al-Qiyas

al-Qiyas (The Syllogism) is a logical treatise by the Andalusian philosopher and jurist Ibn Rushd al-Hafid (d. 595 AH / 1198 CE), dedicated to the exposition and systematic analysis of formal syllogistic reasoning based on the logical corpus of Aristotle al-Qiyas+1.

Purpose and Foundational Concepts

The work defines a syllogism as a statement composed of more than one premise such that another distinct statement—the conclusion—necessarily follows by virtue of the premises themselves and not accidentally al-Qiyas. Ibn Rushd states that the ultimate aim of examining the syllogism is demonstration (al-burhan), through which complete demonstrative knowledge of existing things is attained, since every demonstration is a syllogism, though not every syllogism is a demonstration al-Qiyas+1.

The treatise establishes the foundational elements of syllogistic theory, including the definitions of premises (muqaddamat), terms (hudud), and the distinction between complete (kamil) and incomplete (ghayr kamil) syllogisms al-Qiyas+1. A complete syllogism is one whose necessary conclusion is immediately evident without requiring additional steps, whereas an incomplete syllogism requires intermediate steps derived from the stated premises to demonstrate its validity al-Qiyas. Ibn Rushd also delineates the parts of a categorical syllogism, which consists of two premises sharing a single middle term (al-hadd al-awsat) that links the minor term (al-hadd al-asghar) and the major term (al-hadd al-akbar) al-Qiyas+1.

The Syllogistic Figures

Ibn Rushd organizes the analysis of categorical syllogisms into three natural figures (ashkal) based on the position of the middle term:

• The first figure (al-shakl al-awwal): The middle term serves as the predicate in the minor premise and the subject in the major premise; its universal moods are the most complete and primary, producing all four categorical conclusions al-Qiyas+1.
• The second figure (al-shakl al-thani): The middle term serves as the predicate in both premises, naturally yielding negative conclusions al-Qiyas+1.
• The third figure (al-shakl al-thalith): The middle term serves as the subject in both premises, yielding particular conclusions al-Qiyas+1.

Ibn Rushd rejects the fourth figure posited by Galen, maintaining that human intellect does not naturally construct syllogisms in that order, and that any valid inference drawn from such an arrangement is merely an unnatural inversion reducible to the first figure rather than an independent natural figure al-Qiyas+1. He demonstrates how valid moods in the second and third figures reduce back to the first figure, either through direct conversion ('aks) of premises or through proof by contradiction (qiyas al-khalf) al-Qiyas+1.

Method and Logical Analysis

The work explores modal syllogisms, analyzing combinations of assertoric, necessary, and contingent or possible (mumkin) premises across the various figures al-Qiyas. It also investigates cases where true conclusions can result from false premises, distinguishing between premises that are wholly false and those that are partially false al-Qiyas+1. Beyond formal structures, Ibn Rushd provides rules for reducing complex arguments and rhetorical passages found in written texts and discourse into their underlying syllogistic figures, as well as examining the logical structure of inferential signs (al-'alamah) and conditional arguments al-Qiyas+1.