The President is authorized to use the Armed Forces of the United States as he determines to be necessary and appropriate in order to ... defend the national security of the United States against the continuing threat posed by Iraq[.]
What did Congress have in mind, in using the term "Iraq?"
Jack answers by pointing out that there's no geographic qualifier in this critical part of the statute; moreover, words like "Saddam Hussein" or "government of Iraq" were conspicuously omitted. All this leads him quite reasonably to conclude that the President can determine, right now, whether any group in Iraq poses a threat to the United States that warrants a military response---even a group outside Iraq, to the extent it supports activities ongoing inside the country. To put the argument another way, if something or someone threatens U.S. national security, and involves Iraq, then under the 2002 AUMF, the President can use force. Obviously ISIS fits this bill.