This observation does suggest strong counters to arguments against God. For example, if the atheist argues:
We can explain everything that happens without reference to God. Since God is an
additional hypothesis, beyond what is needed to explain what we
observe, we should discard him as a hypothesis.
You can construct a parallel argument like this:
We can explain everything we experience without reference to an
external world. Since the external world is an additional hypothesis,
beyond what is needed to explain what we experience, we should discard
it as a hypothesis.
Both arguments have the same form, so the atheist is forced to either discard his argument or argue that
We can explain everything that happens without reference to God.
is on firmer ground than
We can explain everything we experience without reference to an external world.
This is a tall order, especially since we actually can't explain everything that happens, with or without reference to God.
Here's another example. The atheist argues:
When people have experiences of talking with God or seeing God at
work, it's simpler to just assume they are hallucinating and there
is no actual God there.
The obvious response is:
When you think you are drinking a cup of coffee it is simpler to
just assume you are hallucinating and there is no actual cup of
coffee there.
Solipsism is the simpler explanation at least in the sense that it requires fewer entities. Which suggests another common example:
Your theory of God requires everything that my theory requires:
matter, forces, etc. and in addition you require an additional entity,
so your theory is more complex. You should just discard the additional
entity.
Answerable by:
Your theory of an outside world requires everything that my theory
requires, a mind and mental events, and in addition you require an
additional entity, so your theory is more complex. You should discard
the additional entity.
Another example:
Your strong intuition that life and the universe in general show
a deliberate design is unfalsifiable and therefore unscientific,
and since science is the measure of all things, your intuition
has no value.
Can be countered with
Your strong intuition that the things you experience are real
is unfalsifiable and therefore unscientific, and since science
is the measure of all things, your intuition has no value.
It's less clear that it can stand as a strong positive argument, a strong argument for the existence of God. It can, perhaps be used in a weak positive argument in this form:
I believe in God because (G1) I have a strong intuition that he causes
things I see in the world and because (G2) I have experienced
communicating with him. I believe in the outer world because (E1) I
have a strong intuition that when I perceive a physical object, it is
because that object caused my perception, and because (E2) I have
experienced the outer world. Since G1 is directly analogous to E1 and
G2 to E2, if E1 and E2 are sufficient to make me believe, then G1 and
G2 should be sufficient to make me believe.