In a recent post I said that I don't believe that dead corpses can be brought back to life. I don't. I don't believe it happened to Lazarus; I don't believe it happened to Jesus; I don't believe it will happen to me. As I said in that post, to say that Jesus was raised from death or that Jesus lives is to say that he was raised into the memory of the Christian community. He is alive in us in as much as we live our lives following him, doing what he did. It isn't about belief or doctrine or being asked to turn off our brains and accept 1st century pre-scientific thinking; it's all about the way we live our lives.
That is not to say that I have any dispute with the notion that Paul believed in and preached a bodily resurrection. It is clear in 1 Corinthians 15 that Paul's Christian faith depended on his belief in a bodily resurrection of Jesus. But this is exactly where it becomes important to read scriptures in their historical context. Paul was a Pharisee, that party within Judaism that believed there was going to be a future bodily resurrection of the dead and a restoration of God's just realm on earth.
Before Paul was converted to Christianity he believed in a bodily resurrection of the dead. Paul carried that belief with him as he became an apostle of Jesus. He believed that the resurrection of Jesus was the "first-fruits" of the resurrection to come. He believed that with the bodily resurrection of Jesus the general bodily resurrection was now underway and the time of God's decisive act of restorative justice on the earth was at hand. (1 Thessalonians 4:13-5:11)
What Paul likely faced at Corinth was incredulity at his views about resurrection. It was a common Greek view as old as Plato that the body is but a shadow of reality and the soul is the essence of what makes us human: "So 'tis well said of the deceased that the corpse is but a ghost; the real man--the undying thing called the soul--departs to give account to the gods of another world..." (Laws 12) This was the typical view of life after death in the world of the gentiles in which Paul traveled and preached. But Paul holds fast to his Pharisaic beliefs as he addresses the Corinthians about this issue. And of course, we don't ultimately know how they responded or if Paul won them over on this issue.
That this - belief in bodily resurrection - became the view of orthodox Christianity is beyond dispute. But despite the proper orthodox views on bodily resurrection, there can be little doubt that the popular view of most Christians is that life after death is all about survival of a soul, not the body.
In any case, it is possible to understand and appreciate the context of Paul's beliefs and writings about resurrection, and then say that we, living in a different time and context, don't believe that dead bodies can be resuscitated. Being a Christian doesn't hinge on this belief. Being a Christian is about choosing to follow in the way of Jesus.