Really, we should all be honest with ourselves. Can any of us really say we believe in something that cannot be shown to be false? And yet I see perfectly sane men and women who are absolutely confident in their belief in God.
We all know that nobody can prove or disprove God just as nobody can prove or disprove that there is an invisible flying celestial teacup circling the planet Jupiter, if I may borrow Bertrand Russell's analogy. No sane person believes in this celestial teacup. But there are perfectly sane people who believe in God. And I don't mean the sort of belief that you and I probably have. I'm talking about an honest-to-goodness, heaven-strike-me-dead-if-it-ain't-true kind of belief. I've read of people who are willing to be killed rather than renounce this unfalsifiable God.
It has never ceased to amaze me that in 16th century England people were willing to die rather than confess that there are two or seven sacraments, depending on whether a Protestant or a Roman Catholic was in power at the time. Many Christians seem to set much store on the willingness of someone to die as proof of the veracity of the cause. Since the early Christians were willing to die for the faith, it must necessarily follow that Jesus did rise from the dead, so they argue.
Martyrdom does not at all show that God or the resurrection or the celestial teacup is real. It only shows how illogical, unthinking and anti-intellectual the human brain can be. We see a lot of such examples in nature - the picture of beached whales come to mind immediately. These are whales that head for the beach and certain death for no apparent reason. The instinct of every living thing is to preserve its life. Beached whales and martyrs have overcome that instinct as a result of some faulty brain wiring. It does not do one jot of good to the credibility of the cause for which martyrs have laid down their lives.