Is Art For the Artist or the Consumer?

During a recent recording session, I had a conversation about creating music and art for yourself vs. creating it for others. In some ways you create art for yourself, because it is a fulfilling thing that expresses a part of you. In other ways, the moment you have created something, it is no longer yours and suddenly becomes the emotional property of someone else.

So which is it? How can art be both for ourselves and for others’ enjoyment?