I think you will all find that I am fond of syllogisms. I find that the case of the resurrection is as simple or complex as it is made, but it ultimately hinges on this argument:
P1. If one genuinely testifies to their genuine belief in an event’s occurrence, and they have access to knowledge that would allow them to know whether or not the event occurred, then the event must have occurred.
P2. Several persons testified to their genuine belief in Jesus’ resurrection, and these several persons had access to information that would have allowed them to know whether or not the resurrection occurred.
C. Therefore, the resurrection of Jesus occurred.
P1. This premise is not objectionable. People will often raise an objection like the fact that many Muslims believe in Muhammad with sincerity, but that response negates the second half of my premise. These hypothetical Muslims believe because their culture ingrains in them the fact that Muhammad was of Allah, not because they have access to information that would reveal the truthfulness of the religion, so they are unlike the disciples who testified to Jesus.
P2. Objections can be raised to this premise, but each point is backed by New Testament scholarship, so I think my opponent will find it rather difficult to object to either point. I will expand on this point just for clarity sake after I write the conclusion.
C. The conclusion flows from the premises. If no valid objection can be made regarding either premise, one must accept the conclusion.
Which persons believed and would have known if Christ rose? I will argue that James, Peter, the author of the Gospel of John, and Paul genuinely believed that Christ rose, and that they had access to information that would allow them to know.
Were they lying/non genuine in anyway? I do not think there is really any scholarship at all that will pose the non genuine belief of my examples, and their genuineness is certainly the scholarly consensus, so I doubt my opponent will argue against this point, but I will briefly defend the idea. As recorded in the letters of Paul, Christians who preached the gospel were persecuted, and often imprisoned and killed as he was. The author of the gospel of John mentioned that some believed he would not die until the return of Christ, but he said that this was not the case, and he certainly could be killed. James mentions persecution several times in his short letter, and in the Gospel of John we see a prophecy that Peter will be killed for his faith. Even if you disagree with the premise that it is a prophecy, as a normal historical document, we would conclude that John is being self serving in using the martyrdom of Peter for his agenda, so we can not find good reason to doubt the death of Peter. Regardless of specific details, why do these people suffer? People only do what they want, so why does this group of people choose to endure possible death and imprisonment? They tell us why explicitly. Paul does not think the pains of this world are comparable to the joys that are to come. Their motivation is that they view the suffering as temporary before a greater reward that they will receive because Christ really is the messiah and has promised it to them. Additionally, the gospels record embarrassing and degrading facts about the followers of Jesus which are unlikely to be included if one was forging facts. I highly doubt this section will be objected to, but if it is, I have plenty more I can say on the subject.
Did the persons have access to the information that would allow them to know if Christ rose or not?
Seeing as we agree that these people were genuine in their belief of the resurrection, we must ask why. Peter denied Jesus for his fear of association. Paul was a Pharisee killing Christians because he thought they were liars. James was Jesus brother and thought Christ was a madman, and John was a member of the apostles who watched him die. What would make these down trodden people come to genuine belief in his bodily resurrection? Well, they and all of the historical evidence tells us. Jesus Christ was crucified on the cross at the hands of Pontius Pilate, and three days later they witnessed him alive again, and saw the crucifixion wounds in his glorified body. They ate with him for an extended period of time, were taught by him, he appeared to many, and he returned to heaven. This information is not compatible with being mistaken. One does not mistake a dead man teaching them for 40 days, and certainly many people at a time do not. But what hallucinations? The data is not compatible with hallucinations either. Hallucinations do not occur via audio, touch, hearing, and sight over a time period of 40 days. They simple are not a plausible option. Paul is sort of in his own category. He claimed that he saw Jesus multiple times, became a Christians and stopped killing them, and then confirmed with the disciples that the Jesus he knew was the same one he did.
In conclusion, according to the data at hand, the reasonable and logically mandated explanation for the evidence regarding the resurrection is that Jesus Christ rose from the dead. Jesus taught that if we repent of our sins and turn to God, we can be forgiven, and on him our punishment will be laid, rather than on ourselves in hell.