleg Institute of Advanced Study, Georg August Universität, Göttingen, in 2009–2010, received a Berlin Prize Fellowship from the American Academy in Berlin in 2008, a Fulbright Senior Research Award in 2003–2004, and has also held a number of other fellowships.
Significant focuses of her research have included comparative analyses of differing accounts of the nature of objectivity and reason, issues of rule-following and skepticism, as well as the limitations of formal logic, analysis, and mathematics.
[6] Floyd has written a large number of peer-reviewed papers, and has served as editor for several series, primarily about analytic philosophy.
[4] She has served as the editor of one volume, Future Pasts: The Analytic Tradition in Twentieth Century Philosophy, a collection of essays all related to Burton Dreben's belief that analytic philosophy was a failed effort to bring to philosophy the level of clarity offered by science, and his further belief that it was most important because of its failure to do so.