muslim logicians’ critique of alexander’s categorical propositions

Alexander’s interpretation of categorical propositions relies on his understanding of modality. when he explains necessity, actuality, and contingency he draws a correspondence between modality and temporal terms. according to him, if a proposition like “all a is b” is a necessary assertion it means “every a always holds b”. on the other hand, an actual proposition means “every a is now holding b”. lastly, a contingent proposition means “every a is sometimes either b or not b, but can hold b”. as a result of alexander’s explanation of modality limited in temporal terms, a proposition like “all a are b” is true only if the term a points out to something that exists always, or now, or sometimes in the external world. because in a true proposition like “all a are b”, if members of a hold b always, or now, or sometimes; then they must exist always, or at least now, or sometimes. alexander’s understanding leads to another conclusion, which is that the term a must indicate a certain category of the external world, so members of a can exist always, or now, or sometimes. in other words, the truth-maker of propositions is their correspondence to the external world.nonetheless, muslim logicians such as ibn sīnā (d. 428/1037), naṣīr al-dīn al-ṭūsī (d. 672/1274), quṭb al-dīn al-rāzī al-taḥtānī (d. 766/1365) criticize alexander’s understanding of modality and categorical propositions. do we have to think about the category of propositions’ terms? is it impossible to make a true assertion about something never exists in the external world? is it impossible to make certain predication without being certain about the members’ external existence? these kinds of questions are the starting point of ibn sīnā, ṭūsī, and rāzī’s critics of alexander’s interpretation. their critics can be summed up under two headings: i) if alexander’s commentary of modality and categorical propositions is true then it would be impossible to make certain assertions about mathematical entities. because throughout the history of philosophy there is no agreement about the existence of mathematical entities. nevertheless, according to them, we can demonstrate the certainty of some mathematical propositions regardless of their external existence. ii) according to them alexander’s explanation leads that every universal concept is a particular concept. because if “all a” is understood as “all a existed always, or now, or sometimes externally” then the universal concept would be restricted by external existence. whereas, there could be some a which has not existed, or not existing, or will not exist, or never exist, but still the members can be conceptualized as a. in this work, alexander’s understanding of propositions and muslim logicians’ critics of him will be presented in a both historical and doctrinal framework.