The argument claims that since all known mental activity has a physical basis (the brain), there are probably no disembodied minds. But God is conceived of as a disembodied mind. Therefore, God probably does not exist.
The problem with this argument is that it takes incredibly specific premises and claims to draw a general conclusion from them. It claims that the idea of a non-physical God makes no sense, therefore there probably is no God.
As a syllogism, it would look like this:
1. All known thought is a physical phenomenon.
2. There probably is no non-physical mind (from 1).
3 God is a non-physical mind.
There probably is no God.
But what about a physical God?
This argument is not a good argument against the existence of God because God's existence is not contingent on whether or not he has a physical body. It simply does not attack a critical issue. A Latter-Day Saint, for example, would respond to this argument by saying, "Sure, but didn't Jesus eat fish after His resurrection?"
|"Touch me not... not that you could anyways."|
If God has a physical body, then this argument has absolutely no force, and even Christians can't agree on whether or not He has a body.
In other words, this is an argument against the rationality of a Christian God with which many Christians would actually agree, and that is not a good sign for the argument.
But even if God has no physical body, we should hesitate when speculating in this way.
For example, this same kind of reasoning was used by scientists to suggest the existence of Aether. It was thought that all known waves propagated through a physical medium. If space has no physical medium, then light should not be able to travel through space. We should not be able to see stars and planets. Therefore, there must be some sort of medium, aether, through which light waves propagate. We now know this to be false. Light is, in part, a wave that requires no physical medium.
A wave that requires no medium seems as impossible as thought with no body, yet we do see celestial bodies.