“The Personality of Godhead Lord Śrī Kṛṣṇa is in every living being along with the individual soul. And this fact is perceived and hypothesized in our acts of seeing and taking help from the intelligence.” (SB 2.2.35)
This is a profound verse!
By our intelligence we can know that Sri Krishna is in our own body. From the purport:
“He [the devotee] can perceive that intelligence is the form-direction of the Paramātmā plenary portion of the Personality of Godhead.”
“Now we come to the point that the things which are seen by a little use of intelligence cannot be animate unless we accept someone as the user of or director of the intelligence. Intelligence gives one direction like some higher authority, and the living being cannot see or move or eat or do anything without the use of intelligence. When one fails to take advantage of intelligence he becomes a deranged man, and so a living being is dependent on intelligence or the direction of a superior being. Such intelligence is all-pervading. Every living being has his intelligence, and this intelligence, being the direction of some higher authority, is just like a father giving direction to his son. The higher authority, who is present and residing within every individual living being, is the Superself.”
“Realization of the Superself by the individual self is the beginning of self-realization, and by the progress of such self-realization one is able to realize the Supreme Personality of Godhead by intelligence, by the help of authorized scriptures, and, principally, by the grace of the Lord.”
Here it is stated that we 1) ought to see that our intelligence is different from ourselves, and 2) that, in order for our intelligence to work it must be guided by some higher authority. That higher authority is the Paramatma, the Superself. Thus we can deduce the existence of God from the existence of intelligence. Intelligence is in itself a proof of the existence of God.
One way to understand this is by realizing that intelligence in its sane condition, reasons according to the laws of logic. Acceptance of the laws of logic are programmed into the intelligence from our birth (and before). But the laws of logic could not exist without God. The laws of logic are, for all practical purposes, objective, changeless, universal and eternal. They are made of thought-stuff, not of perceivable matter. Thus they require a personal God (one with the ability to think) for their existence and continued maintenance.
We also use our intelligence to make knowledge claims like “A is true.” But all knowledge claims presuppose a source of perfect knowledge. You cannot make a knowledge claim that is based on uncertainty. Perfect knowledge requires omniscience. Unless you know everything whatever you believe to know might be contradicted by what you do not know. So either you have to be omniscient to know anything, or you need to have knowledge from someone who is omniscient, and has the power to give you certain knowledge. Such a person is God. God is thus the necessary pre-condition for intelligibility. Without God you cannot know anything. You would not even be able to trust your senses, mind and intelligence without God. But you do trust your senses, mind and intelligence – at least to some degree. And therefore you ought to accept the existence of God.
So these are some ways in which the existence of our own intelligence is proof of the existence of God. When the atheist claims to know anything (which he is, even if he is denying it, since that is self-contradictory) he is stealing the laws of logic and presupposing the existence of omniscience; a source of perfect knowledge – both of which only make sense in a theistic worldview.
– Ajit Krishna Dasa