The sentence on the other side of this post is false.
The sentence adjacent to that sentence is not needed, but take the sentence out and the post falls apart.
This post doesn't make sense, but then this post does make sense.
The sentences in this post are each manifestly self-consistent.
This post is self-consistent.
The sentence on the other side of this post is true.
The sentence "this post is self-consistent" is true (it'd be a pretty lame puzzle if it weren't). Look for weaknesses in the sentences that seem to be contradictory. What does "the other side of this post" mean?
Take out the word "manifestly" and the post is harder to crack.
The goal is to try to figure out how this post could make sense. Imagine that this post was written in some context, and that somebody stumbles on these sentences while noting that context. In their eyes everything would make sense. In our eyes, isolated and left alone, things don't make sense. Try to find the context.
As the title suggests, this puzzle is entirely intrinsic. Its resolution does not refer to any outside objects or events. As mentioned in the third hint, the answer would be obvious to anyone finding this puzzle in context, and yet the outside context is irrelevant. The answer is in the presentation. Find how this puzzle is presented. Find what this puzzle is written on.