Question: "What is theology proper / Paterology?"
Answer: Theology proper is the study of God and His attributes. Theology proper focuses on God the Father. Paterology comes from two Greek words which mean "father" and "word" - which combine to mean "the study of the Father." Theology proper answers several important questions about God:
Does God exist? God exists and ultimately everyone knows that He exists. The very fact that some attempt so aggressively to disprove His existence is in fact an argument for His existence.
What are the attributes of God? In the words of the hymn writer, "immortal, invisible, God only wise"most blessed, most glorious, the Ancient of Days, Almighty, Victorious, thy great name we praise." Knowing God's attributes leads to glorifying and praising Him.
What does the Bible teach about the Trinity? Though we can understand some facts about the relationship of the different persons of the Trinity to one another, ultimately, it is incomprehensible to the human mind. However, this does not mean it is not true or not based on the teachings of the Bible.
Is God sovereign, or do we have a free will? When we talk about free will, we are usually concerned with the matter of salvation. Few are interested in whether we have the free will to choose salad or steak for our dinner tonight. Rather, we are troubled over who exactly is in control of our eternal destiny.
Theology proper discusses God's omnipresence, omniscience, omnipotence, and eternality. It teaches us about who God is and what He does. Paterology focuses on how God the Father is distinct from God the Son and God the Holy Spirit. Only by knowing who God is and what He does can we properly relate to Him. Many people have unbiblical perceptions about God that affect how they understand Him. Some people see God as a brutal tyrant, with no love or grace. Other people see God as a loving friend, with no justice or anger. Both perceptions are equally incorrect. God is full of mercy, love, and grace - and at the same time righteous, holy, and just. God grants mercy and sends judgment. God punishes sin and forgives sin. God will grant believers entrance into Heaven and send unbelievers to Hell. Theology proper gives us a more complete understanding of who God is and what He does.
Romans 11:33 is perhaps a good summary verse for theology proper / Paterology: "Oh, the depth of the riches of the wisdom and knowledge of God! How unsearchable his judgments, and his paths beyond tracing out!"