The irony here is that even though the Little Monk warns his parents about the dangers of Galileo's radical theories, the Little Monk becomes entranced by the truth of those theories as well.
Near the beginning of the play, the Little Monk has a good point: the danger of revealing such a "radical" theory that the earth travels around the sun. The Little Monk has poor parents who are devout Roman Catholics. Their one comfort is their faith in God and their believe in the one true Church. The danger of Galileo's theory for the Little Monk's parents is that the earth is not the center of God's thought process and, therefore, that the Little Monk's parents are not being monitored by a caring God who knows all of their doings and sufferings.
In a sense, the Little Monk believes that true belief in Galileo's theories would take his parents' hope away, leading them away from the Faith that sustains them in their poverty. Just the fact that Galileo's findings (that the earth revolves around the sun) call the Roman Catholic Church's truths (including that the sun revolves around the earth) into question. Despite the facts themselves, any discrepancy here can cause people to doubt the Church. Of course, the Little Monk is entranced by the truth of Galileo's theory and becomes a true believer, despite the teachings of the Church.
In conclusion, we can say that the Little Monk is absolutely enraptured by truth, both the truth of Galileo's theories and the truth of what might happen as a result of them.