What is the rational response to all of the scientific proof that our moral intuition is inconsistent?
In my opinion, the trolley problems and the Singerian arguments discussed in this video are far from sufficient to show that our moral intuition is actually inconsistent (though it probably is). These examples lead to problematic results only under naive utilitarian assumptions, which are not only unrealistic, but also turn out to be much more incoherent than human folk morality on closer examination.
Our moral intuitions in fact do a very good job of arbitrating and coordinating human action given the unpredictability of the real world and the complexity of the game-theoretic issues involved, which utilitarianism is usually incapable of handling. (This is one of the main reasons why attempting explicit utilitarian calculations about real-life problems is one of the surest ways to divorce one's thinking from reality.) Singerians and other fervent utilitarians are enamored with their system so much that they see human deviations from it as ipso facto pathological and problematic, but as with other ideologues, when the world fails to conform to their system, it's usually a problem with the latter, not the former.
Our moral intuitions in fact do a very good job of arbitrating and coordinating human action given the unpredictability of the real world and the complexity of the game-theoretic issues involved, which utilitarianism is usually incapable of handling. (This is one of the main reasons why attempting explicit utilitarian calculations about real-life problems is one of the surest ways to divorce one's thinking from reality.)
If you have many convincing examples of this, you should write a post and sway a lot of people from utilitarianism.
Joshua Greene manages to squeeze his ideas about 'point and shoot morality vs. manual mode morality' into just 10 minutes. For those unfamiliar, his work is a neuroscientific approach to recommending that we shut up and multiply.
Greene's 10-minute video lecture.