An expression is completely formal when it is context-independent and precise (i.e. non-fuzzy), that is, it represents a clear distinction which is invariant under changes of context. For example, "I'll see him tomorrow" will have a different meaning when uttered by different people or on different dates. On the other hand, the expression "Karen Jones will see John Smith on October 13 1992" will normally always refer to the same event, independently of person, moment or circumstances.
An advantage of the present definition is that it is more or less equivalent with the sense of "formal" as it is used in mathematics and the sciences. A scientific theory is called "formal" when it is expressed in a form (usually mathematical) such that there is no ambiguity as to the meaning and implications of its expressions. This implies that the same statement read by two different scientists, at different moments and in different parts of the world is supposed to be interpreted in exactly the same way. Even computers, which are totally unaware of context, should be able to interpret a fully formalized statement. Striving to "formalize" theories or hypotheses is an essential part of the quest for objectivity, universality and repeatability that characterizes scientific research (Heylighen 1992b).
It must be noted, though, that complete formal description is in principle impossible. Even in pure mathematics it is recognized (through the theorem of Gödel) that it is in general impossible to explicitly state all the necessary and sufficient conditions for a particular expression to be valid. There always remains an element of indeterminacy, and completely unambiguous description is impossible. This is confirmed in the physical sciences by Heisenberg's "Uncertainty Principle", which is related to the "Observer's Paradox" in the social sciences. On a more intuitive level, the principle can be explained by noting that the meaning of an expression can only be fixed by means of a definition, which explicitly states the background knowledge or information about the context needed to understand the expression. However, the definition itself contains new expressions which need to be defined themselves. But those second-order definitions again contain new terms which must be defined, ..., and so on, in an endless chase for a complete description of the world.
On the other hand, expressions must have a minimal formality in order to be understandable at all. If the meaning changed with the slightest variation of context between the utterance of the expression and its interpretation, communication would be impossible, as the sender and the receiver of the message will never share exactly the same context. For example, there will always be a certain lapse of time passing between the moment a sender forms an expression in his or her mind, and the moment the receiver has processed that expression. Sender and receiver will also always have a somewhat different background knowledge and awareness of the present circumstances. So, a minimal invariance of meaning over changes of context is necessary.
Similarly, complete fuzziness merely signifies that any interpretation is as likely as any other one, and that implies that the expression is totally devoid of meaning or information.
We must conclude that formality is a relational concept: an expression can be more or less formal relative to another expression, implying an ordering of expressions, but no expression can be absolutely formal or absolutely informal. All linguistic expressions will be situated somewhere in between these two extremes. Where exactly on that continuum the expression will lie, depends on the choices made by the one who produces the expression, which in turn depends on the situation and the personality of the sender.
Reference: Heylighen F. & Dewaele J-M.: "Formality
of Language: definition and measurement", submitted to Applied