In 1 Corinthians 2, Paul continues with much the same point that he had begun in the second half of chapter one. There, Paul reminded the Corinthians that God's wisdom was not human wisdom. While the world's wisdom consists of wealth, power, and influence, God wisdom consists of righteousness, sanctification, and redemption. This wisdom has been revealed specifically is the scandal and foolishness of a crucified messiah, namely Jesus. However, Paul also says in chapter one that it is revealed in the Corinthians themselves; that is, many of them were weak, lowly, and despised when God called them but God's Spirit worked them in spite of, or perhaps precisely because of, their lowliness.
Paul continues this argument in chapter 2 by saying that his own preaching fits precisely this same bill. Paul did not come to the Corinthians preaching with high and mighty flashes of rhetoric or with worldly wisdom. It wasn't because Paul was an especially skilled speaker that the Corinthians believed. Instead, he spoke in weakness and in fear and in trembling. It wasn't that Paul offered persuasive arguments that the Corinthians couldn't logically refute. Instead, Paul says that he resolved to know nothing among the Corinthians except Christ and him crucified and that it was because of demonstrations of the Spirit and power that the Corinthians believed.
This word that is translated as demonstration (ἀποδείξει) is a term that Paul borrows from the art of rhetoric. It means something like a convincing proof that follows logically from the premises that have been argued. Paul's use of this word here then is full of irony. Rhetoric, the study of speech and persuasion, was a highly regarded body of knowledge in the Greco Roman culture of Paul's day. It seems pretty obvious from what Paul has said in this letter that it was highly regarded among the Corinthians as well. But Paul says rhetoric, persuasive words of human wisdom, are precisely how the gospel did NOT come to the Corinthians. But the gospel did come with its own convincing evidence; not flashy speeches or well respected philosophies but with powerful acts of God's Holy Spirit which transformed the Corinthians and confirmed the truth of Paul's preaching among them.
In v.6 and the following, Paul goes on to fine tune and summarize the point that he has been making all along; the gospel is indeed wisdom but not according to the worlds standards. Paul says that if the wisdom of humanity was compatible with the wisdom of God, then the rulers of the world would not have crucified the Lord of glory. If they had known God's wisdom, then they would have recognized Jesus as that wisdom and not put him to death. Paul then says that this is just as it is written "what no eye has seen, no ear has heard, what no human mind has conceived, the things that God prepared for those who love him". It is widely debated as to what exactly Paul is quoting here since there is no Old Testament reference which matches these words exactly. It could be a conglomeration of Old Testament texts or a reference to some writing now lost to us. However it is worth noting that it closely parallels the idea of Isaiah 64:4 which is an appropriate context for the point Paul is making. Isaiah 64 is a call for God to "rend the heavens and come down" and thereby set the world right according to God's righteousness. This is, of course, precisely what Paul believes God has done in Jesus. God has come down to earth, setting the world right by the righteousness of God; only God is doing it in a way that no eye has seen and no ear has heard, in a way that no human being could have possibly thought up, by God becoming human, a crucified human.
Paul says that God himself has revealed all of this to us by his Spirit. And this is a decisive point in Paul's argument; that we can not learn these things on our own. The mystery of God's wisdom is not something that we can just figure out, it is not something we can logically deduce. If we could, it would be just like every other form of wisdom and the Corinthians would be right to approach it that way. Instead, Paul says, God's Spirit must reveal it to us. After all, who can possibly know the mind of God? Paul says by analogy we can't even know the thoughts of another human being unless they reveal them to us. How much more with the infinite and immeasurable God? We can't possibly come to recognize the crucified messiah as the manifestation of God's wisdom unless God's Spirit reveals it to us as such.
Fortunately, God's mystery does not remain a mystery. God does reveal it to us by his Spirit. Paul ends this section of his argument by saying "but we have the mind of Christ". Paul's point in this passage is not that the Corinthians are ignorant of the mystery of God but only that they did not come to know it by their own ability. The Corinthians do indeed have the mind of Christ but this is only the case because of what God's Spirit has done among them.
The Church would do well to remember this. The Word is not something given to us to do with as we please. Nor is our faith something of which we can logically convince those around us. We could not and would not ourselves have come to know God through the mystery of the crucified messiah were it not for the revealing work of God's Spirit among us. As a result, all of our proclamation, all of our words and actions as the Church mean precisely nothing if God does not make them his own words and actions by the power of His Holy Spirit. Our preaching, our reading of scripture, our worship, our evangelism, our discipleship, all of our practices must be done within the power of the Holy Spirit or they are mere babbling about nothing.