The Rule of Existence (Assumption/Entailment) and Logical Consequence On Ibn Sīnā’s Thesis

Abstract

The rule of assumption/entailment has been articulated in Islamic philosophy at least in two ways: (1) a's being b assumes/entails a's existence; (2) that a is b is true entails that a exists is true. Ibn Sina explores this rule in the latter form in logic (Kītāb al-‘ibāra). I call this form the rule of existence. I argue that for Ibn Sina the rule of existence is not a logical rule but a metaphysical entailment. To this end, I first abstract a definition of logical consequence from Ibn Sina’s considerations on the subject, using contemporary tools of logic. I then show that, according to this definition, the rule of existence is not logical. After that, I argue that based on my interpretation of Ibn Sina’s thesis, a number of formalizations of his categorical propositions that are popular in contemporary literature, are fundamentally mistaken. Moreover, I show how my interpretation of Ibn Sina can accommodate almost all the logical rules that he has already confirmed, especially the rule of contraposition. Based on exegetical considerations, I argue that Ibn Sina believes in the non-uniformity of the analysis of propositions. From this, I argue that the rule of contraposition proves to be valid.

Keywords

• the rule of assumption/entailment
• the rule of existence
• logical consequence
• metaphysical entailment
• the rule of contraposition