Carolyn: The artist Marc Quinn has displayed, behind a glass plate, biologically replicated fragments of Sir John Sulston's DNA, calling it a "conceptual portrait" of Sulston. But to be a portrait, something must bear a recognizable resemblance to its subject.
Arnold: I disagree. Quinn's conceptual portrait is a maximally realistic portrait, for it holds actual instructions according to which Sulston was created.
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
should be considered to be art
Neither speaker has an opinion. Nobody discusses what is or is not art, only what is or is not a portrait.
should be considered to be Quinn's work
Neither speaker has an opinion. Nobody discusses whether the work is appropriately considered Quinn’s.
bears a recognizable resemblance to Sulston
Arnold has no opinion. He doesn’t suggest that the portrait does or does not resemble Sulston. Arnold simply applies a different rule, unrelated to resemblance, for determining that something is a portrait.
contains instructions according to which Sulston was created
Carolyn has no opinion. She doesn’t speak to whether the DNA fragments contain instructions according to which Sulston was created.
is actually a portrait of Sulston
This is a point of disagreement. Carolyn’s implicit conclusion is that it’s not a portrait of Sulston. Arnold’s conclusion is that it is a portrait of Sulston.