Full Idea
At one level logic can be regarded as a theory of signs and formal rules, but we cannot neglect the meaning of propositions as they relate to states of affairs, and hence to possible properties and objects... there must be the possibility of truth-values.
Gist of Idea
Logic is not just about signs, because it relates to states of affairs, objects, properties and truth-values
Source
Dale Jacquette (Ontology [2002], Ch. 2)
Book Reference
Jacquette,Dale: 'Ontology' [Acumen 2002], p.44
A Reaction
Thus if you define logical connectives by truth tables, you need the concept of T and F. You could, though, regard those too as purely formal (like 1 and 0 in electronics). But how do you decide which propositions are 1, and which are 0?