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Non-verbal communication in classical logic

Ronald Fuller
Presented at the 2019 Winter Meeting of the Association for Symbolic Logic.

Uninterpreted logical structures are generally considered to have no meaning. But in disciplines of applied logic, such as information management and software engineering, uninterpreted structures are meaningful. Put another way, logical vocabularies and sentences can express meaning even when the value of object constants are unknown, incorrect or absent. Meaning can be conveyed by the mode of presentation alone. Frege called this sense, Carnap called it intension.

The Stanford Encyclopedia of Philosophy says outright "In classical first-order logic intension plays no role." This is misleading. It is true that no awareness of meaning is needed for a person or machine to analyze uninterpreted statements, or to create derived statements from them. And it is true that many such statements are indeed meaningless. Logicians use meaningless structures to teach and study logic. But when formed properly and meaning is intended they do convey meaning. When formed improperly and meaning is intended they convey an approximation or guess at the intended meaning, which can lead to problems.

Modern institutions rely heavily on disciplines of applied logic. For example, many institutions organize information into relational databases, which are based on logic. Leaders often want to combine or compare information between organizations but cannot because the metalanguage descriptions of similar relations are different, so some intended statements cannot be derived.

Logic literacy is necessary to convey any intended meaning using logic. The decline of logic education during the 20th century and the ensuing decline of logic literacy is the root cause of many difficult and costly challenges facing modern organizations.