I wanted to point out that truth/falsity is not the dichotomy you think it is. They're both positive claims. A positive claim contains an assertion that creates a circumstance about which we view reality. A negative claim, because of its dismissal of the positive claim, and thus dismissal that that claim has any basis in reality supporting it, does not need a basis for itself; only the diametric positive claim's lack.

I could come up with dozens of examples of statements that are both true and false, the point isn't to come up with lies, rather to come up with non-truths.

In fact, I posit that many statement made outside the realm of logic can be twisted enough to appear to be both true and not true, for instance: "The sky is blue." The sky does indeed appear to you and I to be blue and therefore the statement can indeed be interpreted as true. However, its blue appearance to us is due to the refraction of sunlight in our atmosphere, not to its inherent nature, by which reasoning, the statement is shown to be not true. Really, this can be pushed back so far as to make the truth and falsity meaningless concepts if you wanted to.

Come to think of it, I think that would make an appropriate capstone. Doublespeak: any comment you make sounds differently according to the listener, anyone listening would hear only what you wanted them to hear. An ally would hear exactly what you mean, for instance, while an enemy, in order to cut through the obfuscation, would have to make an opposed skill check.