Ali al-Qushji 's Definition of Number in Terms of Its Sources and Influence

Abstract

In this study, Ali al-Qushji 's 'definition of number' will be analyzed in terms of unity, plurality, one, many, quantity, sum, counting, and related concepts. First, to emphasize the importance of the subject, the discussions of the 'definition of number' in contemporary philosophy of mathematics will be briefly reviewed. Then, Ali al-Qushji 's approach to the subject will be examined through his works al-Muhammadiyya fi al-hisab and Sharh alTajrid, and his thoughts will be analyzed. In addition, for a comparison with Ali al-Qushji 's approach, Shams alDin Ifahani's commentary Tasdid al-Qawa'id fi sharh Tajrid al-aqa'id and Sayyid Sharif's ashiya will be briefly discussed. The background of the attitude Ali al-Qushji represented will be built on works by members of the Tabriz school of mathematics-astronomy, especially Niam al-Din al-Nisaburi, Ibn Hawwam, Kamal al-Din al-Farisi, and Jamal al-Din al-Turkistani, as well as Abu al-asan al-Bahmani and Ali b. al-Gharbi. Additionally, the book Miftah al-hussab by Jamshid al-Kashi of the Samarkand school of mathematics-astronomy, of which Ali al-Qushji was a member, will be addressed. Then, the debate triggered by Ali al-Qushji in Istanbul will be traced, focusing on mathematicians such as Fanarizade Ali Chalabi and the accounting mathematician Katib Ala al-Din Yusuf. A brief evaluation will be made of the projections of all these discussions in the work of Taqi al-Din Raid.