Concepts: Particular and Universal, and Six Cases of Universals

1. From expressions to the concepts they signify

The preceding lesson distinguished simple expressions, complete compounds and incomplete compounds. The question there concerned whether parts of an expression signify parts of its meaning and whether the utterance is complete.

We now turn to the meaning conceived through an expression. Both “human” and “Zayd” can function as simple terms, yet their concepts differ: humanity may be instantiated by numerous individuals, while Zayd names a specified person.

Logic addresses this difference through universality and particularity. The distinction later supports definitions, the five predicables and logical propositions.

2. The meaning of mafhūm

المفهوم أي ما حصل في الذهن قسمان: أحدهما جزئي، والثاني كلي
A concept—what is present to the mind—is of two kinds: particular and universal.

A mafhūm is the meaning grasped by the intellect. Hearing “tree” evokes the concept of a tree; that concept is not identical with seeing a particular tree.

Distinguish three things: the word, which signifies; the concept, which is understood; and the referent or instance, to which the concept applies. Confusing them produces errors in classifying particulars and universals.

3. The source definition of a particular

أما الجزئي: فهو ما يمنع نفس تصوره عن صدقه على كثيرين
A particular is a concept whose very conception prevents its applicability to many individuals.

The phrase “its very conception” is decisive. It does not merely mean that we happen to encounter one instance in the world. Rather, grasping the intended meaning already prevents its simultaneous identification with distinct individuals.

For example, the identity of this specific person, Zayd, cannot in the same respect be the identity of another distinct person, ʿAmr. It is therefore a real particular.

4. Why Zayd and ʿAmr are particulars

The book gives “Zayd” and “ʿAmr” as examples of particular concepts. “Zayd” here means an already identified individual, not merely the sequence of letters in the name.

“Zayd”: one particular person.
“ʿAmr”: another particular person.
“Human”: a nature that can be shared by many individuals.

Two people can both be named Zayd. This does not make them numerically one individual. A shared written or spoken name is different from the specific identity intended whenever the name is used.

5. Demonstrative expressions and particularity

The source also gives “this horse” and “this wall” as particulars.

“Horse” by itself names a general kind and may be predicated of many horses. “This horse,” in a context where the demonstrative identifies its referent, picks out one determinate horse.

“Wall”: a general concept.
“This wall”: the particular wall identified by pointing.

The referent of a demonstrative must be fixed by context. Saying only “this,” with no identifiable target, does not by itself give the hearer a determinate particular.

6. The source definition of a universal

وأما الكلي: فهو ما لا يمنع نفس تصوره عن وقوع الشركة فيه، وعن صدقه على كثيرين
A universal is a concept whose very conception does not exclude sharing in it or predicating it of many individuals.

A universal need not actually possess many existing instances. It suffices that the concept itself does not preclude multiple instantiation. “Human” applies to Zayd, ʿAmr and others, without any one's unique personal identity being part of the nature signified.

For a particular, the meaning itself bars plurality; for a universal, the meaning itself does not.

7. The textbook examples: human and horse

كالإنسان والفرس
Such as human and horse.

Human: Zayd, ʿAmr, Fāṭimah and many other people may instantiate this concept.
Horse: animals differing in color, size and age can all fall under the concept horse.

Universality does not turn all these individuals into one external object. One common meaning is truly predicable of distinct instances, while their individual differences remain.

8. Actual instances are not required

Suppose no member of a certain kind of animal survives. If the nature described could apply to distinct individuals, the absence of current instances does not destroy its universality.

Conversely, “this precisely identified person who stood before me yesterday” remains particular by its referent, whether that person is now alive or dead.

Keep two questions distinct:
1. Can the meaning itself apply to many? This decides universal versus particular.
2. Are any instances of that meaning actually present? This concerns their existence.

9. Why “the concept itself” matters

The qualification “the concept itself” matters because multiplicity may fail for a reason external to the meaning, even when that meaning would not itself prohibit multiple instances.

Observing just one familiar sun in the sky at some historical moment does not prove that the general concept of a sun rules out other such celestial bodies.

By contrast, the identity of one determinate individual excludes a distinct person being numerically that very individual. Thus restricted external existence is not the same as intrinsic particularity.

10. An alternative definition in the text

أما الكلي: فهو ما جوز العقل كثرته من حيث تصوره. وأما الجزئي: فهو ما لا يكون كذلك
A universal is that whose multiplicity the intellect permits in respect of its conception; a particular is not like this.

“In respect of its conception” serves the same purpose as “its very conception” in the first definition.

“Bird”: its concept does not exclude several birds, so it is universal.
“This particular bird”: the identity fixed by the demonstrative cannot be numerically identical with several distinct birds, so it is particular.

11. Many names are not many instances

Repeated use of the same word does not establish universality. One word may be used as a proper name for several different people, yet in each occurrence it can designate one determinate individual.

If three people are called “Zayd,” their common name does not make the identity of one of them a universal.
If “human” applies to the same three people, the human nature is shared and the predication is universal.

The decisive question is whether a concept is predicable of distinct instances, not how often its word is used.

12. The broad division of universals

فصل: الكلي أقسام
Section: universals have several divisions.

The book classifies universals according to whether their referents can exist and, where possible, how many are actually found. The commentary organizes the possibilities into six cases.

The meaning of “universal” does not change across these cases. Universality concerns conceptual predicability; the sixfold classification concerns external existence, impossibility and numbers of instances.

13. Case 1: no external instance can exist

أحدها: ما يمتنع وجود أفراده في الخارج، كاللاشيء، واللامكن، واللاموجود
First are concepts whose instances cannot exist externally, such as “non-thing,” “non-possible” and “non-existent” in the text's terminology.

The discussion concerns general headings for which a genuine external instance is impossible. The mind can discuss such a heading; doing so does not bring a corresponding object into existence.

Important distinction: being intelligible as a topic of thought is different from being instantiated in reality. Absence of external referents does not by itself turn every concept into a particular.

14. Case 2: possible but uninstantiated

وثانيها: ما يمكن أفراده ولم توجد، كالعنقاء وجبل من الياقوت
Second are concepts whose instances could exist but do not actually occur, such as the ʿanqāʾ and a mountain of ruby.

“A mountain of ruby” combines intelligible descriptions; the concept does not immediately entail a logical contradiction preventing any conceivable instance.

The book's ʿanqāʾ example illustrates the distinction between logical possibility and an imagined or unverified external referent; it is not evidence that such an animal actually exists.

15. Case 4: only one possible actual instance

The same passage includes “the Necessary Existent, exalted”. Classical theological arguments hold that the Necessary Existent is uniquely one, so a second is ruled out by an independent metaphysical proof.

The important point is that the impossibility of another instance is established by reasoning outside the bare general form of the concept. This must not be confused with a proper name that simply identifies a particular person.

This is a theological and philosophical illustration whose premises belong to the tradition's metaphysical argument, rather than to the naming of an individual.

16. Case 3: one instance exists, others are conceivable

The book uses “the sun” as an example. Within its historical illustrative framework, observing one sun does not mean that the generic concept automatically rules out a second possible instance.

If “sun” is considered as a kind of luminous celestial body, nothing in the general concept alone creates a contradiction in conceiving several such bodies, even when only one is observed in a given setting.

Criterion: one actual instance, others conceptually possible. This is a logical illustration, not a claim about the number of stars in modern astronomy.

17. Distinguishing the two single-instance cases

Two cases may both exhibit one actual instance, yet differ radically.

Case 3: one exists and an additional instance is ruled out by another argument; the book uses “the Necessary Existent.”
Case 4: one exists and other instances remain conceivable; the book uses “the sun.”

The actual count is one in both, but their modal status differs. Therefore the observed number of instances cannot replace the criterion of universality itself.

18. Case 5: numerous but finite instances

ما وجدت له أفراد كثيرة إما متناهية كالكواكب السيارة
A universal may have many actual instances, yet finitely many, such as planets.

The classical text refers to seven wandering planets according to its historical astronomy. The point is only to illustrate a finite count, not to establish modern astronomical classifications or totals.

In this case many instances belong to a bounded collection. Their being finitely numerous does not prevent “planet” from functioning as a universal concept.

19. Case 6: multiplicity not fixed by a finite bound

أو غير متناهية كأفراد الإنسان والفرس والغنم
Or without a finite limit, as in the individuals of humans, horses and sheep.

The illustrative purpose is to show indefinitely extendable multiplicity for kinds whose concepts are not confined to a pre-set count of specimens. Any new human can be human; any new horse can instantiate horsehood.

This does not assert that an actually infinite number of people or animals exists. The lesson concerns the open applicability of a universal, not an empirical census.

20. Six cases in one comparison

The six cases can be organized by possibility and instantiation:

1. External instances are impossible: “the non-possible.”
2. Instances are possible, but none actually exists: “a ruby mountain.”
3. One exists; another is ruled out by a distinct proof: the Necessary Existent.
4. One exists; another is possible: the historical illustration of the sun.
5. Many exist in a finite set: the older example of the wandering planets.
6. Multiplicity is not fixed by a finite pre-set count: humans, horses and sheep.

The cases distinguish external instantiation and modal status. They do not change what it means for a concept to be universal.

21. Existence in the mind versus outside it

A person may conceive “a mountain of ruby” even without ever encountering such a mountain. Having its meaning in the mind and finding a corresponding thing outside the mind are distinct matters.

Similarly, mentioning an impossible description does not establish an external instance of it. The description can be considered, but existence is a further question requiring evidence.

This matters because universal versus particular is determined by the structure of a meaning, while existence or nonexistence concerns what reality and argument establish.

22. An objection to the definition of universal

On printed page 30 the commentary raises an objection. A vague perception of a distant specific object, or an infant's early undifferentiated recognition, may appear to fit more than one individual.

If any possibility of matching multiple people were sufficient, then an imprecise image of one particular thing would become a universal merely because it is hard to identify its source.

The objection shows why superficial resemblance or ambiguity among individual cases cannot substitute for the technical account of universality.

23. The answer: common applicability versus substitution

أن المراد بالصدق في تعريف الكلي هو الصدق على وجه الاجتماع
The predicability intended in the definition of a universal is applicability through a shared meaning, not mere substitution of one candidate for another.

The concept “human” applies to Zayd and ʿAmr together in the same respect: both are human. One need not withdraw it from Zayd to apply it to ʿAmr.

A vague personal image differs: the observer may take it as Zayd or instead as ʿAmr, but the image's intended identity is not thereby a nature commonly predicable of both. The commentary marks this contrast as collective common applicability versus alternation.

24. Resemblance is not a shared universal nature

Two people may have similar height, clothing and facial features. If someone at a distance confuses them, that is uncertainty of identification, not numerical identity between the two people.

“Is that person Zayd or ʿAmr?”: two alternative possible identifications.
“Zayd and ʿAmr are human”: one human nature is predicated of both.

The first is about which individual has been perceived; the second is about sharing a single universal nature. The definition of universal concerns the second.

25. A further subtlety: the universal is one in thought

One might mistakenly argue that a universal is a single concept in the mind, and therefore must itself be particular. But having one understood meaning is not the same as being applicable to only one external individual.

“Human” is one intelligible meaning and yet is truly predicable of both Zayd and ʿAmr. The identifying concept of Zayd, by contrast, does not apply as that same individual identity to ʿAmr.

Thus the unity of a mental concept does not imply particularity. The criterion is the concept's capacity for common predication.

26. Worked classification of four expressions

1. “Zayd”: particular when it denotes one determinate person; the same identity cannot apply to another person.
2. “Human”: universal, since several individuals may instantiate humanity.
3. “This horse”: particular by demonstrative identification; the general meaning “horse” remains universal.
4. “A mountain of ruby”: even if no such mountain exists, several possible examples would satisfy the description; it is universal.

The classifications depend on individual determination and possible common predication, not the mere number now observed.

27. Consolidation and transition

A mafhūm is a mentally understood meaning. It may be particular or universal.

A particular is a concept whose very meaning excludes predication of many, such as the identity of one designated Zayd.
A universal is one whose meaning does not exclude such predication, such as human or horse.

External instances of universals may be impossible, merely possible, singular or numerous. Universality is not determined by a present census. The commentary's objection further distinguishes ambiguous alternative identifications from true shared predication.

The following section compares two universal concepts through equality, inclusion and disjointness. That is the subject of Level 007.