Divine hiddenness and absence

1. (Premise) God is hidden.
2. (Premise) If x is hidden, then x exists.
3. Therefore, God exists.

This argument is logically valid, of course. Moreover, it's hard to dispute premise 2. So the question is whether premise 1 is true. Here is an argument for premise 1.

4. (Premise) Many people experience that God is hidden.
5. (Premise) If many people experience that s, then probably s, barring further evidence to the contrary.
6. So, probably, God is hidden, barring further evidence.

The important thing in connection with 4 is to distinguish the experience that God is hidden from the lack of experience that God is manifest. Obviously, the lack of experience of God as manifest will not do as the start of a theistic argument. But to experience God as hidden is different from just failing to experience God as manifest. It is a genuine kind of spiritual experience of God.

Here is another valid argument:

7. (Premise) God is absent.
8. (Premise) If x is absent, then x existed, exists or will exist.
9. (Premise) God is an essentially eternal being.
10. (Premise) If an essentially eternal being existed or will exist, then that being exists.
11. So, God existed, exists or will exist. (7 and 8)
12. So, God exists. (9, 10 and 11)

I don't know if this argument is sound, because I don't know if God is absent. But there may well be some sense of "absent" in which it is correct to say that God was absent in Mother Teresa's time of darkness (presence and absence after all are things that can hold in various respects), and that sense of "absent" is sufficient, I think, to yield premise 8. (We wouldn't say of a being that never exists, such as the Tooth Fairy, that it is absent.) Again, to support 7, one would need an argument based on experience akin to 4-6, and one would need to distinguish experience of absence from the absence of experience of presence.

I think this shows that the so-called atheological "argument from divine hiddenness" should really be called the "argument from divine non-manifestness." That God is hidden entails that God exists, after all.