In Information Without Truth, the Veridicality Thesis for both natural (environmental) and non-natural (semantic) information is rejected.
The Veridicality Thesis for Natural Information (VTN) can be stated:
(VTN) If a signal s being F carries natural information about an object o being G, then o is G.
This is like Dretske’s definition of information flow, and it entails that if an agent A has natural information about an object o being G when they receive a signal of s being F, then o is G.
Contrary to this, in Information Without Truth a Probability Raising Thesis for Natural Information (PRTN) is given, where the transmission of natural information involves nothing more than the truth of the following probabilistic claim:
(PRTN) If a signal s being F carries natural information about an object o being G, then P(o is G | s is F) > P(o is G | (s is F))
It should be noted that they footnote this definition with the following:
One of us has argued that signal s being F can also carry (negative) natural information about o being G by lowering the probability that o is G.
So what would a general definition about carrying natural information look like? It seems to me that something like this would do the job:
If a signal s being F carries natural information about an object o being G, then P(o is G) P(o is G | s is F)