Jim, if modern science works, it isn't begging the question. There is nothing circular about results...except this conversation, which is predicated on your ignorance of the topic. But here I am violating my own principles. I promise not to reply to your reply.
They would read 'what is evidence' and conclude you cannot trust your senses without justification through logic and since it takes logic to justify logic (which is circular) they would claim only God has that power (or the Truth Fairy). It simply feeds on ignorance of lower level processes - like how the brain uses logic or even how a modern computer chip uses logic. In the later case they could say, yes, computer chips are logical but their intelligence is very limited compared to man. Etc.
I've learned their is nothing you can teach a presuppositionalist in terms of a reductionist, materialist worldview. I've also learned its useless to have a debate between laymen. In addition, it's probably useless to have a debate between experts and non experts.