I understand that it is a naive and very general question. I would like to know when does a theorem of theoretical computer science become interesting to professional philosophers? I understand that the question whether P != NP is pretty interesting to philosophers. Now let's take the conjecture about the existence of one way functions. Is there any philosophical implications of the existence of one way functions?
You might be interested in Scott Aaronson's recent paper Why Philosophers Should Care About Computational Complexity, to appear in Computability: Gödel, Turing, Church, and Beyond, edited by B. J. Copeland, C. Posy, and O. Shagrir, MIT Press, 2012. ECCC TR11-108, arXiv:1108.1791.