Some might wonder why we are discussing various ideas that seem so basic as to be obvious, while others might wonder what such ideas have to do with purification.
As a man thinks, so he does. Correct ideas lead to correct actions; incorrect ideas lead to actions that are, to varying degrees, incorrect or what we might style wrong or harmful, whether to the actor or those his actions affect. Believe it or not, the will is actually a blind faculty; it loves what the intellect presents to it as the good to be pursued.
If we are to be purified, it must begin in our minds. Yes, our hearts must be cleansed of disordered affections and love all lesser goods in proper relation to the supreme good, which is God, but the renewal must begin in our minds. Before a man can make the choice and take the steps to return to the correct road, he must realize that he is on an incorrect road. If this increasingly-insane world is to return to sanity, the process must begin with thinking straight (or correctly) about God, ourselves, and the world in which we live.
Ideas are immensely powerful. The disorder we see all around us is due to the attempts by men to implement whatever incorrect ideas they hold. Many of those in positions of power hold some radically incorrect ideas. What is more, it is clear that many of those in power are sociopaths hell-bent on dominating the rest of us as if we were so many beasts of burden who exist only to serve them. The insanity all around us is the logical fruit of the attempted realization of those ideas. The reason life is more like hell on earth these days is because the most radically incorrect ideas are getting very close to being fully realized.
In a word: ideas are immensely powerful. It is vitally important that we think correctly if we are to live correctly and enjoy the peace of mind and heart that God wants for all of us.