What is a life purpose?
Assuming we are all born with what I call an essence, also called our Self, a purpose is when our Self is expressed on this earthly dimension, through structures and actions.
Another way to say it is, a purpose is both the recognition of one Self and the creation of the expression of it. The word Self-expression is perfect: all doing become an expression of your essence.
Where does paradox fit in this picture? Our Self is beyond time, while whatever you do take time, but there is only the moment of now.
Have fun!