Disciplines are sometimes considered
formal when they have developed a set of
axioms which can be described with a certain "magic" amount of completeness and rigor.
Mathematics is widely given as an example of formality. Others have postulated that any process which can be conducted by a
machine should qualify as "formal" (incidentally, this
excludes mathematics as a whole from formality).
The key danger in formality is in perceiving it as a yes or no proposition, when, in fact, it is always an unbounded continuum.