Okay - I was using (for some odd reason) non-arbitrary and unambigious as synonyms - even though they are not (I gave a lecture on arbitrary reasoning and God - and apperantly it was on the brain this morning).
So let me correct myself and requote myself:
If I prayed for a cessation of pain - and recieved it - immediatly - I have experienced unambigious evidence for God and prayer.
I think Frank, to hold that this evidence is unambigious - is to hold that cause and effect ARE ambigious. This makes you very Humian - but also makes science pretty damned impossible.
So if science is impossible - I think that all evidence, to you, is ambigious. Which, ofcourse, is not the way you live. You are reading this right now and are convinced that because the light to your eyes caused you to see it that is must be there. I say this - if religious experience is ambigious - like you say it is (as you did when you stated that you don't know what ended my pain - and niether do I) then all experience is ambigious. Experience is science. Experience is the only way (if there is a way) to truth.
However, I want to grant that I do not know whether God caused my cessation in pain - I believe I have inductive evidence to the fact. Much like I have inductive evidence that the 'law' of gravity will hold for my future actions. Science can never do better than inductive evidence for causes unseen.
For instance, black holes cannot directly be obseved - they must be indirectly observed by viewin thier effects (positive particle emission and the like). That is not a decuctive proof at all - it is, at best, inductive, and it probably more likely to be abductive.
I say that my religious experience is no more invalid than black holes and virtual particles.
Okay - now that that is fixed I can move on:
I was using inductive as moving from a general principle to a finely focused one. The example that Aristotle gives when attempting to define Inductive reasoning is if you are looking in a pool of water and see one carp and see he is black - then another - then another - then 2,000 more that are black - you can induce (with a decently high percentage of truth) that all carps are black.
In this way black holes are induced to 'emit' positive particles. We cannot deduce this because we are not sure that black holes even exist - but we can give - with a acceptable amount of certainty that they do.
I say this - the more that I pray - and my prayers are answered the more inductive evidence I have to make the claim that God exists.
I think what you are trying to say is that none of this can count as evidence - because it is ambigious (hey I got the word right!).
I say that if that is true - much of the evidence you have in your life, if not all, is ambigious - such as believing in wind (you can't see it - you are relying on authority - but you can see you arm hair move) is ambigious and should be thrown out. Even if you were to scientifically 'prove' wind - you could not be sure that what you felt before was wind and must take this as your first peice of evidence.
This leads me to say, as I said above, that when EXPERIENCED, the evidence is unambigious and can count as evidence toward a claim such as 'there is a God'.
TTF
p.s. hope that is clearer and allows a response from you.