Mohammad Saleh Zarepour: Ṭūsī, Samarqandī, and Daštakī on the Liar Paradox

Ṣadr al-Dīn al-Daštakī (d. 1498) has proposed a solution to the liar paradox which has strong similarities to a modern solution that is proposed by Alfred Tarski. In this presentation, I argue that Daštakī’s solution can be taken as a synthesis of two earlier solutions proposed by Naṣīr al-Dīn al-Ṭūsī (d. 1274) and Šams al-Dīn al-Samarqandī (d. 1322). Ṭūsī argues that if we endorse the correspondence theory of truth, then self-referential sentences (e.g., the liar sentence) cannot have any truth-value. On the other hand, Samarqandī clarifies how the truth value of a sentence in which truth/falsity-predicates are iterated can be determined by analysing and breaking down the compound sentence in question to simpler sentences. Relying on these two elements, Daštakī develops a theory of truth in which every sentence with iterative truth/falsity-predicates can be analysed to a hierarchy of sentences each of which expresses the truth/falsity of the sentence in the lower level. He argues that such a compound sentence (with iterated truth/falsity predicates) have a truth value only if its counterpart hierarchy ends in a sentence which does not express truth/falsity of another sentence. Since the liar sentence does not satisfy this condition, it has no truth value.

Mohammad Saleh Zarepour is a Postdoctoral Research Fellow at the Department of Philosophy of the University of Birmingham. Before going to Birmingham, he was a Humboldt Postdoctoral Research Fellow (2019–2020) at Munich School of Ancient Philosophy, LMU Munich. He did a PhD (2019) in the Faculty of Divinity at the University of Cambridge and another one (2015) in the Department of Philosophy at Tarbiat Modares University (TMU), Tehran. He works on philosophy of language, philosophy of religion, and philosophy of mathematics from the perspectives of both contemporary analytic philosophy and medieval Islamicate philosophy. Mohammad Saleh Zarepour is the author of Necessary Existence and Monotheism: An Avicennian Account of the Islamic Conception of Divine Unity (CUP, forthcoming) and the co-editor of Mathematics, Logic and their Philosophies (Springer, 2021).