When some among the Christians at Corinth falsely claimed “that there is no resurrection of the dead” (NKJV), the apostle Paul pointed out in 1 Corinthians 15:12–19 what the logical consequence would be: that Jesus Himself didn’t rise. “And if Christ is not risen, then our preaching is empty and your faith is also empty.” Christianity is confirmed by Jesus’ resurrection, and it’s refuted if He didn’t rise. If it’s true 1) that Jesus died at some point and 2) that He was alive afterward, then He must have risen from the dead.
The historical evidence is clear that Jesus was executed. As even resurrection skeptic John Dominic Crossan said, “Jesus’ death by crucifixion under Pontius Pilate is as sure as anything historical can ever be. For if no follower of Jesus had written anything for one hundred years after his crucifixition, we would still know about him from two authors not among his supporters. Their names are Flavius Josephus and Cornelius Tacitus” (Jesus: A Revolutionary Biography, p. 145).
As for Jesus being alive afterward, 1 Corinthians 15:3–8 provides us a list of witnesses including individual disciples, groups of disciples, and unbelievers (Paul and James). Even secular scholars grant that the passage isn't guilty of embellishment and that the statement is sincere. In the words of Germany’s leading resurrection skeptic, Gerd Lüdemann, “It may be taken as historically certain that Peter and the disciples had experiences after Jesus’s death in which Jesus appeared to them as the risen Christ” (What Really Happened to Jesus, p. 80, emphasis mine).
The focus then is the interpretation of these experiences. How did the witnesses see Jesus alive after He was crucified? Not wanting to admit Jesus was really there to be seen, most skeptics today, including Lüdemann, believe everyone merely hallucinated. However, this contradicts the accepted fact that people saw Jesus even in groups. Hallucinations are made up in a person's mind, not really there for anyone else to see. If you hallucinate an apple in front of you, no one else will see it. If everyone else does see it, then the apple's really there! The same applies to seeing Jesus. Since groups saw Him alive, He really was there to be seen.
Furthermore, even unbelievers like Paul converted upon seeing Jesus risen. (Again, it's unchallenged by secular scholarship that Paul was a persecutor-turned Christian who said his radical transformation was because he saw Jesus.) How could he hallucinate something happening that he "knew" (at least in his mind) to be false? And if he could, how would a single hallucination change his entire life? A modern-day equivalent would be if an outspoken atheist like Richard Dawkins were to suddenly hallucinate Jesus and become a Christian because of it. The radical change Paul underwent cannot be explained by a mere hallucination.
The best explanation is that Jesus was really there to be seen. He died for our sins and rose from the dead, overcoming death. Likewise, we must die to our sins by joining His death, burial, and resurrection in baptism (Rom. 6:1–7).