The senses and mind are designed only to study objects. They do not have access to the subject which is behind the senses and the mind. Similarly, the senses and mind are designed only to study the properties of objects. They do not have access to the nature of the substance beyond the properties. So, either we have to remain inconclusive about these two, or we can rely on the Vedas as the authority. The Vedas reveal both these as pure consciousness. No other experience or logic can prove or disprove these two axioms because they are beyond their jurisdiction. We can only take these as axioms and work out the logical implications. The implications, when analyzed carefully, are found not contrary to experience. So they can be accepted without any conflict with logic or experience. The benefit of the implications is astounding. It brings an end to all sorrow.
Anything that can be objectified is not me. Thus, the body, the mind and the apparent subject cannot be me. I, called the Atman, am the pure conscious witness, which merely illumines everything. I do not have any qualities and so I am beyond all changes. So I am beyond all limitations of space, time and causation. The fundamental substance of the universe is consciousness. Everything is an appearance of names and forms in the infinite partless consciousness, which is called the Brahman. Thus Atman and Brahman are the same. It is only the limiting adjuncts that make them appear as though different.
I, the Atman, cannot be affected by anything. I am ever free. It is only my wrong understanding of my true nature that made me think that I am limited and bound. Right understanding of my true nature shows me that I have never been limited or bound. This understanding is knowledge (jnana) and this knowledge is itself liberation (moksha).