In §9 ch. 1, the Pope recalls the role of faith and reason as expressed by the First Vatican Council in Dei Filius.
This relation between faith and reason is much older than the First Vatican Council; it has been already taught by St. Thomas Aquinas.
Mysteries undetectable by human reason exist, such as the truth that God is triune, three Divine Persons in One God (cf. Summa Theologiae, I.32.1). God has revealed these truths, and they can only be known by faith.
In Summa Theologiae, I.2.2, Thomas characterizes the existence of God as provable by deducing the cause (God) from His effects (creation).
On the other hand, in Summa contra Gentiles, IV, 27, he characterizes the fact the God incarnated himself in the man Jesus as a mystery which has to be accepted by faith.
Added after edit of the original question:
The admonition "Know yourself!" refers to the questions of §1:
- Who am I?
- Where have I come from and where am I going?
- Why is there evil?
- What is there after this life?*
The Pope presupposes that these questions have a definite answer, which he simply calls the "truth" in §2. The Christian revelation as well as human reason - in short: faith and philosophy - are the two means to find out this truth.
§3 emphasizes that philosophical thinking is not restricted to a Christian context. Instead it is a human capability found in all nations.
§4 explicates the warning that the answers obtained by different philosophical systems may differ. And that in general a philosophical answer must not be considered the only true answer. Only the method of philosophical thinking can be considered unrestrictedly valid. Unfortunately, at this point the Pope does not explain what he considers the characteristics of the philosophical method. Nevertheless, he enumerates some results which he considers unrestrictedly true:
- the principles of non-contradiction, finality and causality
- the concept of the person as a free and intelligent subject, with the capacity to know God, truth and goodness.
- certain fundamental moral norms which are shared by all.
§5 brings into sight what the Pope considers a deficit of the contemporary philosophical investigation: The focus on the human individual. The Pope complains
Abandoning the investigation of being, modern philosophical research has concentrated instead upon human knowing.
He means that understanding the Christian salvific history - that what he names the truth - is no longer the aim of contemporary philosophy.
In addition, dealing with the boundaries of human epistemic capabilities can result in the attitude of agnosticism. And questioning the Christian message as a fixed point of konwledge may favour a position of relativism. Both may lead to scepticism and to challenging what had been accepted before. I think the Pope means challenging the Christian philosophy and the Christian worldview.
A further challenge are the different and sometimes even contradictory results of non-Christian philosophies.
§6 admonitors the bishops of the Catholic church to intensify their proclamation of the Christian worldview. The Pope recalls that the church has a mission to proclaim the truth. The introduction ends with the admonition to align this proclamation to the young generation.