Mathematics, Logic, and their Philosophies

Mojtaba Mojtahedi is Assistant Professor at the Department of Mathematics, Statistics and Computer Science, College of Science, University of Tehran. He is graduated from Sharif University of Technology in 2013. His research interests include provability logic, intuitionistic logic and arithmetic.Shahid Rahman is full-professor of logic and epistemology at the Université de Lille-Nord-pas-de-Calais, Sciences Humaines et Sociales. He is also researcher at the UMR-CNRS 8163 : STL, member (2016-2018) of the Conseil Scientifique du Réseau national des Maisons des Sciences de l’Homme, member of the commission of the Institute Eric Weil, and director (for the French side) of the ANR-DFG Franco-German project  2012-2015 (Lille (MESHS)/Konstanz, Prof M. Armgardt): Théorie du Droit et Logique/Jurisprudenz und Logik. Prof. Rahman works span both philosophy of logic and its history, including a dialogical perspective on Constructive Type Theory. He is the leading researcher in the field of the dialogical conception of logic to which he contributed with publications in, among other fields, non-classical logics, legal reasoning, Aristotle, Arabic Logic and Epistemology. Prof. Rahman is the main editing director of two collections of books in Springer, namely, Logic, Epistemology and the Unity of Science (more than 40 volumes edited so far), and Logic, Argumentation and Reasoning, Perspectives from the Social Sciences and the Humanities.Mohammad Saleh Zarepour is a Humboldt Postdoctoral Research Fellow at Ludwig Maximilian University of Munich. His areas of expertise include philosophy of mathematics, philosophy of language and philosophy of religion from the perspective of both contemporary analytic philosophy and medieval Islamicate philosophy. He has published articles in various journals, including Synthese, Archiv für Geschichte der Philosophie, Oriens, Acta Analytica, Religious Studies, Sophia, and Dialogue.

• Chapter 1. Introduction (Mojtaba Mojtahedi, Shahid Rahman, and Mohammad Saleh Zarepour).- Chapter 2. Extension and Interpretability (Albert Visser).- Chapter 3. Residuated Expansions of Lattice-Ordered Structures (Majid Alizadeh and Hiroakira Ono).- Chapter 4. Bounded Distributive Lattices with Two Subordinations (Sergio Celani and Roman Jansana).- Chapter 5. The Termination Condition of Gossip Protocols (Rahim Ramezanian, Rasool Ramezanian, and Hans van Ditmarsch).- Chapter 6. On equivalence (Wim Veldman).- Chapter 7. Unification in basic logic (Mojatba Mojtahedi).- Chapter 8. Binary Modal Companions for Subintuitionistic Logics (Dick de Jongh and Fateme Shirmohammadzade Maleki).- Chapter 9. From Intuitionism to Many-Valued Logics through Kripke Models (Saeed Salehi Pourmehr).- Chapter 10. The Intuitionistic Logic of Language (Mehrnoosh Sadrzadeh).- Chapter 11. Non-Conditional Contracting Connectives (Luis Estrada-González and Elisángela Ramírez-Cámara).- Chapter 12. The Struggle between Syntax and Semantics in Mathematics (Siavash Shahshahani).- Chapter 13. De-Modalizeing the Language in an Empiricist-Friendly Way: The Case of Physics (Kave Lajevardi).- Chapter 14. Avicenna on Deductions from Contradictory Premises (Behnam Zolghar).- Chapter 15. On Descriptive Propositions in Ibn Sīnā: Elements for a Logical Analysis (Shahid Rahman and Mohammad Saleh Zarepour).- Chapter 16. TBA (Ali Farjami).- Chapter 17. Empiricism of Avicenna Reconsidered (Seyed N. Mousavian).