How is Logical Implication Analyzed and Formulated? A Critical Review of the Article "on Historical Aspects of Hajihosseini’s Logical Systems"

Document Type : Original Article

Authors

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

2 Ph. D in Philosophical Logic, Department of Philosophy, Faculty of Literature and Humanities, University of Isfahan,

10.48308/kj.2024.233342.1196

Abstract

In natural language, we sometimes come across arguments contain non-functional connectives. Classical logic is not able to analyze and formalize these arguments. Moreover, logical implication in a valid argument has four properties: Truth-preservation, Necessity, Formality, and Universality. In classical logic, which evaluates EQT and EFQ as valid and correct, the second property, necessity, is not guaranteed. Hajihosseini in book “A New Outlook on Elements of Logic” has paved the way for solving these two problems by establishing two logical systems, one functional and one non-functional, and extending these systems.
In this context, however, Asadollah Fallahi, in his article On Historical Aspects of Hajhosseini’s Logical Systems, published in Knowledge, No. 88/1 (Spring/Summer 2023), has attributed three claims to the author of the book: 1) The separation of functional and non-functional fragments is one of the author's innovations. 2) Classical logic confused material implication and deduction and considered them one. 3) The metatheorem of deduction is incorrect because the relation between the premises is an extensional conjunction. In this article, we demonstrate that none of the above claims were made in the book and that any confusion results from a selective reading of a detailed passage and a lack of understanding Fallahi, also, argues that any contradiction can be derived from a contradiction in the functional system. Moreover, transitive relations in arguments are valid in both functional and non-functional systems, contrary to Tennant's classical relational logic.

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References

Hajihosseini, Morteza (2022), Two Non-Classical Logic Systems: A New Outlook Elements of Logic, Isfahan: Isfahan University Press (In Persian)
Hajihosseini, Morteza; Bahmanpour, Hamideh (2023), “A Critical Examination of a Criticism on the Truth Functional System of Basic Propositional Logic Are The Ways of Proving the EQT and EFQ Principles Closed?”, The Mirror of Knowledge, 23(3): 167-200
Hajihosseini, Morteza; Bahmanpour, Hamideh (2023), “Critical Review of a Critique of the Non-Truth-Functional System of Propositional Logic; Are the Theses of Aristotle and Boethius Proved?”, in Logical Studies, 56(2) (forthcoming)
Hajihosseini, Morteza; Alvand, Masoud (2023), “The Relevance Logic Theory and the Truth-functional System Theory; A Comparison and Evaluation Based on the Inference to the Best Explanation and Priest’s Quantitative Model,” Journal of Philosophical Investigations (forthcoming)
Fallahi, Asadollah (2023), “On Historical Aspects of Hajhosseini's Logical Systems,” in Shinakht, 88(1)
Tennant. N, 2017, Core Logic, Oxford, Oxford University Press
Vidal-Rosset.J.(2017) ‘Why Intuitionistic Relevant Logic Cannot Be a Core logic’, Notre Dame Journal of Formal Logic, Vol. 58, PP 241-248

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History

  • Receive Date: 04 October 2023
  • Accept Date: 29 February 2024

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