We present our research into the use of the logical structure of natural language discourse to generate estimates of the quantity of semantic content contained within a passage. These estimates of the degree of meaningfulness are recovered from the logical form of the passage, without actually recovering its meaning or necessitating real understanding. We first consider analysis of statements in the propositional calculus, then consider analysis of the logical within propositions, as formalized by the predicate calculus. Along the way, we consider several questions related to logic and meaning and introduce several interesting results. The theory and methodology we develop has potential application to a natural language preprocessor for a priori skimming and the production of abstracts, although for now the input should be specified in logical form, rather than in a natural language.