Logic has little value in philosophy because the terms have no specific inherent meaning. The solution seems to be to fix specific meaning to terms, but your stuck using meaningless terms to do so. Queue a recursive waste of time.

Though people are used to ambiguity and love extracting meaning from arbitrary stories, so it's not all that obvious of an issue. At its core philosophy is not about extracting meaning through analysis it's about conveying what someone has already desided to be true.