We don't have outside corroborating sources to verify the deaths of the disciples as martyrs. We don't have original copies of the gospels. In short, we have the Bible to tell us how things went down. One source isn't enough. So, to point at the disciples martyring themselves as a sign of Jesus's death and resurrection is not a good argument. This is a pretty poor and old apologist argument that relies on those needing reassurance of faith that the unprovable stories give themselves self-validation. I thought this was a dumb argument when I read it in McDowell's terrible "More Than A Carpenter" and I think it's a poor argument now.
Even beside that point, people die for lies or falsehoods all the time. David Koresh is an example. Would you burn for a lie? No? Well I guess Koresh really was Jesus come back to save us. Oops! Screwed the pooch on that one! All those people surely wouldn't have allowed themselves to die if Koresh wasn't telling the truth... right?
And while the Islamic suicide bombers weren't first hand witnesses to Mohammed's deeds, that doesn't stop them from blowing themselves up in his and Allah's name. But I guess they are killing themselves and others for a lie, but that's okay because their religion is fake.... isn't it?
I've written on some issues relevant to Rotten Arsenal's comments here. I think most people are aware of the erroneous nature of the comparison between the disciples of Christ and David Koresh and suicide bombers. And his comment about "original copies of the gospels" doesn't carry much weight, given the evidence we have for the reliable transmission of the texts. But some other points bear mentioning, or repeating, since some critics of Christianity seem to be ignorant or forgetful of them (some of these are meant to respond to Rotten Arsenal, but not all of them):
- The apostles are among the relevant early Christian sources, but they aren't the only ones. If a non-apostle meets the same criteria as an apostle in this context, then that non-apostle is relevant to a consideration of the larger issue involved.
- Martyrdom isn't all that's relevant. So is suffering in general, though it does make sense to differentiate between degrees of suffering.
- The issue is probability, not certainty. Arguing that it would be possible that somebody like an apostle died for a known lie, such as by giving one or two examples of others who have done such a thing, would weaken the force of the Christian argument, but it wouldn't eliminate it. A general tendency isn't disproven by an exception.
- The Bible isn't our only source. We also have data from Josephus, Clement of Rome, Tacitus, and other early sources relevant to the suffering and death of the early Christians. Not all of the sources give us all of the relevant data, but the overall scenario that a knowledgeable Christian is going to refer to when making the argument in question is derived from a wide variety of sources, including extra-Biblical sources.
- The Bible isn't just "one source" in this context. It's a collection of documents written by multiple sources.
- Christian sources can credibly report information relevant to Christianity, much as Jews credibly report information relevant to the Holocaust, Romans credibly reported information relevant to the Roman empire, etc. Just as Christian sources could have had bad motives or could have been in a bad position to judge an issue for some other reason, so could other sources. There's value in disinterested or hostile corroboration, but historians often accept historical claims without such corroboration, and so should we. For some examples of the reasons why, see here and here.
- The earliest Christians referred to John the Baptist's doubts about Jesus' identity, Judas' betrayal of Jesus, Paul's rebuke of Peter, and other examples of error, including rejection of the faith, among their leaders. We know that they were willing to criticize their leaders, and if it's to be argued that other apostles, for example, went the way of Judas in rejecting the faith prior to death, it should be explained why those other apostles' reputations didn't similarly go the way of Judas' reputation.
- The sort of apathy of Christianity's enemies that critics often assume needs to be demonstrated, not just assumed. For some examples of the evidence we have against common assumptions of apathy, see here. People don't normally crucify their opponents, imprison them, and send out messengers to argue against them across a wide geographical spectrum, for example, if they're highly apathetic about those opponents. The idea that somebody like the apostle Peter denied the faith before his death, or that claims of his martyrdom didn't arise until a few decades or more after his death, yet the early enemies of Christianity were too apathetic to leave any traces of such an objection in the historical record, is something that needs to be argued rather than just asserted. The ability of the early enemies of Christianity to notice and object to what the Christians would have been doing in some of the scenarios skeptics propose needs to be given more consideration than skeptics often give it. Many objections of the early enemies of Christianity are reflected in the historical record. The early Christians refer to hundreds of charges of contradictions in the New Testament, the non-historicity of Biblical events, immoral behavior by Christians, etc. If the earliest Christian reports about the suffering and death of men like Paul and Peter were false to the degree skeptics suggest, where do we see objections along those lines reflected in the early arguments of Christianity's enemies?
Again, the above are just some of the considerations that ought to be taken into account. For more on this subject, see here.