From a letter by the Rebbe:
I do not accept your assertion that you do not believe.
For if you truly had no concept of a Supernal Being Who created the world with purpose, then what is all this outrage of yours against the injustice of life?
The substance of the universe is not moral, nor are plants and animals. Why should it surprise you that whoever is bigger and more powerful swallows his fellow alive?
It is only due to an inner conviction in our hearts, shared by every human being, that there is a Judge, that there is right and there is wrong. And so, when we see a wrong, we demand an explanation: Why is this not the way it is supposed to be?
That itself is belief in G-d.
