Signal and Truth

A green light is neither 'true' nor 'false'; rather, it is either appropriately used, or not, according to commonly-accepted practice.  Likewise, 'P is true', for proposition 'P', means 'the sequence of symbols that constitute it is used appropriately, according to commonly-accepted practice'.  Mathematical propositions are no exception: 'A + B = C' formulates the interchangeability of the symbols 'A', 'B', and 'C'.  Kant's thesis that Mathematical propositions are 'synthetic' verges on that Semiological thesis, and Principia Mathematica is, at bottom, a program for the construction of a system of symbols.  Formal Logic implicitly recognizes that Truth is not an intra-symbolic relation when it distinguishes Vocabulary and Syntax from Semantics, and Validity from Soundness.  So, Leibniz' axiom 'A = A' vs. Hegel's 'A = not-A' is a Semiological, not an Epistemological or a Metaphysical, disagreement.  Of course, these words are no exception to the analysis.