The speech by the prosecutor is one of those moments in literature where it would be easy to pass it off as a misfire or, more bluntly, a really boring bit. However it is these moments, like the descriptions of the landscape in The Seven Pillars of Wisdom or the scientific observations of the whale in Moby Dick that encapsulate the whole point of the book. Here it is used to show that logic can’t lead to faith.
And in this proof of his argument is the wonderful description of the condemned man measuring the distance to the gallows and thinking how much time he has to this street and then to that and that it’s not so bad … all the way to the rope. Here there is faith against logic.
So the whole book is about how society (that’s why this is a murder mystery with a court scene) is drifting away from what Father Zosima hoped would be the future of Russia towards the more secular and scientific future of no morality. Dostoyevsky is trying to show that you can’t have faith with reason, that logic and absolute proof can’t lead you towards absolute belief. He is saying belief and truth start from within and can only be seen by ourselves. Nobody else can see our truth because each person’s truth is different – only we know where our heart is (the money bag) and what the truth even if we can’t prove it.