Can you help me understand God's perfect will versus His permissive will?
The "perfect will" of God is what you find in Romans 12:2
Do not be conformed to this present world, but be transformed by the renewing of your mind, so that you may test and approve what is the will of God-what is good and well-pleasing and perfect (Romans 12:2).
Notice that here turning one's back on the world, and having one's mind renewed (by God) enables one to discern and experience God's will for you, a will (or we might say purpose or plan) which is good, which is a delight to us and to God, and which has no flaws, no missing pieces -- complete.
Because God is omniscient, He knows what He will accomplish in us. He knows what we will do, and what we would do, in any given circumstance. Thus, His plans for us will never fail; they will never be flawed by some missing piece of information, some unknown detail. God's plan and purpose for each and every believer is for our good, and for His glory (see Romans 8:28).
This includes all the suffering and tragedy that comes to us in life (see 2 Corinthians 1:3-7; 12:7-10).
Having said that there is a "perfect will" let us not conclude that there is an imperfect will of God, so that we might fear we will miss His "perfect will" and be forever doomed to live out a life of misery and failure and frustration. His perfect will takes into account our ignorance, our weakness, or sins, and even the sins of others against us (Genesis 50:20).
The Bible speaks of the "will of God" in several different ways, and it is important to understand the differences.
(1) The decreed will of God. This is God's eternal, foreordained plan and purpose, which will not change and cannot be thwarted. It includes our salvation (Ephesians 1:3-6, etc.) and His choice and calling of Israel (Romans 11:1-2, 29). God's covenant purposes and promises are a part of His decree, and He will not and cannot "change His mind" about these things (see Exodus 32:13). (If you look at verse 14 of Exodus 32, you might say, "But, look, God did change His mind!" No He didn't. The text says that God "changed His mind" about destroying Israel, and making a new nation of Moses. Moses' whole argument is that God made a covenant, and He cannot change His mind, because He is God. God's "changing His mind about destroying Israel" is really His not changing His mind, about saving this nation and bringing them into the land, in fulfillment of His covenant with Abraham.)
(2) There is what we might call the "perceptive will" of God. This is God's will, expressed in the form of principles or precepts given to men. The command not to murder lets us know it is God's will for us not to murder others. The command not to steal makes it clear that God's will for us is not to steal. If I say, "I have discerned that it is God's will for me to rob banks, and to kill those who get in my way", we can confidently say that is not God's will His written Word is the expression of His will. In this sense, many people are seeking God's will when it is already obvious. You don't have to pray about living with your boyfriend; God has spoken (Hebrews 13:4; 1 Corinthians 6:9-20).
(3) There is also God's preferential (desiderative) will. This has to do with what gives God pleasure, and what does not. We know that God loves to show mercy, and yet He will execute judgment (Exodus 34:6-7). It is on this basis that Moses appeals to God to forgive Israel, not only here, but many times (see Numbers 14:17-19). Not only Moses, but others prayed that God would show mercy (Nehemiah 9; Daniel 9). God takes pleasure in the salvation of sinners; He does not take pleasure in pouring out His eternal wrath on sinners (Matthew 18:14; 1 Timothy 2:3-4; 2 Peter 3:9; Ezekiel 18:32; 33:11). When we come to things which are not clearly prescribed as sin, or things which are commanded, our desire should be to do that which pleases God (Romans 12:1; Colossians 1:10; 2 Corinthians 5:9; Ephesians 5:10).
(4) There is what we might call God's "permissive will." This is what God allows, even though it is sin. God allowed Joseph's brothers to betray him, and to deceive their father, so that He might bring the Israelites (few in number) to Egypt, where God would spare them, and they would greatly multiply (Genesis 50:20). God allows man to reject the gospel, to willfully disobey His laws, to persecute the righteous, and so on. But in all of this, God is still in control, and His purposes are being accomplished. His "decretive will" often allows or permits (His permissive will) men to violate His preferential will (what gives Him pleasure) and His prescriptive will (His Word). God's permissive will is never outside His decretive will. God "permits" those things which will lead to the accomplishment of His decretive will.
(5) There is also God's "directive will." This is God's personal guidance in our lives. It does not violate any of the "wills" above. There are times when God wants us at a certain place, doing a certain thing. The Bible most often will not provide us with this direct and personal revelation of His will. I can think of God's directive will being revealed in the "Macedonian call" (Acts 16:6-10). I can see it in the direct guidance of Philip (Acts 8:26) and of Peter and Ananias (Acts 10:1-23). God does guide us personally and directly, but it seems that this is not as common as some would like. This seems to be required at certain points of our life, when specific guidance is needed (see also 1 Timothy 4:14?).
(6) There may be yet another category, that I might call the "discerned" will of God. This is my perception of God's will for my life, which comes through wisdom. You may wish to look at the lesson I've done on this in Proverbs.