Peter Singer thinks that we should push the fat man. Why? What are the philosophical convictions underlying this judgment?
The context of this question is what is known as the "trolley problem," a thought experiment which addresses the problem of intentions in ethics.
The central premise of the problem is that you are the conductor of a trolley. The brakes on the trolley have failed and ahead of you on the track is a group of five workers that the trolley will kill if something is not done to stop the trolley. There are two main variants of the problem, a "spur" version in which you have the option of steering the trolley onto a spur where there is only a single worker, and the "fat man" variant in which you are given the choice of pushing a fat passenger in front of the trolley to slow it down and save the five workers. A third variant involves your standing on a bridge and having the option of jumping down yourself or pushing a fat stranger.
For most philosophers, these variants provide different moral dilemmas. Singer, though, removes your intentions from the moral equation, and argues that in both cases we are sacrificing a single life to save five lives and thus that the choices are clear and do not lead to a dilemma. Singer argues that our reluctance to push the fat man is sheer sentimentality, and that we should override our intuitions to behave in the manner that saves the greatest number of people.
There are two weaknesses in Singer's arguments. The first is that there seems to be an underlying size prejudice here; if you change "fat man" to "gay person" or "black person" it becomes apparent that part of the underlying premise is a sort of size prejudice. The second problem with Singer's argument is that it ignores the way your choices create your own moral character. Overcoming an innate prejudice against murder, even if the murder is logically justified, removes some of your moral inhibitions, something which is not necessarily good.