Al-Sijistani's and Maimonides's Double Negation Theology Explained by Constructive Logic

Famous medieval philosophers Al-Sijistani and Maimonides argued that the use of double negation helps us to better understand issues related to theology. To a modern reader, however, their arguments are somewhat obscure and unclear. We show that these arguments can be drastically clarified if we take into account the 20 century use of double negation in constructive logic. 1 Double Negation Theology: A Brief Reminder What is double negation theology. Abu Yakub Al-Sijistani (d. 971) and Moses ibn Maimon (1135–1204), also known as Maimonides, claimed that while while God is essentially incomprehensible, it is possible to gain some knowledge of God by using double negation; see, e.g., [15, 19]. For example, one cannot say that God is good, but it make sense to say that God is not not-good. Why double negation? The reasoning behind the use of double negation is, to a modern reader, rather obscure and unclear. In this short paper, we will show, however, that the use of double negation can be made much clearer to the modern reader if we take into account the 20 century developments in constructive logic. 2 What Is Constructive Logic: A Reminder Constructivity in mathematics before the 20 century. Strictly speaking, mathematics is about proving results. However, from the ancient times, mathematicians were also interested in constructing objects. The need for constructions is motivated largely by applications. For example, to predict where a satellite will be at some future moment of time, we need to