then to dismiss the valid points he has about rampant irrational beliefs on the grounds that some religious people don’t have them
I don’t think a person would dismiss points he/she considers valid. As far as I know, those who criticise Dawkins do not do it on the grounds that some people don’t have “irrational beliefs” (what are then “rational beliefs”?) but on the grounds of what he has written about belief in God, religion etc as such.
I appreciate the effort you put into this conversation as I’ve seen many religious people in discussions such as these assert something along the lines of, “We don’t have to justify our beliefs, we have faith,”
I usually do my conversations on forums frequented mostly by atheists, since they make me articulate my thoughts for my own benefit, as well as broaden the perspective of my own worldview (and hopefully also of that of my partner in these discussions).
You are right, there are people who say that, as there are people who say “We do not have to justify our rejection of any form of belief in God or religion, because we know they are all irrational, superstitious, unscientific, comparable to some silly claims (like that with the teapot) etc”. And you are also right that it is useless to debate such people. Since I spent so much time trying to answer your objections, I obviously do not see you as one of those, in spite of feeling that we have started to go around in circles, our dialogue degenerating into parallel monologues.
I would be interested in more of your ideas about why a claim of a transcendent God transfers to not being able to test empirical claims about His actions, but transcendent claims about mathematics do not prevent us from empirically testing what they imply in objective reality.
You touch upon FOUR topics here. One thing is the belief in God, another His interaction with the physical world. And also, one thing is pure mathematics, another the applicability of this or that part of it. In both cases the second part, Divine Action or applicability of mathematics, is the more complicated thing to analyse and explain. This thread, as I understand it, was only about the first of these four topics. Nevertheless, let me try.
In mathematics truth is purely formal, one actually does not use it very explicitly. Mathematics is built on undefinable, elementary concepts like set, natural number, relation etc, and concepts derived from them with properties a priori assumed about them. These a priori assumptions are called axioms and the function of pure mathematics is to study what can be derived using pure logic from these axioms.
Another thing is the application of mathematics, more precisely of mathematical models, of some phenomena of physical reality and their adequacy, for a particular practical or theoretical (explanatory) purpose. Refer to Eugene Wigner’s “unreasonable effectiveness of mathematics” or Einstein’s “as far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality”.
The other two topics are even more complicated, so I can be only sketchy, concerning naturally only the Christian position.
First of all, perhaps you are right that I should have called Jesus’ Resurrection untestable rather than unfalsifiable, although the distinction here is murky since strictly speaking it is not clear how to translate it into contemporary scientific language in which it could be shown to be true or false. The same with Virgin Birth.
One general comment about “miracles” (other than the two above): Events that can be recorded by scientific instruments as violations of known natural laws would simply be absorbed by science as new observations, new facts. A new, more embracing, theory (and/or natural laws) would be sought by scientists to explain them. Seeing these unexplained events as the result of some direct divine act would simply mean a return to the many times discredited god-of-the-gaps argument. Also, a “miraculous healing” always involves some willpower, some faith in the source of healing (c.f. Jesus’ “your faith has healed you”), even when contemporary medicine cannot explain this acting of the mind on the body. No prayer has yet brought back an amputated leg.
However, a Christian — scientist or not — who believes in God will probably not agree that everything he/she sees as God’s intervention can be this easily explained away. A Google search for “divine action” will provide over one hundred and fifty thousand links. Most of these display a naive understanding of science (or theology or both), but not all, including some from authors who are established scientists.
Some make use of quantum physics, chaotic systems, evolution, emergence, complexity or top-down causation “overpowering lower level causal forces”, etc in order to find clues in contemporary science that allow for an account of special, providential divine actions, without postulating violation of natural laws. However, no interpretation has been found that would satisfy all Christian theologians and would not contradict accepted physical theories. There are many things, not only concerning Divine Action but also science as such, that still lack satisfactory explanation — just think of the epistemological enigmas of quantum physics or human consciousness.
Sorry, I feel I did not answer your request, but this is all I could put together.