A misconception of logic in its diffusion across non-mathematical environments: The embarrassing mistake of relying on natural language

In this paper we criticize a widespread practice in the teaching, use, and dissemination of first-order logic in non-mathematical environments. This practice consists in the presentation of the truth-conditions of logical formulas by means of sentences in natural language – e.g., if ‘s’ represents Socrates and ‘H’ represents the property of being human, ‘Hs’ is true iff Socrates is human. We will argue that it is inadequate a presentation of the semantics of first-order logic and that it is problematic for the study of natural language. Our argumentation is three-fold. First, there are constructions in natural language that do not behave as this logic requires. Second, the use of natural language is not able to provide an explanation of the semantics of individual constants and predicates. Third, this practice instigates the idea that natural language possesses a formal structure, and does so unreflectively and without justification.