You can argue both sides, I had to do it a lot in my last philosophy course (Asian philosophies and religions, great class, a real midnblower). It's still important to make the stance you are going with known before you start.
The way I've always liked to do it is say which point I'm agreeing with, give the reasons why, and then go into the reasons why the other one *could* be valid, but is still not quite as right. When making an persuasive paper, the best way is to take one side, agree with the one, and shoot the other down. You still have to thoroughly explain both sides, but it gives it more of a focus and impact when you pick one from the beginning.
This is basically what I've been told to do since about the 8th grade, after we were finally told to cover both sides on persuasive essays.
NOTE: Stream of consciousness can be one of the best writing styles for poetry, but is one of the worst for persuasive essays, or position and research papers. Yours is a little like that, and you definitely want to stay away from that. Even for a philosophy paper, the more clearly your point gets across, the better. There's a reason why no one likes Kant.