It seems to me that we can establish a number of distinct
epistemological frameworks within which communication is
viable.
1. The speaker claims that p is true only within a certain worldview
(which the addressee can comprehend).
2. The speaker claims that p is true only within a certain worldview
(which the addressee can comprehend) and that the worldview should
be shared by people in general.
3. The speaker claims that p is true only within a certain worldview
(which the addressee can comprehend) and that the worldview is
be shared by people in general.
4. The speaker claims that p is true only within a certain worldview
(which the addressee can comprehend) and that the worldview is and
should be shared by people in general.
5. The speaker claims that there is such a thing as objective reality
and that p is true of objective reality.
(When I say "claim", feel free to read "presuppose" where it seems
more appropriate.)