Carolyn makes no conclusion, but she implies one. If it's true that Marc Quinn has put DNA fragments behind glass and called it a "portrait" of Sir John, and if it's also true that to be a portrait, something must bear a recognizable resemblance to its subject, then it's a short leap to "DNA doesn't look like Sir John, therefore Marc Quinn's 'portrait' is not actually a portrait." Arnold disagrees. He calls the work a "maximally realistic portrait." His rationale is that "it holds actual instructions" for creating Sir John.
Okay, so what have these two disagreed about? Make sure you make a prediction before looking at the answer choices. (By the way, we're on Section 3, #3, of the June 2007 LSAT.)
The question says "The dialogue provides most support for the claim that Carolyn and Arnold disagree over whether the object described by Quinn as a conceptual portrait of Sir John Sulston..."
I think I can predict the answer here. Carolyn implies, pretty strongly, that Quinn's work is not a portrait. Arnold calls it a "maximally realistic" portrait. So if there's an answer choice that says "Quinn's project is a portrait," then that's the answer--there is no way Carolyn and Arnold agree on that proposition. Let's see:
A) It is very difficult to see how this can be the point of disagreement, when neither Carolyn nor Arnold even used the word "art" in their statement.
B) No way. They are not arguing about whether Quinn's project should be attributed to Quinn. They are arguing about whether it's a portrait or not.
C) No, I don't think so. Carolyn suggests that the project does not resemble Sir John, but Arnold doesn't say "yes it does." Instead, Arnold says it is the instructions by which Sir John was created. Instructions for building something don't necessarily look like the thing itself (the code underlying Super Mario Brothers does NOT look like a video game), so I don't think John would argue with Carolyn on this point.
D) Carolyn takes no position on this, so it can't possibly be their point of disagreement. I sure hope E says something like "Quinn's project is a portrait," otherwise I'm going to feel mighty stupid.
E) Yep, this is exactly what I predicted. Carolyn says "no" to this, but Arnold says "yes." Therefore this is what they're arguing about--so it's our answer.