I try to stress a point I've already made in Stephen Yablo's Aboutness and logical subtraction, but from another perspective.
From what Yablo is saying in his appendix to Aboutness (http://assets.press.princeton.edu/releases/m10013.pdf) in section 21:
p&q and p are both false in this world, and neither is any falser than the other. But there is a clear sense in which p&q adds falsity to p if q is false (it commits a further offense against truth beyond that committed already by p) and adds truth if q is true (it is true where it goes beyond p).
What interests me the most now is making sense of why A adds truth to B: Yablo's claiming that A adds true to B in the sense that "it is true where it goes beyond p" suggests me this reading, but I am not sure it is the correct one:
A adds truth to B because, when A is false, it is false just in virtue of the falsity of B.
From this, Yablo then claims that A adds truth to B, when B is false, because there is a fact that would be sufficient with B to make A true. I do not understand why this should be the correct explanation of "being additionally true".
Edit: adding a point that might be of interest. In Aboutness (2014), on page 148, Yablo claims: "Asked to explain why p&q adds falsity to q when p is false, we point out that it is false for a reason (viz., ¬p) that can obtain equally well when q is true—which is the same as q → ¬(p&q) being true for such a reason."
This seems to suggest the following reading:
(p&q) adds falsity to q when p is false because p implies ¬(p&q) and (◇p∧q) - p is compatible with q.
But why does he states that p must imply
if t is a reason for ¬(p&q) that can hold when q → ¬(p&q)?