The general opinion of the Scholastic back in the Middle Ages was that the pagan could be converted by reason.  Thomas Aquinas, for instance, was known for his proofs for the existence of God.  Though a moderate realist, Aquinas thought that if the reasons were convincing, it would change the heart.  Unfortunately for Aquinas, in Christianity existence precedes essence, that is to say, experience always comes first and reason comes along to explain it.  What we need to believe is that if we preach Christ crucified, his blood shed for the forgiveness of sin, God will manifest himself and the sinner will experience salvation, not just understand something about it.  People seldom, if ever, change their beliefs based on reason when there entire experience in a culture goes against those reasons, but let someone preach the word in demonstration of the Spirit and of power and the sinner will be converted. 

            What I am trying to say is that if you do not have a real belief in God reason alone won't change the heart and alternatively, if you do not believe in God and I give you more reasons to believe so, you will be more strongly convinced of that belief.  Effective preaching requires the backing of God to make manifest the power of the cross.  Simply giving sermons that appeal to reason and confirmed belief systems will not produce the born again Christian, neither will encyclicals nor rational argumentation.  Existentialism makes us aware of what we are in the here and now, in our soul and being, not what we are in our head.  St. Paul did not use enticing words of man's wisdom, he preached from the Spirit, he gave utterance, words flowed from the Spirit like prophesy or tongues.