To the moderate theist who says he or she believes some things based on science/rationality/reason/etc. and some based on faith, I reply that the algorithm that sorts claims between categories is responsible for all evaluations. This means that when he or she only selects reasonable religious claims to be subject to reason, reason is responsible for none of the conclusions, and faith is responsible for all of them.

In the same way, apparently pure System 1 judgments are best thought of as a special case of System 2 judgments so long as System 2 decided how to make them.

I think implicit in almost any decision to use System 1 judgments is that if System 2 sees an explicit failure of them, one will not execute the System 1 judgment.