The basic idea here is Hilary Putnam's, not mine:
Sumner holds, with Richard Rorty (although Putnam claims that Rorty actually abandoned this view!), that objectivity is simply a matter of consensus: to say that "X is objectively true" is equivalent to saying "X is held to be true by me and my community."
There are a number of problems with this view, and Putnam exposes one in a clever way: What about Rorty's idea that truth is just a matter of consensus? Is that idea true?
Per Rorty, the way to test this is to see if it is the consensus in the relevant community of experts. But, in fact, the overwhelming majority of philosophers reject this view. So if we take Rortian relativism seriously, we must convict it of proving its own falsehood.