Reducing an involved logical argument (or a detailed empirical study) to its essential elements usually makes it more accessible and can help us focus future research. Reister's comment on our paper purports to provide such a summary of our findings. Indeed, it might appear that he has demonstrated that our conclusions were obvious from the outset. Unfortunately his comment is an example of why we began this response by noting that simplification usually (rather than always) improves understanding. In this case it has led to incorrect conclusions.
