Document Type : Scientific-research

Authors

• Morteza Hajihosseini ¹
• Mohammadhosein Esfandyari ²

¹ Associate Professor of Philosophy, Department of Philosophy, Faculty of Literature and Humanities, University of Isfahan, Isfahan, Iran.

² Ph.D in Philosophial Logic, Dept of Philosophy, faculty of Humanity, University of Isfahan, Isfahan, Iran

Abstract

The two propositions "If the sun rises, the sky is bright" and "If it rains, the ground is wet" can be formulated in classical logic to yield the following conclusion "If the sun rises, then the ground is wet or if it rains, then the sky is bright."; intuitively, however, this argument does not seem to hold. In the book A New Outlook on the Elements of Logic, the author classified primitive connectives into two types, truth-functional and non-truth-functional, and showed the syntactic and semantic behaviour of non-truth-functional primitive connectives. In addition, the author introduced rules for the inference and reference of connectives to establish a non-truth-functional propositional logic system. By assigning the non-truth-functional system of propositional logic to the domain of causal, conceptual, and logical relations and formalizing the above argument in this system, the author shows its invalidity. Asadollah Fallahi, in his article Hajhosseini's Non-Truth-Functional Semantics, Falsafeh (available online on June 11, 2023), criticizes the semantics of this system with scattered criticisms. In this article, we will examine these criticisms in five groups: The behavior of the negation operator, the model and its components, the semantics of the non-truth-functional system and modal logic, the concept of validity, and the meta-theorems of completeness and decidability. We will also show that apart from one case of a trivial error, which is overstated in his critique, the other criticisms are due to the following: Failure to abandon presuppositions, deviation from some requirements of the critique, error in the understanding and interpretation of some formulas, errors in the interpretation and evaluation of some arguments, use of fallacious methods, neglect of some contents of the book, and resort to irrelevant grounds in the critique of the contents.  

Keywords

• Non-truth-functional System
• Negation operators
• Intensional relations
• Model
• Completeness
• Decidability

Main Subjects

• philosophy