The Ir/rationality of Absolute Certainty

The conversation this afternoon in Epistemology was over this question:

Is it irrational to hold certain beliefs to be non-negotiable, absolute, come-what-may, no-matter-what-I’ll-believe?

Mrs. Guisleman says it isn’t, that it is inconceivable for there to be a proof proving, for example, that Christ did not rise from the dead or that Jesus is God (a couple of her no-matter-what beliefs).

I disagree, and believe that it’s an appeal to ignorance (just because you cannot think of possible opposing evidence does not mean it will never exist) and what were absolute non-negotiables at one time in Christianity (ie, beliefs that defined what a Christian was) are no longer held to be true at all, let alone no-matter-what beliefs (ex. indulgences).

Your take on it all?