Today's prompts might have a layer of dust on them, they're so old, but the great ones are never too old to be useful. Each of them focuses on your character in a way you probably haven't before and can deepen your characterization. While you MIGHT one day use what you write here in a final draft, what is more likely is that it will inform what you already have but never actually see the page itself, so it is extra important to remember that this isn't for publication but to work on your craft and to have fun.
Pick a character already developed on paper or in your mind. Create a one page "tangent thought" within the mind of your character about philosophy. They must consider it in a way that is consistent with their other characterization. This aspect of philosophy should be something that you as the writer find fascinating; however, your character MUST NOT agree with you about it--at least not directly. You must explore this fascinating philosophical subject through the mind of a character that completely disagrees with you and do it with as much integrity as you possibly can.
Take a character within your own fiction and give them a quirk that is consistent with their persona. (A music lover may wear headphones everywhere. Or perhaps someone who loves movies goes out to catch a matinee every day.) Now take that quirk to a shocking extreme that is inconsistent with another aspect of their persona. (The workaholic who wears headphones even in meetings or the person going to a movie even though there's funeral arrangements for their spouse to be made.) You might end up with something too goofy to keep, or something that feels original and refreshing. The important thing is that you demonstrate that a human being is not a schema of priorities that always work out. Sometimes all of us do things that go against our nature. Being consistent with our inconsistency is the real trick.
Have your character describe something remarkable--a place, an event, or a person. Have their description reveal more about them as a character than the actual remarkable thing they are describing. If, for example, clothing is not very important to them, they aren't likely to recall the details of who was wearing what, but if they are very into cars, they may remember exactly what each person was driving.