I think I would rather die than be unable or unwilling to answer that question. If your thoughts aren't developing and being influenced by anybody, then what are they being influenced by? How are you growing? Who previously influenced your thoughts if no one does now? Is there no one that you look up to for insight? Why wouldn't you share that info?
I watched someone dodge and get annoyed with the "Who are you reading?" question from a student today; the image will haunt me the rest of the month.