Existence itself is illogical... So I think the purpose of life is different for everyone.
The "purpose" of life doesn't necessarily mean the grand answer to everything. To me, it means to find your purpose.
I personally believe that the purpose of life is to be happy. I also believe that life is more than the physical, and that it is something spiritual as well. To keep it as open-ended as possible, I'd just say that the purpose of life is to live.