Full Idea
The concepts of truth and falsity are not symmetrical. The asymmetry is visible in the fundamental principles governing them, for F is essentially more complex than T, by its use of negation.
Gist of Idea
True and false are not symmetrical; false is more complex, involving negation
Source
Timothy Williamson (Vagueness [1994], 7.5)
Book Reference
Williamson,Timothy: 'Vagueness' [Routledge 1996], p.208
A Reaction
If T and F are primitives, controlled by axioms, then they might be symmetrical in nature, but asymmetrical in use. However, if forced to choose just one primitive, I presume it would be T.