Thanks for article. I've had the chance to now read the Pope's speech. I hesitate to comment due to my lack of knowledge and expertise in this area, but his emphasis as I understand it that narrow modern reason (radical skepticism) is leaving out the wider understanding of reason as including the reason of our Being (logos) seems central.
In this wider understanding of reason the church draws on Greek philosophical concepts of goodness and truth. He says there is an ongoing attempt to deHellenize the Christian religion (i.e. remove this Greek influence) by some which would make it more subjective and irrational.
So the danger as I understand it comes not just from radical Islam but also from radical skepticism which would undermine ultimately the very notions of goodness and truth and our very Being which is grounded on this.
This speech I assume again will be talked about for a very long time. Moral self-examination in light of goodness and truth is painful for everyone given we are all sinners. Hopefully Muslims and radical secularists would realize this Pope does not appear to be holding out a standard which he is not also applying to himself and the church, and as such is an invitation to dialgue.