- (Premise) God is hidden.
- (Premise) If x is hidden, then x exists.
- Therefore, God exists.
- (Premise) Many people experience that God is hidden.
- (Premise) If many people experience that s, then probably s, barring further evidence to the contrary.
- So, probably, God is hidden, barring further evidence.
Here is another valid argument:
- (Premise) God is absent.
- (Premise) If x is absent, then x existed, exists or will exist.
- (Premise) God is an essentially eternal being.
- (Premise) If an essentially eternal being existed or will exist, then that being exists.
- So, God existed, exists or will exist. (7 and 8)
- So, God exists. (9, 10 and 11)
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.