Definitions in Logic: Complete and Incomplete Ḥadd and Rasm

Definiendum versus definiens; the four definitions explained through worked classical examples Read the bilingual lesson for Definitions in Logic: Complete and Incomplete Ḥadd and Rasm and test your understanding with a focused quiz.

Lesson

1. Using familiar concepts to explain an unfamiliar one

Earlier lessons distinguished genus, species, differentia and property. Here we use already understood concepts to explain an unfamiliar essence. A learner who knows the words “animal” and “rational” may combine them in the traditional logical definition “rational animal” to understand the essence of “human.” The terms reflect the book’s classical classification.

2. What are a definiens and an explicative definition?

The book calls an expression made from known concepts that clarifies an unfamiliar concept a muʿarrif or qawl shāriḥ. The item being defined is the muʿarraf (definiendum); the expression used to explain it is the muʿarrif (definiens). For example, “human” is explained using “rational animal.” Although the introduction discusses combining concepts, the text later accepts a near differentia or a distinctive property alone in certain incomplete definitions.

3. Do not confuse what is defined with its definition

Muʿarraf is the thing being defined; muʿarrif is the explanation used to define it. In “human — rational animal,” the former is the definiendum and the latter the definiens. “Human — laughing-capable animal” has the same definiendum but a different definiens, based on a property rather than an essential differentia.

4. The fourfold classification

The book divides explanatory definitions into complete and incomplete essential definitions (ḥadd) and complete and incomplete descriptive definitions (rasm). First ask whether the formulation relies on essential components or a distinguishing non-essential property. Then examine whether it uses the nearest appropriate genus together with the relevant differentia or property, or a more remote or shorter formulation. “Incomplete” does not automatically mean false.

5. Five terms to recall before classifying definitions

Species: human. Proximate genus: animal. Remote genus: body or growing body. Proximate differentia: rational (in the traditional sense of intellect). Property: capable of laughter, traditionally expressed by ḍāḥik. The property distinguishes in the classical teaching example but is not treated as an essential constituent of the human essence.

6. The classical hierarchy from body to human

The instructional hierarchy runs: body → growing body → animal → human. For human, animal is the proximate genus, while body and growing body are more remote genera. This is the source’s traditional conceptual hierarchy, not a replacement for modern biological taxonomy.

7. The meaning of an essential definition (ḥadd)

A ḥadd explains what something is through elements treated as constitutive of its essence. “Human — rational animal” combines a general essential component with a differentiating one. Explaining a human instead through a distinctive capability such as laughter belongs to the book’s account of rasm, not ḥadd.

8. Complete essential definition

A complete essential definition consists of the proximate genus plus the proximate differentia. The book’s model is “rational animal” for human: animal is the proximate genus and rational is the proximate differentia. Word count alone does not establish this classification; the logical roles of the components do.

9. Why the complete ḥadd is complete

The proximate genus locates the species in the nearest broader class. The differentia then distinguishes it within that class. “Animal” alone remains too broad. “Rational” alone supplies a differentia but omits the proximate genus. Their combination constitutes the complete ḥadd in the source’s terminology.

10. Two forms of an incomplete essential definition

The source gives two forms of ḥadd nāqiṣ: a remote genus with the proximate differentia, as in “rational body,” or the proximate differentia alone, as in “rational.” Both include the essential differentiating factor but lack the full proximate-genus structure of the complete ḥadd.

11. Where “rational body” is incomplete

“Body” is a genus of human but not its nearest genus in this classical hierarchy. “Rational” is the proximate differentia. The formula thus uses a remote genus where the complete definition would use “animal.” Replacing body with animal gives the book’s complete ḥadd.

12. Why the differentia alone can be an incomplete ḥadd

Although definitions are introduced as combinations of understood concepts, the textbook explicitly allows the proximate differentia alone as an incomplete ḥadd. “Rational,” in the book’s technical sense, points to the defining difference but omits the proximate genus. It conveys a useful essential distinction without giving the complete structure.

13. Comparing complete and incomplete ḥadd

For the same definiendum, human: “rational animal” is complete (proximate genus + proximate differentia); “rational body” is incomplete (remote genus + proximate differentia); and “rational” alone is incomplete (differentia only). Identify the target and the logical role of each term before assigning a label.

14. Descriptive definition (rasm) uses a property

A rasm identifies a thing through a distinguishing feature treated as outside its essence. The book uses ḍāḥik, the capacity for laughter, as a traditional example of a human property. It is not the same logical role as nāṭiq, the essential differentia. The contrast is essential characterization versus recognition through a distinctive attribute.

15. Complete descriptive definition

Rasm tāmm combines the proximate genus with a distinctive property. The textbook’s model is “laughing-capable animal” for human. Animal provides the nearest genus; laughing-capable provides the property. It is complete as a rasm, not a ḥadd, because a property replaces the essential differentia.

16. Rational animal versus laughing-capable animal

Both expressions begin with the same proximate genus, animal. Their second components differ logically: rational is treated as a proximate differentia, while laughing-capable is treated as a property. Therefore the former is a complete ḥadd and the latter a complete rasm. The logical role of the component—not superficial word pattern—determines the type.

17. Two forms of incomplete rasm

Rasm nāqiṣ consists either of a remote genus plus a distinctive property (“laughing-capable body”) or the distinctive property alone (“laughing-capable”). Both retain a property but omit the proximate genus. Consequently, they are incomplete descriptive definitions, not incomplete essential definitions.

18. Work through “laughing-capable body”

Body is a remote genus and laughing-capable is a property; the result is an incomplete rasm. Change body to animal and it becomes a complete rasm. Change the property to the proximate differentia rational and the expression becomes an incomplete ḥadd. There are two independent decisions: genus distance and differentia versus property.

19. A single comparison for all four forms

For human: rational animal = complete ḥadd; rational body or rational alone = incomplete ḥadd; laughing-capable animal = complete rasm; laughing-capable body or the property alone = incomplete rasm. First decide between differentia and property, then between proximate genus and remote or absent genus.

20. A four-question classification method

1. Identify what is being defined. 2. Determine whether the key term is an essential differentia or a distinctive property. 3. If a genus appears, determine whether it is proximate or remote. 4. If there is no genus, check whether a differentia or property alone is given. Example: human — laughing-capable body uses a remote genus and property, so it is an incomplete rasm.

21. Worked answers from selected textbook prompts

For human: “rational animal” is complete ḥadd; “rational body” and “rational” alone are incomplete ḥadd; “rational substance” uses a remote category and so illustrates incomplete ḥadd. For horse, the traditional expression “neighing animal” illustrates complete rasm when neighing is treated as its distinctive property. Classification presupposes knowing the intended definiendum.

22. Not every true description is an adequate definition

A true attribute is not necessarily a distinguishing definition. “Human is an animal” is too broad to define human. “Human is a walking thing” is not a distinctive property because other beings also walk. In the classical model, “rational animal” is offered as a complete essential definition because it includes both the proximate genus and distinguishing essential factor.

23. Two subtle misconceptions

Two-word expressions are not automatically complete definitions: “rational body” is still an incomplete ḥadd because body is a remote genus. A distinguishing feature is not automatically an essential differentia: ḍāḥik is treated as a distinctive property in the source. Here “incomplete” describes structure, not necessarily uselessness or falsehood.

24. Self-check five definitions

Assume each expression defines human: rational animal — complete ḥadd; rational body — incomplete ḥadd; laughing-capable animal — complete rasm; laughing-capable body — incomplete rasm; laughing-capable alone — incomplete rasm. Reclassify them in a different order and revisit the difference between differentia and property wherever uncertain.

25. Lesson conclusion and transition

The thing being defined is the muʿarraf; its explanatory account is the muʿarrif or qawl shāriḥ. Complete ḥadd combines proximate genus and differentia. Incomplete ḥadd uses remote genus and differentia, or differentia alone. Complete rasm combines proximate genus and property; incomplete rasm uses remote genus and property, or property alone. The book then moves from the discussion of conceptions into judgments.

Practice questions

Question 1

In “human — rational animal,” human is the:

Definiendum
Definiens
Proximate differentia
Property

Question 2

In that same example, “rational animal” is the:

Definiendum
Definiens
Common accident
Species

Question 3

How many principal classes of definition does the textbook list?

Question 4

What mainly differentiates ḥadd and rasm?

Only the former is Arabic
Essential components versus distinctive property
Ḥadd has one word
Rasm is always false

Question 5

In the book’s classical hierarchy, the proximate genus of human is:

Body
Growing body
Animal
Substance

Question 6

In defining human, nāṭiq is treated as the:

Property
Proximate differentia
Common accident
Remote genus

Question 7

For human, ḍāḥik functions as the:

Proximate genus
Proximate differentia
Distinctive property
Species

Question 8

“Rational animal” for human is:

Complete ḥadd
Incomplete ḥadd
Complete rasm
Incomplete rasm

Question 9

“Rational body” for human is:

Incomplete rasm
Incomplete ḥadd
Complete rasm
Complete ḥadd

Question 10

For human, “rational” alone is:

Complete ḥadd
Incomplete rasm
Incomplete ḥadd
Complete rasm

Question 11

“Laughing-capable animal” for human is:

Complete rasm
Complete ḥadd
Incomplete ḥadd
Incomplete rasm

Question 12

“Laughing-capable body” for human is:

Complete ḥadd
Complete rasm
Incomplete ḥadd
Incomplete rasm

Question 13

For human, ḍāḥik alone is:

Incomplete ḥadd
Incomplete rasm
Complete ḥadd
Complete rasm

Question 14

Which combination makes a complete ḥadd?

Remote genus + property
Proximate genus + proximate differentia
Proximate genus + property
Remote differentia + common accident

Question 15

What makes a complete rasm?

Proximate genus + property
Remote genus + differentia
Differentia alone
Proximate genus + differentia

Question 16

Why is “rational body” not a complete ḥadd?

Rational is a property
Body is a remote genus
It is one word
Humans are not bodies

Question 17

Why is “laughing-capable animal” not a complete ḥadd?

It lacks animal
It has three words
Ḍāḥik is a property, not a differentia
Ḍāḥik is a genus

Question 18

What is lost if nāṭiq is removed from “rational animal”?

The differentiating factor
The genus while property remains
A remote genus is added
It becomes complete rasm

Question 19

If a definition has two words, what follows?

It must be complete ḥadd
It must be complete rasm
Classification still depends on the components
It must be a judgment

Question 20

In the traditional example, ḍāḥik means:

Laughing constantly
Capability for laughter
Only making others laugh
Capacity for speech

Question 21

If “neighing animal” defines horse, with neighing treated as a property, it is:

Complete ḥadd
Complete rasm
Incomplete ḥadd
Incomplete rasm

Question 22

In “rational substance” for human, substance is a:

Proximate genus
Proximate differentia
Property
Remote category/genus

Question 23

Why does “human — animal” fail as a complete ḥadd?

Animals make no sound
The proximate differentia is missing
The term body appears
It includes a property

Question 24

Why is “walking” not equivalent to the textbook’s distinctive property for human?

Only humans walk
Other kinds also walk
It is a proximate differentia
It is the proximate genus

Question 25

Replacing the proximate genus by a remote one, while keeping the differentia, yields:

Incomplete ḥadd
Complete rasm
Incomplete rasm
The same complete ḥadd

Question 26

Keeping the proximate genus but replacing differentia with property changes:

Incomplete to complete ḥadd
Complete ḥadd to complete rasm
Complete rasm to complete ḥadd
Incomplete rasm to incomplete ḥadd

Question 27

Remote genus plus a distinguishing property yields:

Complete ḥadd
Incomplete ḥadd
Complete rasm
Incomplete rasm

Question 28

Remote genus plus proximate differentia yields:

Incomplete ḥadd
Incomplete rasm
Complete ḥadd
Complete rasm

Question 29

The proximate differentia alone is classified as:

Complete rasm
Incomplete ḥadd
Incomplete rasm
Complete ḥadd

Question 30

A distinctive property alone is:

Incomplete rasm
Incomplete ḥadd
Complete ḥadd
Complete rasm

Question 31

What does incomplete mean in rasm nāqiṣ?

Necessarily false
Missing the complete prescribed structure
Meaningless
Misspelled

Question 32

What is a reliable first step in classification?

Count words
Identify the target and role of each component
Look only at the last word
Call every phrase ḥadd

Question 33

What context is important when classifying “rational body”?

Book color
The intended definiendum
Font
Page number

Question 34

Can a distinctive property simply be treated as a proximate differentia?

Yes, always
No: property is non-essential, differentia essential
Only if short
Only in two examples

Question 35

What do rational animal, rational body, and rational alone share?

Property
Proximate differentia
Proximate genus
Common accident

Question 36

What do laughing-capable animal, laughing-capable body and laughing-capable alone share?

Distinctive property
Proximate genus
Proximate differentia
Species

Question 37

What main topic follows the discussion of definitions?

Judgments (taṣdīqāt)
Morphology
Jurisprudence
Arithmetic

Question 38

Muʿarraf is the phrase that provides the definition.

Question 39

In “rational animal,” animal is proximate genus and rational is proximate differentia.

Question 40

Every two-term definition is a complete ḥadd.

Question 41

Ḍāḥik is the proximate differentia of human in the book.

Question 42

An incomplete ḥadd may consist of the proximate differentia alone.

Question 43

Complete rasm uses a proximate genus plus a distinctive property.

Question 44

An incomplete rasm must be false.

Question 45

A genus being proximate or remote is relative to the thing defined.

Question 46

Giving one broad genus always completes a definition.

Question 47

The discussion of explicative definitions belongs to the section on conceptions.

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