It’s the opposite of deduction. We didn’t sit down and try to figure something out.
It’s as if the computation happened so deep within our head, like all this time the basic facts were already there and in our subconscious minds they are stirring around until by chance one set of facts come together that happen to imply something new and the reaction creates an explosion big enough to get the attention of our conscious mind.
And at a conscious level we say “aha! I instinctively know something is true. But why?” And here’s where the 99% perspiration comes. We have to go back to find out why it’s true.
Ok sometimes we discover we were wrong. Other times we discover conclusively why we were right.
But almost always we can’t decide conclusively one way it another but we find reasons for what we believe.
And we believe what we believe. Rationally. We felt it instinctively. And that belief, that sensation is a thing. Its a signal. That we had that inspiration serves as information to us. We have faith in our beliefs.
To lack such faith would be to invite the padded cell.
So that’s another piece of evidence to go along with the facts. And it just might, again perfectly rationally, tip the balance.
Cheap Talk 
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February 6, 2013 at 12:26 am
Brittany
The padded cell comes from *too much* faith…think of someone with a persecutory delusion. Tell him that nobody’s after him, and he’ll reply, “that’s what someone would say if everyone were in fact after me.” The cell comes from conclusively deciding in the face of reasonable alternatives. GK Chesterton opens up Orthodoxy with a story like this.
Too little faith probably causes laziness or ennui. There is probably a fuction for effort e(faith) s.t. e”<0. We need faith in something to get us out of bed, but too much can cause us to stop looking for explanations.