1. Paradoxical atheism, perhaps? You seem to mean, by an instance of
God, something that is in every sense cognisable, but the usual
concept of God surely embraces an inherent mystery.

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2.  [Not posted on the list]
Daniel Dubuisson: "An atheist who denies the existence of the
soul and of God ... accepts, often unknowingly, the spirit and terms
of a debate (the soul/body dichotomy, a universe governed, or not,
by divine providence) that religion has chosen."
    (The Western Construction of Religion, 12)

If one doesn't start with theism, then atheism itself is senseless.

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3. I'm with Aaron on this one. There is nothing paradoxical in his
atheism.

If someone tells me their concept of God embraces an inherent mystery,
I'm not sure what to think (what is it to "embrace" something you
can't make sense of?). But if they tell me that, in a context which
suggests that "embracing an inherent mystery" is just a positive way
of endorsing incoherence  -- so  that an atheist of Aaron's kind  has
somehow tripped themselves up by agreeing with mysterian theists  --
then it seems to me that incoherence is being piled on incoherence. An
incoherent concept is one which cannot  have instances. There are no
round squares for me to consider worshipping or not worshipping, nor
could there be, so I need not worry that by failing to worship a round
square I am stumbling into error. If as I'm inclined to think there
could no more be a God of the kind people mostly seem to think they
are telling me about when they talk about God, than there could be a
round square, then likewise I need not worry that I may be stumbling
into error by failing to worship such a God.

I don't want to argue here about whether the concept of God is
incoherent. But please, let's not have people tell those of us who say
so, that in so saying we are somehow paradoxically agreeing with
theists. Endorsing incoherence doesn't turn it  into coherence, nor do
those who point out perceived incoherence thereby endorse incoherent
doctrines - or concepts.