When Peter gets to Cornelius's house, he states that he wouldn't normally have attended a Gentile's invitation, "but God has shown me that I should not call any person common or unclean." (10:28) Wait! God never told him that! There is no place in the whole Bible where God tells Peter that he shouldn't call people common or unclean. It's just not there. However, Peter doesn't say God told him, he said God showed him. But again, God never showed him anything about people. Earlier in chapter ten God showed Peter a vision of animals and encourages Peter to "kill and eat". Peter refuses, saying that he's never eaten anything unclean. This is where the heavenly voice says, "What God has made clean, do not call common." (vs 15) So, God showed Peter about animals and Peter figured out that He was talking about more than just animals. The Holy Spirit's instruction to go with these Gentiles and Cornelius's obvious humility and desire to learn things pointed to this conclusion. In fact, it was almost necessary that he infer this conclusion . . . .WAIT A MINUTE!
This is an almost perfect example of what preachers/teachers/theologians mean when they say "necessary inference". While Peter was never out-and-out told that no person was common or unclean, he was given so many hints along those lines that any other conclusion was impossible. If he was thinking about God's revelations at all, then this was the conclusion he had to come to. This conclusion is later backed up by the Holy Spirit falling upon the Gentiles, proving that no man was common or unclean due to his race. Also notice that this wasn't the product of wishful thinking on Peter's part, nor was it the result of taking one bit of revelation and twisting it beyond its original intent. After Peter considered all that God had revealed to him on this subject, this was the only conclusion possible.
Another thing to look at is the first 18 verses of chapter 11. When the Jewish Christians accosted Peter in Jerusalem, he was not able to answer them in the way of the OT prophets; he could not say "Thus sayeth Jehovah" because God had never told him directly to do what was done with Cornelius. So, how did he answer? He told them of the vision. He told them that he was ordered to go with these men "nothing doubting" (the only direct verbal statement of God during this whole incident). He recounts what Cornelius had told him regarding the angel's visit. He tells of the outpouring of the Holy Spirit upon Cornelius and that the incident brought to mind a saying of Jesus. He summed it all up by saying, "Who was I, that I could withstand God?" (11:17). Upon hearing this, the Jewish Christians praised God that the Gospel was extended to the Gentiles, too. But what was Peter's justification built on? One generalized statement of the Lord and one statement by the Holy Spirit to go, one rather cryptic vision, a Gentile's claim to having seen an angel, and the rather emphatic proof of God's approval of what was going on. (By the time the Holy Spirit had fallen upon them, Peter had already preached the Gospel to them; he had already come to his conclusion by that point -- the Holy Spirit's outpouring was for the benefit of others.) To understand what God wanted and approved of, Peter and the rest of the Jewish Christians examined all the evidence available, the whole of God's revelation on the subject to that point, and came to a conclusion. In other words, they had to exercise their gray matter upon the subject and think.
Yes, God expects us to think about His revelation and our religion. Isa 1:18 "Come now, and let us reason together, saith Jehovah: though your sins be as scarlet, they shall be as white as snow; though they be red like crimson, they shall be as wool." God wants us to think, just as He implored the ancient Israelites. The "wise of this world" scoff at religion and label it the domain of unthinking brutes -- and many do unthinkingly follow religious leaders to horrible ends -- but the religion God set up is a religion for thinkers. Not that you have to be super smart. Not that it is extremely difficult to understand. But God has given us His word and expects us to understand it. To do so, we must read and think about it. Understand it as a whole, rather than wresting individual bits of it. See what God is clearly implying about how we should live our lives.
Peter figured it out and he was an uneducated fishermen. Surely we can follow his example.
"It is important for doubters to understand that many of us believers came to the point of faith by first studying the evidence and using -- not abandoning -- our reasoning powers to analyze it. I discovered that to believe in Jesus Christ does not require us to discard our intellect." ----David Limbaugh "Jesus on Trial"