Yes, philosophy has clarified mathematics.
In 'Naming Infinity', by Loren Graham and Jean-Michel Kantor, they argue that Russian mathematicians in the early 1900s were able to introduce new concepts to set theory due to their philosophical (and religious) perspective on free will and naming things.
"At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory."
I think this is a clear example of how our approach to mathematics depends on our philosophical beliefs. Both the French and the Russian mathematicians saw mathematics as a language that describes reality. For the French, this prevented them from advancing in set theory, since it ran against their beliefs of a continuous and orderly world. Meanwhile, the Russians were able to solve the contradictions in set theory and pave the way for new mathematical disciplines. Egorov and Luzin thought free will and the power of names were universal truths that existed in every discipline, not just philosophy or religion. They saw discontinuous functions as a way to describe freedom of choice. Ultimately, their perspective brought about a lot of progress in mathematics.