It often is, but you don’t truly come into contact with anything permanent, and all of the 5 aggregates are impermanent. Your idea, perception, or sensing of any sort of permanent thing such as a law or concept are created and ceased.
Saying “there is some self behind the impermanent processes of the mind” is a self theory. It is subtle in that you may still be calling the impermanent processes self, but either way, The Buddha mentioned many self theories beyond just materialism:
DN1
‘That which is called “the eye”, “the ear”, “the nose”, “the tongue”, and also “the body”: that self is impermanent, not lasting, transient, perishable. That which is called “mind” or “sentience” or “consciousness”: that self is permanent, everlasting, eternal, imperishable, remaining the same for all eternity.’
…
“The self and the cosmos are eternal, barren, steady as a mountain peak, standing firm like a pillar. They remain the same for all eternity, while these sentient beings wander and transmigrate and pass away and rearise.”
…
The Realized One understands this: ‘If you hold on to and attach to these grounds for views it leads to such and such a destiny in the next life.’ He understands this, and what goes beyond this. And since he does not misapprehend that understanding, he has realized extinguishment within himself. Having truly understood the origin, ending, gratification, drawback, and escape from feelings, the Realized One is freed through not grasping.These are the principles—deep, hard to see, hard to understand, peaceful, sublime, beyond the scope of logic, subtle, comprehensible to the astute—which the Realized One makes known after realizing them with his own insight. And those who genuinely praise the Realized One would rightly speak of these things.