Some explanations in social science, psychology and biology belong to a higher level than other explanations. And higher explanations possess the virtue of abstracting away from the details of lower explanations, many philosophers argue. As a result, these higher explanations are irreplaceable. And this suggests that there are genuine higher laws or patterns involving social, psychological and biological states. I show that this ‘abstractness argument’ is really an argument schema, not a single argument. This is because the argument uses the ‘is lower than’ relation, and this relation admits of different readings. I then suggest four rigorous definitions of the ‘is lower than’ relation, and show that the abstractness argument’s prospects are much brighter for some of these definitions than for others. To show this, I evaluate the so-called ‘disjunctive threat’ to the abstractness argument.