Logic in the Post-Traditional Era
Selected Models
DOI:
https://doi.org/10.31973/hpr79e30Keywords:
Development, Logic, Contemporary, Multi-valuedAbstract
Logic has long been one of the fundamental pillars of philosophical thought, from Aristotle to the modern era, where traditional logic—particularly in its syllogistic and formal structure—maintained dominance in methods of analysis and inference for many centuries. However, the evolution of philosophical and scientific thinking, especially since the seventeenth century, has revealed the limitations of this model and led to the emergence of new directions aimed at reconstructing logic on different foundations. This research aims to trace the conceptual and epistemological shifts that affected the structure of logic after its departure from the Aristotelian framework, by presenting selected philosophical models that contributed to this transition.
The study is based on the premise that contemporary logic was not merely a formal development of analytical tools, but a reflection of deeper transformations in how philosophers understood language, knowledge, and the mathematical structure of reason. It analyzes key philosophical models that played a role in this shift, beginning with Leibniz, who offered a preliminary vision of the “universal calculus” as an attempt to expand the boundaries of traditional logic. The research then explores the contributions of George Boole and Augustus De Morgan in laying the algebraic foundations of logic, thus paving the way for the emergence of modern symbolic logic, which opened new possibilities in logical form and structure.
The paper further examines the subsequent shifts that marked a qualitative transformation in logical theory, particularly through the work of Gottlob Frege, who reformulated logic by linking it to mathematics and language. It also considers later developments by philosophers who sought to move beyond even classical symbolic logic. The research concludes with the model of Nicolai A. Vasiliev and Mieczysław Bochvar, both of whom made significant contributions to many-valued and paraconsistent logics, representing an advanced
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References
الجابري، محمد عابد. (1982). مدخل إلى فلسفة العلوم. مركز دراسات الوحدة العربية، لبنان.
الجالي، زكريا منشاوي. (2010). المؤثرات المتبادلة بين المنطق والرياضيات: النسق نموذجًا. دار الوفاء لدنيا الطباعة والنشر، مصر.
الفندي، محمد ثابت. (1986). أصول المنطق الرياضي. مكتبة المعارف، بيروت.
النشار، علي سامي. (2000). المنطق الصوري منذ أرسطو حتى عصورنا الحاضرة. دار المعرفة الجامعية، القاهرة.
بلانشي، روبير. (1970). المنطق وتاريخه من أرسطو إلى راسل (ترجمة خليل أحمد خليل). دار الطليعة، لبنان.
زيدان، محمود فهمي. (1969). المنطق الرمزي: نشأته وتطوره. دار النهضة العربية، بيروت.
دوب، جوزيف. (2013). مبادئ المنطق الصوري القديم والحديث (ترجمة محمد يعقوبي). دار الكتاب الحديث، القاهرة.
ديمتريو. (1997). تاريخ المنطق: من اليونان إلى القرن العشرين (الجزء الأول: حول الجذور المعرفية للعقل) (ترجمة فؤاد كامل). الهيئة المصرية العامة للكتاب، مصر.
راسل، برتراند. (1965). أصول الرياضيات (الجزء الأول) (ترجمة محمد مرسي أحمد وأحمد فؤاد الأهواني). دار المعارف، مصر.
عابر، عبد العزيز. (2013). الأبعاد الحسية لمنطق حساب القضايا عند أرند هايتينج. مجلة كلية الآداب، جامعة جنوب الوادي، مصر.
كافاياس، جون. (2010). في المنطق وفي نظرية العلم (ترجمة محمد بن ساسي). دار سيناترا، المركز الوطني للترجمة، تونس.
كمال هاملي، و نادية بوجلال. (2023). المنطق الكلاسيكي من لايبنيتس إلى فريجه: مقاربة تاريخية إبستمولوجية. مجلة الحكمة للدراسات الفلسفية، 11(2)، 271–300. مجلة الحكمة، الجزائر. DOI: https://doi.org/10.34277/1460-011-002-014
محلوس، حميده. (2017). إشكالية تطور المنطق المعاصر: بين الدوافع الداخلية والتأثيرات الخارجية (أطروحة دكتوراه غير منشورة). جامعة الجزائر، الجزائر.
محمد علي، ماهر عبد القادر. (1985). فلسفة العلوم والمنطق الرياضي. دار النهضة العربية، القاهرة.
محمد علي، ماهر عبد القادر. (1994). التطور المعاصر لنظرية المنطق. دار النهضة العربية، مصر.
Boole, G. (1854). An investigation of the laws of thought on which are founded the mathematical theories of logic and probabilities. Walton and Maberly, London. DOI: https://doi.org/10.5962/bhl.title.29413
Frege, Gottlob. (1967). Begriffsschrift: A formula language, modeled upon that of arithmetic, for pure thought (S. Bauer-Mengelberg, Trans.). In Jean van Heijenoort (Ed.), From Frege to Gödel: A source book in mathematical logic, 1879–1931. Harvard University Press, Cambridge, MA.
Peirce, C. S. (1998). On the logical conception of mind (MS L75, c. 1902). In The Peirce Edition Project (Ed.), The essential Peirce: Selected philosophical writings (Vol. 2, 1893–1913). Indiana University Press, USA.
Al-Jabiri, M. A. (1982). Introduction to the philosophy of science. Center for Arab Unity Studies, Lebanon.
Al-Jali, Z. M. (2010). Mutual influences between logic and mathematics: The system as a model. Dar Al-Wafaa for Printing and Publishing, Egypt.
Al-Findi, M. T. (1986). Foundations of mathematical logic. Al-Ma'arif Library, Beirut.
Al-Nashar, A. S. (2000). Formal logic from Aristotle to our present age. University Knowledge House, Cairo.
Blanché, R. (1970). Logic and its history from Aristotle to Russell (Trans. Khalil Ahmad Khalil). Al-Tali‘a Publishing House, Lebanon.
Zaidan, M. F. (1969). Symbolic logic: Its origin and development. Dar Al-Nahda Al-Arabiya, Beirut.
Doob, J. (2013). Principles of ancient and modern formal logic (Trans. Muhammad Ya‘qubi). Dar Al-Kitab Al-Hadith, Cairo.
Demetrio. (1997). History of logic: From Greece to the twentieth century (Part I: On the epistemological roots of reason) (Trans. Fu’ad Kamil). Egyptian General Book Organization, Egypt.
Russell, B. (1965). Foundations of mathematics (Part I) (Trans. Muhammad Morsi Ahmad & Ahmad Fu’ad Al-Ahwani). Dar Al-Ma‘arif, Egypt.
‘Aber, A. (2013). The sensory dimensions of propositional calculus in Arend Heyting’s logic. Journal of the Faculty of Arts, South Valley University, Egypt.
Cavaillès, J. (2010). On logic and the theory of science (Trans. Muhammad Bin Sassi). Sinatara Publishing House, National Center for Translation, Tunisia.
Hamli, K., & Boujelal, N. (2023). Classical logic from Leibniz to Frege: A historical epistemological approach. Al-Hikma Journal for Philosophical Studies, 11(2), 271–300. Al-Hikma Journal, Algeria.
Mahlous, H. (2017). The problem of the development of contemporary logic: Between internal motives and external influences (Unpublished doctoral dissertation). University of Algiers, Algeria.
Muhammad ‘Ali, M. A. Q. (1985). Philosophy of science and mathematical logic. Dar Al-Nahda Al-Arabiya, Cairo.
Muhammad ‘Ali, M. A. Q. (1994). The contemporary development of logic theory. Dar Al-Nahda Al-Arabiya, Egypt.
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