When he hardens his own heart, that is his free will at work. But when God hardens his heart, that is no human free will.
Some say that Pharaoh made such a habit of hardening his heart that in the end he could not longer control himself; he had effectively abdicated his free will and it hardened by itself – in Biblical language, God hardened it.
The sages say that sin starts like a casual traveller; it becomes a welcome guest; in the end it takes over your house.
Another view is that it starts like a spider’s web, which is soft enough to be removed by a tiny touch; eventually it becomes as tough as a cable which cannot be broken. If this is the case, the hardening of Pharaoh’s heart is never anything other than his own doing.
Nonetheless, the philosophers are all exercised by the problem of how free will and determinism can co-exist.
A major statement of the dilemma is the rabbinic saying in the name of Rabbi Akiva, “Everything is determined, but free will is given.”
One of the many answers is that both parts of the dilemma are valid and what creates the problem is the mathematical one of the relationship between them: how much free will do we have, how much is determined?
There are thinkers who point out that the answer depends on who you are. The amount of free will given to a person differs according to their background and experience. No two people have the same genetic inheritance, nor are they have influenced by the same factors. Nor do they respond to events and influences in precisely the same fashion.
The Mussar (“ethical instruction”) movement teaches that life and free will begin where heredity and education leave off.