Suppose you're a protestant, and you want to convince other people to do what the Bible says to do. Would you persuade them by showing them that the Bible says that they should?
Now suppose you're a rationalist, and you want to convince other people to be rational. Would you persuade them with a rational argument?
If not, how?
ADDED: I'm not talking about persuading others who already accept reason as final arbiter to adopt Bayesian principles, or anything like that. I mean persuading Joe on the street who does whatever feels good, and feels pretty good about that. Or a doctor of philosophy who believes that truth is relative and reason is a social construct. Or a Christian who believes that the Bible is God's Word, and things that contradict the Bible must be false.
Christians don't place a whole set of the population off-limits and say, "These people are unreachable; their paradigms are too different." They go after everyone. There is no class of people whom they are unsuccessful with.
Saying that we have to play by a set of self-imposed rules in the competition for the minds of humanity, while our competitors don't, means we will lose. And isn't rationality about winning?
ADDED: People are missing the point that the situation is symmetrical for religious evangelists. For them to step outside of their worldview, and use reason to gain converts, is as epistemically dangerous for them, as it is for us to gain converts using something other than reason. Contemporary Christians consider themselves on good terms with reason; but if you look back in history, you'll find that many of the famous and influential Christian theologians (starting with Paul) made explicit warnings against the temptation of reason. The proceedings from Galileo's trial contain some choice bits on the relation between reason and faith.
Using all sorts of persuasive techniques that are not grounded in religious truth, and hence are epistemically repulsive to them and corrosive to their belief system, has proven a winning strategy for all religions. It's a compromise; but these compromises did not weaken those religions. They made them stronger.
Good idea. I mean that EVERYBODY, rationalist atheist and christian alike, starts with an axiom or assumption.
In the case of rationalist atheists (or at least come such as myself) the axioms started with are things like 1) truth is inferred with semi=quantifiable confidence from evidence supporting hypotheses, 2) explanations like "god did it" or "alpha did it" or "a benevolent force of the universe did it" are disallowed. I think some people are willing to go circular, allow the axioms to remain implicit and then "prove" them along the way: I see no evidence for a conscious personality with supernatural powers. But I do claim that is circular, you can't prove anything without knowing how you prove things and so you can't prove how you prove things by applying how you prove things without being circular.
So for me, I support my rationalist atheist point of view by appealing to the great success it has in advancing engineering and science. By pointing to the richness of the connections to data, the "obvious" consistency of geology with a 4 billion year old earth, the "obvious" consistency of evolution from common ancestors of similar structures across species right down to the ADP-ATP cycle and DNA.
But a theist is doing the same thing. They START with the assumption that there is a powerful conscious being running both the physical and the human worlds. They marvel at the brilliance of the design of life to support their claim even though it can't prove their axioms. They marvel at the richness of the human moral and emotional world as more support for the richness and beauty of conscious and good creation.
Logically, there is no logic without assumptions. Deduction needs something to deduce from. I like occams razor and naturalism because my long exposure to it leaves me feeling very satisfied with its ability to describe many things I think are important. Other people like theism because their long exposure to it leaves them feeling very satisfied with its ability to describe and even prescribe the things they think are important.
I am not aware of a definitive way to challenge axioms, and I don't think there is one at the level I think of it.