Set theory vs category theory and foundations of mathematics.

I have been mulling the following remarks in a critical and striking (because it ends with a series of quotes from Pierre Bourdieu) review by Mary Tiles of a recent book by Penelope Maddy, "The conclusion would seem thus to be that there are no philosophical foundations for set theory; its grounding lies in the mathematical practices for which it was once proposed as a foundation. And since presumably the same could be said for category theory there should be no question of which is the correct foundational theory, although Maddy makes no mention of category theory." (The thought is anticipated earlier in the review by a parenthetical remark: "in this mathematical sense set theory is not unique; category theory can also play that foundational-in-the-sense-of-unifying role.") Tiles' claim is not idiosyncratic because one can find it repeated in the Stanford Encyclopedia: "Category theory is an alternative to set theory as a foundation for mathematics." I find all of this a bit odd because according to the same textbook definition of a category seems to rely on sets, but compared to my fellow bloggers here at NEWAPPS I am terrible at math (and have not yet read Steve Awodey textbook on category theory!) so maybe others can enlighten me...