ABSTRACT. 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.

Keywords: semantics of first-order logic; translational semantics; natural language semantics; formal semantics; logic teaching; formal structure of natural language

How to cite: Andrade-Lotero, Edgar, and Julián M. Ortiz-Duque (2019). “A Misconception of Logic in Its Diffusion across Non-Mathematical Environments: The Embarrassing Mistake of Relying on Natural Language,” Linguistic and Philosophical Investigations 18: 77–96.

Received 28 November 2017 • Received in revised form 7 February 2018
Accepted 8 February 2018 • Available online 27 February 2018


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Department of Applied Mathematics
and Computer Science,
Universidad del Rosario, Bogotá
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Independent Scholar

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