A Critical Analysis of a Critique on Truth-Functional System Semantics Is the Conclusion of an Argument Independent of the Premises?

In Classical Logic, an argument is deemed valid if and only if it lacks a counterexample. However, arguments like  and  are considered valid based on this definition, despite natural intuition challenging their validity. A New Outlook on the Elements of Logic introduces a novel definition for argument validity, rendering the aforementioned arguments unprovable. This new definition necessitates revisions in argument evaluation, the substitution rule, the definition of logical truth, methods for determining argument validity and invalidity, as well as the definition and procedure of soundness and completeness proofs in Classical Logic. The establishment of the Truth-Functional System of Propositional Logic stems from this revised definition.Asadollah Fallahi critiques this system in "Hajhosseini’s Truth-Functional Semantics," published in Philosophy and Kalam, 2023, Vol. 56, issue 1. While proposing scattered criticisms, this article reveals that, aside from one critique requiring rectification due to an inadvertent mistake, the other criticisms stem from fallacies, unfounded accusations, non-compliance with certain critique conditions, incorrect formulation of the definition of a valid argument, and oversight of consequences arising from new conditions for argument validity and its definition.