Validity of the laws of Non-contradiction and Excluded middle; Logical or Psychological (Review of misunderstandings and misinterpretations, self-made accusations and types of fallacies in a criticism)

Abstract
In Classical Logic, the law of non-contradiction and the law of excluded middle are considered theorems and have proof. Recently, Morteza Hajihosseini has written a book titled Two Non-Classical Logic Systems, A New Outlook on Elements of Logic (2017) and also published the second edition (2023) of it. In this book, he established two truth-functional and non-truth-functional systems in logic. In this logic, the law of non-contradiction and the law of excluded middle are in the form of a rule that every line of the argument is written based on them and are therefore considered unprovable.
Asadollah Fallahi has recently written several criticisms on this book in the form of separate articles and the author of the book has responded to each of these articles separately. Fallahi, in his last review of the book titled "Philosophical Foundations of Hajhosseini's Logics" Volume 14, Issue 2, February 2024 in Contemporary Wisdom Journal, critiques the philosophical foundations of the truth-functional and non-truth-functional systems, including the author’s views on the law of non-contradiction and the law of excluded middle and their consequences, without clarifying his stance on whether a non-formal language is presupposed or not.
In this article, we first explain the philosophical and epistemological foundations of logical systems and compare these systems with respect to these foundations. Then, we respond to Fallahi’s criticisms one by one.
Keywords: Logical system, The law of non-contradiction, The law of excluded middle, Natural language, Natural intuition.
Introduction
With its philosophical assumption that there is a non-formal language to be paraphrased, classical logic has been founded to provide an exact formal method for mathematical arguments and as well as their logical explanation. In this logic, the law of non-contradiction and the law of excluded middle are considered to be as theorems for which there is proof. Recently, Morteza Hajihosseini wrote a book titled Two Non-Classical Logic Systems, A New Outlook on Elements of Logic (2017) whose second edition was released in 2023. In this book, the author begins with this philosophical assumption that there is a non-formal language that the formal language is trying to represent, and then he discusses the consequences of this assumption. Furthermore, with the aim of providing a precise formal method for the arguments in natural language and explaining them logically, he established two truth-functional and non-truth-functional systems in logic. In this logic, the law of non-contradiction and the law of excluded middle function as rules based on which every line of the argument is written and are therefore considered unprovable.
Materials & Methods
The research method used in this article is descriptive-analytical. In this article, we have systematically examined each critique that Fâllāhī has leveled against the book Two Non-Classical Logic Systems, A New Outlook on Elements of Logic and have responded to them based on the book itself.
Discussion & Result
In this article, we first explain the philosophical and epistemological foundations of logical systems and compare these systems with respect to these foundations. Then, we respond to Fallahi’s criticisms singly. Finally, our responses to these criticisms, presented in the form of the conclusion of this article, are summarized under the following headings:
Firstly, Fallahi, not clarifying his stance on meta-systematic non-formal language, the value of intuition and its role in evaluating logical problems, and instrumentalism, has, as explained in our response to the criticisms, muddled up various logical, epistemological and psychological problems.   
Secondly, Fallahi, with his arbitrary interpretation of applied logic and its distinction from theoretical logic, has not only blocked the application of logical systems in non-formal languages but has also reduced theoretical logic to an artificial and featureless system. Despite acknowledging the importance of intuitive insights, he has undermined the validity of intuition by employing an incorrect definition of paradox.
Thirdly, except for one criticism which is irrelevant to the philosophical and epistemological foundations of the systems and could be easily corrected, his other criticisms arise from misconceptions, misinterpretations, contrived accusations, and fallacies. Among them, we could refer to the following:
- The misinterpretation that the author of the book considers the axioms to be completely self-evident.
- The misinterpretation that adding axioms to the premises of a correct argument leads to the incorrectness or invalidity of the argument.
- The misconception that the following arguments in the book have been evaluated as false/invalid and are in conflict with some other claims in the book:
A ∨ ~ A ⊢ A ∨ ~ A
A → A ⊢ A → A
- The misinterpretation that the formulation rules in Classical and Non-Classical Logics are incorrect.
- The fabricated accusation that the author of the book considers Classical Logic to be based on the logical atomism of Russell and Wittgenstein, the logical positivism of the Vienna Circle, and the naturalized epistemology of Quine.
- The fabricated accusation that Abdullah Javadi Amoli considers sentences like "Wednesday is a triangle" and "the wall is blind" to be meaningful but false.
-  The fallacy that in philosophy and mathematics some propositions result in their contradiction.
- The fallacy that in logic and epistemology, as opposed to philosophy, "circularity" is allowed.
- The fallacy that counterfactual conditionals are biconditionals, which are caused by the fallacy of False Conversion.
Conclusion
Our analysis of Fallahi's article titled "Philosophical Foundations of Hajhosseini's Logics" reveals that his critiques of the book Two Non-Classical Logic Systems, A New Outlook on Elements of Logic are founded on fallacies, misconceptions, misinterpretations, and unfounded accusations. The responses provided in this paper clearly show that none of these criticisms hold water.