Geoffrey Berg, author of The Six Ways of Atheism, said the argument "[described] the unbridgeable gulf in comprehension (and identification) for a mortal with any supposedly immortal entity."
The arguments claims that:
1. Man is finite (in time, space and power etc).
2. God if he exists is infinite (in time, space and power etc).
3. Therefore mankind cannot possibly recognize God or even know that God exists.
This argument is extremely problematic for several reasons. The first is simply that it is demonstrably false. Man is aware of many things which are infinite, such as numbers or the gravitational mass of a singularity. If Berg's reasoning was correct, then we never would have invented mathematics.
While it may be true that we cannot recognize God, which even theists admit, it does not follow that we cannot be aware of His existence through thought and reason, which is exactly what Aquinas' Five Ways tried to do. It also does not mean that an infinite entity cannot reveal itself through "religious experience."
In other words, the argument asserts conclusions which are not supported by the premises.