But, I won't be holding my breath. I reckon both sides will be playing it safe and keeping close to protocol and issuing meaningless diplomatic platitudes.
I have to say that even as a Christian I thought the Pope's controversial lecture was philosophically clumsy.
If he wanted to make a thesis about the Hellenization of faith vis-a-vis Islam he would have been better advised to have contrasted Ibn Rushd (Averroes) and Al-Ghazali, two Islamic thinkers of the 12th century.
Ibn Rushd was recognised by Christian and Muslim thinkers of his day as one of the greatest authorities on Aristotle. Al-Ghazali saw the influence of Aristotle as harmful to the Islamic faith and wrote against Ibn Rushd. And Islam, I am led to understand, has largely followed Al-Ghazali.
Of course, while the worldview of Aristotle was problematic as history later revealed with the Galileo incident, the methodology of Aristotle's philosophy survives and remains valid. Perhaps this is what the Pope wished to underscore in his reference to the Hellenization of the faith. Or perhaps Gypsy Scholar has captured the essence of the point the Pope was making in that :
"The Pope argued that Christianity itself integrates reason with faith because it trusts in a rational God who acts according to reasonable principles and whose divine rational nature is reflected in both human reason and the order of the universe, whence the Pope's insistence on the "real analogy" between God and human beings."
Aristotle's legacy can be seen in the scholasticism of Aquinas. Scholasticism, moreover, did not remain only with the Church of Rome but survived right into the Protestant reformation. The influence of scholasticism can, for example, be seen in the writings of John Owen and Francis Turretin, who have been among the greatest thinkers and theologians of Protestantism.