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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)?

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There's no propositional abstruse here at all and the author is trying to show by adding true or false propositional statement to compatible proposition about a same subject, it's relevant to add truth or falsity. But by doing same with incompatible proposition about a same subject, then it's just like some common kind of irrelevance fallacy (red herring).

When composing boolean propositional sentence to some existing one in a world w, from your textbook:

Don’t assume something is always added. The proposition "x is red" adds truth to the proposition "x is colored" if x happens to be red, and it adds falsity if x is actually some other color, say blue. But if x is not colored at all (if it is, say, a natural number) in a world w ontologically, then the proposition "x is red" does not add truth OR falsity to the proposition "x is colored".

I think this exposition here is used to illustrate one of Aboutness aims, that is, via correctly composing compatible sentences about something, we can say what we want by saying more relevant true sentences (adding truth) and then indicating a retreat (indicating added falsity to make clear what condition can cause whole argument false), or conversely saying less and indicating an extension... In a word, the gist to understand aboutness here is how to correctly use compositional proposition in logic to help achieve rhetoric or persuading utility in a right way.

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