Notre Dame offers a unique joint PhD degree program between mathematics and philosophy, the program in logic and the foundations of mathematics. For Notre Dame undergraduates of any major, I encourage you to consider the mathematical philosophy minor.
Notre Dame has strong research groups in logic in both philosophy and mathematics. In philosophy, Notre Dame recently came out very well in the speciality PGR rankings in philosophy of mathematics (#2, tied with NYU, Princeton, behind Harvard), mathematical logic (#2 tied with CMU, behind Harvard), and philosophical logic (group 2). In mathematics, Notre Dame has a strong research group in mathematical logic.