> The fact that you can reason about intelligence is a counter argument to this

The fact that we can provide a chain of reasoning, and we can think that it is about intelligence, doesn't mean that we were actually reasoning about intelligence. This is immediately obvious when we encounter people whose conclusions are being thrown off by well-known cognitive biases, like cognitive dissonance. They have no trouble producing volumes of text about how they came to their conclusions and why they are right. But are consistently unable to notice the actual biases that are at play.