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Judging in 1 Corinthians
1 Cor. 2:15 The spiritual man makes judgments about all things, but he himself is not subject to any man's judgment...
1 Cor. 4:5 Therefore judge nothing before the appointed time; wait till the Lord comes. He will bring to light what is hidden in darkness and will expose the motives of men's hearts. At that time each will receive his praise from God."

Could Paul actually be contradicting himself in such close quarters?

Read the first few chapters of 1 Corinthians for full context. In Chapter 1 Paul is having it out with the Corinthians for respecting the traits of human wisdom. Verse 2:15 means that mature believers ("spiritual men") in Christ are able to sift, scrutinize and understand things -- the word here is anakrino, which signifies investigation and sifting.

In Chapter 3 Paul says that the Corinthians are not mature believers -- they have divisions and arguments.

Chapter 4 is a "therefore" chapter in which Paul indicates that because of their immaturity, related in Chapter 3, the Corinthians should not judge the matter of dispute concerning his apostleship and authority -- and the word now, and into 1 Cor. 4, is krino, which has the connotation of making a decision, condemnation, or judgment. There is no contradiction at all, but rather a progression of ideas and argumentation.