Five Greatest Women Philosophers

Aeon Ideas asks, who are the five greatest women philosophers?

Nigel Warburton lists (deliberately restricting himself to the twentieth century):

(1) Simone de Beauvoir
(2) Hannah Arendt
(3) Judith Jarvis Thomson
(4) Patricia Churchland
(5) Martha Nussbaum

Amusingly, he refuses Anscombe a position entirely on the basis of her views of sex, and includes Thomson entirely on the basis of an argument for abortion.

Gene Glotzer lists:

(1) Simone de Beauvoir
(2) Elizabeth Anscombe
(3) Philippa Foot
(4) Martha Nussbaum
(5) Hannah Arendt

Avinash Jha lists (explicitly warning that the list is not so much a list of greatest as simply candidates for it based on personal experience):

(1) Simone Weil
(2) Hannah Arendt
(3) Luce Irigaray
(4) Susanne Langer
(5) Adriana Cavarero

As they all note, it's not a trivial question; there are lots of women philosophers, and it's difficult in their case to use direct influence as a proxy measure for estimating whether you are doing more than just indicating personal preferences, simply because the extent and nature of their influence has often depended on the culture of the day.

These questions are less interesting for who gets on the list than for who gets considered as a candidate and why. Assuming a standard of philosophical greatness in which we must have direct reasoning from the philosopher at first hand (thus eliminating very famous women philosophers like Hypatia, whose reasoning we can only guess at given a few anecdotes and the philosophical movements of the day, and a few fairly influential women philosophers like St. Macrina the Younger, whose reasoning we have but only second-hand), confining myself to those who are dead (since it is at least prima facie reasonable to hold that we need some distance in order to appreciate philosophers properly, and thus eliminating reasonable candidates like Onora O'Neill and Martha Nussbaum) and just using a purely subjective assessment of how seriously the philosopher should be taken today, this would be my first rough attempt (in no particular order):

(1) Lady Mary Shepherd
(2) Edith Stein
(3) Elizabeth Anscombe
(4) Simone de Beauvoir
(5) Simone Weil

But Arendt and Foot are both very reasonable candidates from the original lists, even under the conditions I've suggested. There are women philosophers I would recommend highly, of course, who aren't on the list. I think both Mary Astell and Catherine Trotter Cockburn are seriously worth anyone's time, for instance, but I don't know if I could point to anything giving me reason to rank them comparatively that much better than many other excellent women philosophers.