For myself, I’m not inclined to choose between the different images. Each seems to be useful in its own way. Nevertheless, I believe, the different images do suggest something in common: Philosophy more than the other liberal arts tends to think and rethink its relation to the other arts. Conversations between mathematicians and poets, or between psychologists and physicists, may come and go. But the conversations between philosophy and each of the arts, in contrast, are always ongoing. The “ancient quarrel” between philosophy and poetry, for instance, does not seem to be fading away. And likewise, the implications of developments—both technological and conceptual—in physics and psychology are constant food for philosophy. If philosophy is the mother of the arts, it is a mother that finds it difficult to let go of her children.
Philosophy insists on maintaining its conversations with the arts, I believe, as part of its constant need to rethink itself. “What is philosophy?” is a fundamental philosophical question. In contrast, “What is history?” or “What is mathematics?” are not historical or mathematical questions, but rather questions in the philosophy of history and in the philosophy of mathematics (even though they may be of interest to historians and mathematicians). And like philosophy, philosophers too need to rethink their activity. To be a philosopher, on this conception, means to have a question that never quite closes about what one is doing and why. But the fact that we have those ongoing conversations I mentioned above between philosophy and the arts means that asking this question about the nature of philosophy is not something philosophers can do completely by themselves. Like other philosophical questions, this one too, is discussed and answered (and re-thought, and re-answered) in conversation.