He says that whilst God may be highly improbable, the question is: Does God exist?
After all, you and I are highly improbable (probability that our parents should meet, that exactly that sperm should fetilize that egg, etc.). Yet we can be rightly confident that we exist, can’t we?
The implication is that, whether or not Dawkins is right about God’s probability, we might still be rightly confident of God’s existence.
Seems to me McGrath here trades on an ambiguity, that between epistemic and objective improbability.
Objective vs epistemic probability
Philosophers often distinguish objective and epistemic probability.
Objective probability is the probability of X occurring given Y. E.g what’s the probability of a lightening strike hitting just this spot (given the laws of nature plus these initial conditions), or this dice coming up six if we roll it?
Epistemic probability is the probability of a claim's being true, given the available evidence/grounds.
Something may be objectively improbable but epistemically highly probable. E.g. my existence is objectively improbable, given certain facts (what are the chances of just that egg and sperm meeting?). But the epistemic probability that I exist is very high indeed (for me at least - cogito ergo sum!).
McGrath’s sleight of hand
In the context in which McGrath makes his move, the relevant notion is epistemic probability. Dawkins is suggesting the epistemic probability of God existing is low. It’s unlikely God exists, given the evidence. Belief in God is not well-founded.
It’s this claim McGrath should be dealing with.
McGrath’s counter is to say, in effect, “But something can be very improbable, yet we can still be justified, or have fairly good grounds, for supposing it to be true!” His illustration of this point is: the existence of he and Dawkins is very improbable, yet that they exist is a well-founded claim.
It’s clear, isn’t it, that McGrath is muddling probabilities?
McGrath pretends Dawkins is talking about objective probabilities, when Dawkins is actually (here) talking about epistemic probabilities.
Showing that something can be objectively improbable yet well-founded does nothing to deal with Dawkins' contention that belief in God is epistemically improbable, i.e. not well-founded.
McGrath’s attempt to disarm Dawkins only looks plausible if we fail to notice this unacknowledged slide from one notion of probability to the other.
Dawkins on the objective improbability of God
Actually, Dawkins does also argue that God is objectively improbable. He argues that the objective improbability of eyes, fine tuning, etc. is not reduced by invoking God, for then we have merely replaced one objectively improbable thing with another.
I’ll discuss that another day.