Al-Fārābī's Logic

Origin. Al-Fārābī (c. 870-950). "Second Teacher" (after Aristotle). Aristotelian synthesis. Arabic logical terminology. Foundation of Islamic Aristotelianism.

Models. Aristotelian logic systematized. Five arts of logic. Demonstration highest. Classification of sciences. Logical vocabulary established.

Formalism.

Five arts (ṣināʿāt): burhān (demonstration): certain premises, certain conclusions. jadal (dialectic): accepted premises, probable conclusions. khiṭāba (rhetoric): persuasive premises. shiʿr (poetics): imaginative premises. safsaṭa (sophistry): deceptive premises. Hierarchy of certainty.

Categorical syllogism: Aristotelian figures and moods. Arabic terminology established. ḥadd akbar (major term). ḥadd aṣghar (minor term). ḥadd awsaṭ (middle term).

Conditions for demonstration: Premises true. Premises primary (not derived). Premises more known than conclusion. Premises causes of conclusion. Necessary connection.

Categories (maqūlāt): Ten Aristotelian categories. jawhar (substance). kamm (quantity). kayf (quality). Nine accidents.

Classification of sciences: Logic: tool (organon). Theoretical: physics, mathematics, metaphysics. Practical: ethics, politics. Logic prerequisite to all.

Against Stoic logic: Propositional logic subordinate. Syllogistic central. Conditionals reducible. Aristotelian priority.

Political philosophy: Logic governs virtuous city. Philosopher-king knows demonstration. Others rely on rhetoric/dialectic. Logical hierarchy = social hierarchy.

Symbols.

Term	Arabic	Gloss	Role
qiyās	قياس	Syllogism	The inference form the whole system is built around
burhān	برهان	Demonstration	Syllogism from certain premises; the highest of the five arts
jadal	جدل	Dialectic	Syllogism from accepted premises
khiṭāba	خطابة	Rhetoric	Syllogism from persuasive premises
shiʿr	شعر	Poetics	Argument from imaginative premises
safsaṭa	سفسطة	Sophistry	Argument from premises that only seem acceptable
ḥadd	حد	Term	Also: definition; the limit that fixes an essence
muqaddima	مقدمة	Premise	What the five arts are graded by
mawḍūʿ	موضوع	Subject	The term predication is about
maḥmūl	محمول	Predicate	The term borne by the subject

Metatheory. Al-Fārābī's achievement is a working Arabic technical vocabulary together with a reading of the Organon that fixed the shape of the discipline in Arabic for centuries. From the Alexandrian commentators he took the enlarged Organon in which Rhetoric and Poetics count as logical works, and he ordered the whole by the epistemic grade of the premises, so demonstration, dialectic, sophistic, rhetoric and poetics form one graded series rather than five subjects. He faced a problem Greek did not pose: Arabic has no copula, and he pressed the pronoun huwa into service as an artificial one so that predication could be displayed at all. He separated the metathetic proposition, whose predicate is a negative term, from simple negation, a distinction later authors retained. On the sea battle of De Interpretatione 9 he kept bivalence while denying that either disjunct is determinately true, a solution Averroes and the Latins both took up.

Applies to. Islamic philosophy. History of logic. Aristotelian tradition. Classification of sciences.

Limitations. The framework is Aristotle's and inherits its limits. The syllogistic is a logic of terms, so relational and multiply quantified inference have no place in it, and the propositional forms the Stoics developed are demoted: conditionals are treated as reducible rather than as a logic of their own, which is why that strand had to be rebuilt by Avicenna rather than extended from al-Fārābī. The grading of the five arts is epistemological, not formal — what separates demonstration from dialectic is the standing of the premises, not the shape of the inference, so the hierarchy validates no argument and invalidates none. The textual base is thin: the long commentary on the Prior Analytics is lost and much of the corpus survives only in short treatises or in later citation, so several of his positions are reconstructions.