It seems to me that the fundamental task for the judge is to determine what Congress was trying to do in passing the law. In other words, the task is to interpret language in light of the statute's purpose(s) as enacted by the legislators, with particular attention to those legislative materials that reliably contribute to understanding the statute's meaning.
There are two general philosophies competing today when it comes to judicial interpretation of statutes: what I call the Scalia camp (textualism) and the Breyer camp (purposivism). In short, Scalia believes that when interpreting a statute, judges should look primarily to the words of the statute and almost nothing else. Breyer, on the other hand, believes that judges should use whatever reliable sources they have access to in order to ascertain the legislature's purpose and intent. Katzmann falls very much in the Breyer camp, as do I, so I approached Judging Statutes as a choir member ready for a sermon. Surprisingly, some of Katzmann's arguments actually made me question the Breyer philosophy a little (though in the end I still reject Scalia and remain in the Breyer camp).
One of the biggest points of conflict between the two philosophies is the use of legislative history. Katzmann spends a long time describing Congress's processes for passing legislation and writes about the long paper trail that follows a bill, from committee reports to floor speeches to agency directives. Katzmann argues that judges should use this material in its interpretation, but given how complex the process is and how many different people produce the work product, it's easy to understand Scalia's view that there is no "leglislative intent" because the legislature doesn't speak with one voice, aside from the bill that it votes on and passes. Plus, these committee reports, etc., aren't voted on, they're usually drafted by unelected staffers. To put too much emphasis on these materials would undermine our republican system of government.
On the other hand, Katzmann points out that agencies are often the first bodies to interpret statutes, that they often use legislative history and other materials, and that it's a broadly established doctrine that judges must give deference to agency interpretation of statutes when reasonable (Sup Chevron). Thus, it seems silly to give so much weight to agency interpretation, which relies on legislative history, while completely rejecting legislative history in other contexts.
Fundamentally, though, the best argument in favor of purposivism is the deficiencies of textualism. Scalia has said that we are governed by laws, not the intentions of legislators and presents his approach as some pure objective way of interpreting statutes without bias. Of course, this leaves the judge free to inject her own biases into her analysis without identifying them or transparently confronting them.
Overall I thought Katzmann did a good job of explaining the two approaches to statutory interpretation and agree with his conclusion that purposivism is a better choice most of the time, but it was interesting how he got there.