The law requires more than this to find that causation has been demonstrated, however. The tricky, second part is called "legal causation" or "proximate cause". Nobody has a perfect definition of proximate cause that I know of. The idea though is that in addition to global warming being one of the necessary causes that preceded Hurricane Katrina, global warming must especially cause the hurricane - or at least to have especially caused harm to the newborn child in the hypothetical from Part 1.
Another hypothetical might help here. Suppose you're injured in a car crash caused by someone else's negligence. Rushing you to the hospital, the ambulance gets into an accident that was unavoidable because of the speed necessary to get you to the hospital, and you suffer further injuries. When you recover enough to leave, you are unfortunately injured a third time while driving away from the hospital a normal speed, in another unavoidable accident. What damages to you does the person who first injured you have to pay for?
The "but-for" test is satisfied in all three injuries, but proximate cause exists only for the first two. There is a special relationship between the ambulance's speed, caused by the need to respond by the accident that the defendant created, and the ambulance's crash. By contrast, it's basically coincidental that you were injured a third time while driving normally when leaving the hospital. "Proximate" used to mean what it sounds like - that the defendant was the last cause or nearly the last cause preceding the injury - and that closeness is still helpful, although not determinative, in satisfying proximate cause.
While the mere existence of Hurricane Katrina and any other specific tropical storm is sufficent to satisfy "but-for" causation, it's not enough to show proximate cause. There would have been a different set of hurricanes in 2005 folowing different tracks even without global warming, and it's just coincidental that global warming was one of countless necessary causes that ultimately sent Hurricane Katrina to Mississippi, just like it was coincidental that your first car accident ultimately led to you being in a place where you were injured, leaving the hospital.
That's not the end of the story, though. In addition to making Hurricane Katrina and other specific hurricanes happen, global warming as a general matter makes them worse. The IPCC found (pg. 9) that is "more likely than not" that anthropogenic global warming has already contributed to increasing intense tropical storm activity. I'll bet every lawyer for a fossil fuel company felt a chill when reading that IPCC description, because it closely matches the burden of proof needed to show causation in a civil trial - "the preponderance of evidence".
To the extent that AGW made hurricanes worse, that increase in damaging effect clearly satisfies proximate cause. There's this WMO statement (pg. 6):
A more appropriate question is whether the probability of an event happening in a particular basin has been increased by the ocean warming....The possibility that greenhouse gas induced global warming may have already caused a substantial increase in some tropical cyclone indices has been raised (e.g. Mann and Emanuel, 2006), but no consensus has been reached on this issue.
This basically responds to proximate cause issues, not just the but-for causation (which they get wrong in a preceding sentence, but we can let that pass). And the law doesn't require consensus, "more likely than not" is good enough for a verdict.
So the law would likely find both but-for and proximate causation as a general matter regarding an undefined level of increased damage from hurricanes. But the question people want to ask is whether AGW made a particular storm worse - so did AGW make Katrina worse than it would otherwise have been? I think from a legal perspective the question might not have an answer - not that we don't know the answer, but rather that the question doesn't make any sense. I'll discuss that in the next post, and see how close I can get to an answer if it's possible.
More information on legal causation/proximate cause is here.
UPDATE: softened my suggestion in the last paragraph that the question doesn't have an answer.