Perhaps it has been cited elsewhere in this context, but Hilary Putnam's 1980 short essay "Models and reality" brings together mathematics and philosophy in its discussion of $V = L$ and the Loewenheim-Skolem theorem: http://www.princeton.edu/~hhalvors/teaching/phi520_f2012/putnam1980.pdf
Another source of recent interaction is the field of axiomatic theories of truth (Kripke, Herzberger, Leigh and Rathjen and others). For example: http://www1.maths.leeds.ac.uk/~rathjen/AbsoluteEnd_Truth.pdf
Maybe these are examples of mathematical logic clarifying philosophy...