Purpose is direction, with the thing the direction is towards seen by a self as giving pleasure.
Desire can be seen as a kind of motion. All desire is from and towards, with the combination of from and towards, which is through.
We are always in a possible relation to something which can make us more pleased. Where we know this relation and can accept it, we, or ourselves, have a direction towards it; the direction affirmed, or made will, is a purpose.
There is a relation of increasing knowledge in the following five words: motion; direction; motive; purpose; will.
The going towards something and the acceptance of this going towards, or direction, is purpose.