Imagine that you take a trip to Alpha Centauri, where there is a planet of the same name very much like Earth. You find a group of about 100 people (or creatures resembling humans in all relevant respects) there. This is a good conversational bunch, so you join in on some conversations. A common topic of conversation is about how the group should be governed. There are two dominant ideologies, and most in the group passionately claim allegiance to one or the other.
You soon discover, however, that when it comes to this topic, odd communicatory norms seem to govern the conversations. For example, you discover that if John says Mary believes p1, Mary will deny believing p1. Mary will in turn say John believes p2, but John likewise denies believing p2, and so on throughout the group. You not only discover that every assertion about what another person believes is unreliable, but also that every assertion about what oneself believes is unreliable. For example, when Steve says he believes p3, a whole host of others you talk to produce evidence that suggest Steve is lying or can’t be trusted (say, by showing you video, which may or may not be doctored, of things Steve has said before). Furthermore, it’s clear that most of the statements made are deliberately designed to get you to believe something that’s favorable to the speaker’s ideology.
Clearly, the conversational norms of this group effectively destroy the possibility of meaningful, trustworthy discourse about that topic. You would not be able to know or justifiably believe what Mary believes, or what John believes, etc. Accidentally true beliefs are about as impressive as it gets. The only exception is yourself, of course.
Curiously, though, you notice that no one else seems very bothered by this. The reason, you eventually find out, is that many of the reports (about oneself and others) are partially true, which creates the illusion of meaningful, trustworthy discourse. But you are not taken in by this illusion, because you learned from Frege that “what is only half true is untrue; truth cannot tolerate a more or less.” Beware the politically solipsistic world of Alpha Centauri!