Lecture 7: Definitions, Propositions, and the Road to Syllogism

This lesson completes the discussion of ma'arifat (معرفات), the tools by which unknown concepts are clarified. The instructor distinguished between three layers: the mu'arrif (معرف), the feature or property that makes a thing knowable; the mu'arraf (معرف), the thing being defined; and the ta'rif (تعريف), the wording or mental expression that points us to that clarifying feature. This matters because many disputes arise when people use the same words with different definitions, or when a definition is too vague, too broad, too narrow, circular, or emotionally loaded rather than logically precise.

Al-Akhdari divides definitions into three main kinds: hadd (حد), rasm (رسم), and lafzi (لفظي). A hadd is a formal definition that aims at the essence of the thing. In Aristotelian terms, it is definition by genus and specific difference: for example, a human being is a hayawan natiq (حيوان ناطق), a rational animal. A rasm is a descriptive definition: it does not give the essence, but identifies the thing through a distinctive property, such as defining a human as a laughing animal. A lafzi definition explains an unclear word by giving a clearer synonym, such as explaining ghadanfar by saying it means asad, lion.

A sound definition should be jami' mani' (جامع مانع): inclusive of everything that belongs under the thing being defined and exclusive of everything outside it. Defining a human as merely an animal is too broad; defining an animal as a rational animal is too narrow. A definition should also be clearer than the thing being defined, should not use the very term being defined, should not rely on metaphor without a clear contextual indicator, should avoid ambiguous homonyms, and should not import rulings or judgments into the definition. These rules resemble good analytic practice in Western philosophy: before arguing about a claim, one must clarify terms and avoid circular definitions.

The lesson also treated an important point about capacity versus actual performance. When logicians define the human as natiq (ناطق), they do not mean “currently speaking”; they mean possessing the capacity for intellect or rationality. Thus a mute person, an infant, or someone mentally impaired does not cease to be human. Similarly, “laughing animal” means having the natural potential for laughter, not that every human is actually laughing. The instructor connected this to the mutakallimun’s view that aql (عقل), intellect, is a stable faculty or disposition created by Allah, with bodily organs serving as instruments through which its effects appear.

After completing definitions, the lesson transitions from mabadi al-tasawwurat (مبادئ التصورات), the foundations of conceptualization, to mabadi al-tasdiqat (مبادئ التصديقات), the foundations of assent or judgment. The key new unit is the qadiyyah (قضية), a proposition: a compound statement that can be true or false in itself. Truth, sidq (صدق), is correspondence to reality, while falsehood, kadhb (كذب), is failure to correspond to reality. This differs from commands, questions, wishes, and requests, which are not true or false in themselves.

Propositions are divided into shartiyyah (شرطية), conditional propositions, and hamliyyah (حملية), categorical propositions. A conditional proposition links one statement to another, as in “If the sun is rising, then the day exists.” A categorical proposition predicates one term of another, like “Every human is an animal” or “No human is a stone.” Categorical propositions are then analyzed by quantity and quality: universal or particular, affirmative or negative. These become the basic forms later used in qiyas (قياس), syllogism, where propositions are arranged so that a conclusion follows necessarily—much like a mathematical structure applied to meaningful claims.