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1. [118] Our aim in this book is to enumerate the things from which proposi- tions are composed and into which they are divided, that is, each one of the parts of the premises used generally in all of the syllogistic disciplines. So we say: Every propo- sition is either categorical or conditional. Every conditional proposition is made up of two categorical propositions connected by a conditional particle. Every categorical proposition is composed of and divided into a predicate and a subject. [119] Every predicate and every subject is either a term indicating a meaning (ma
_{ná) or a meaning} that a given term indicates. Every meaning that a given term indicates is either universal or individual.

2. The universal is that to which two or more things can be similar, while the individual is something for which even among two there can be no shared similarity. Furthermore, the universal is something that can be predicated of more than one, whereas the individual cannot be predicated of more than one.

3. The two parts of a proposition may be both universal, as when we say, “Man is an animal,” and other such propositions that are used in the sciences, in dialectic, in sophistics, and in many of the other disciplines. Its two parts may both be individual, as when we say, “Zayd is the one standing,” or “The one standing is Zayd,” though this [type] is rarely used. A proposition’s subject may be individual and its predicate universal, as when we say, “Zayd is a man”; this is used often in rhetoric and poetry and in the practical disciplines. A proposition’s subject may be universal and its predicate individual or individuals, as when we say, “Man is Zayd” and “Man is Zayd,
_{Amr, and Khalid.” These two are used in analogy and} induction when they are reducible to the syllogism. When the subject is a single individual, it is used in analogy; when the subject is many individuals, it is used in induction.

4. The universal meanings that are treated as parts of the categorical propositions include (a) those that are single to which single terms refer; and (b) those that are combined to which combined terms refer—albeit restrictive and conditional combina- tions, not assertoric ones—as when we say “the white man” and “the rational animal”; for “animal” is restricted by “rational” and conditional upon it, and so too “man” is restricted by and conditional upon “white.” Universal meanings combined in this manner clearly can also be divided into single ones.

5. According to the enumeration of many ancient philosophers, there are fi ve simple universal meanings: genus, species, difference, property, and accident.

6. Genus and species. Universals that are predicated of a single individual can vary generally and specifi cally, like “man” and “animal” predicated of “Zayd.” For “man” is more specifi c than “animal.” Since there are simple universals varying gener- ally and specifi cally, each is a proper response to the question “What is this individ- ual?” Among [these universals] there is one above which there is none more general and one below which there is none more specifi c; those that fall between these two ascend in order from the more specifi c to the more general and so on until they stop at the most general of them. The more general of any two of them is a genus and the more specifi c a species. The more general above which there is none more general is the highest genus, and the more specifi c below which there is none more specifi c is the fi nal species.

7. Each of those that fall [120] in between is at once a genus and a species: a genus in relation to the more specifi c one below it; and a species in relation to the more general one above it. All of them are said to be genera, one below another. For example, the individual thing one is looking at is a palm. We did not know that it is a palm, so we ask, “What is this thing we see?” to which the proper response is, “It is a palm,” and “It is a tree,” and “It is a plant,” and “It is a body.” These responses vary with respect to the general and the specifi c, and whichever two of them you take, the more general is a genus and the more specifi c a species. For example, “plant” is a species and “body” is a genus; so too “tree” is a species and “plant” is a genus; and so too “palm” is a species and “tree” is a genus. The most general of them all is “body,” so let it be the highest genus. The most specifi c of them is “palm,” so let it be the fi nal species. “Tree” and “plant” fall in between “palm” and “body,” and each of them is both a species and a genus. “Tree” is a genus of “palm” and a species of “plant”; and “plant” is a genus of “tree” and a species of “body.” “Tree,” “plant,” and “body” are genera arranged one under the other in descent from the highest genus in order from the more general to the more specifi c, and so on. So the highest genus is a genus that is not a species, being the genus of all the genera under it. The fi nal species is not a genus, being a species of all the species above it. In sum, the genus is the more general and the species the more specifi c of any two universals that serve as a proper response to the question, “What is this individual?”

8. Every universal predicate is a proper response to the question, “What is it?” For it is the predicate for the “What is it?” question. Now, since every genus is more general than the species that is below it, it is predicated of more than a single species. Similarly, every fi nal species is predicated of more than one individual. The individuals whose fi nal species is one and the same are those that differ in number, like Zayd and an individual horse, and an individual ox. Now since every genus is predicated of more than one species and of the individuals of each of [the species], it is predicated of the individuals differing in number in the “What is it?” method. It is certainly not inconceivable that there are many individuals, each one of which is under a fi nal species different from the one that another is under, and every fi nal species of them is under a genus different from the one that another is under, and every genus of them is under another more general genus different from the one that another is under,

until every genus of them in this order will stop at a highest genus different from the one that another ascends to, so that [all of] these are so many highest genera.

9. When there are [multiple] species under one genus and there is no inter- mediate genus between them, that genus is the proximate genus of [121] those species, and those species are cognate species. Every genus above that proximate [genus] is the remote genus of those species. The species that are under differing genera are non- cognate species. The genera that are not one under another are four. They are: the highest genera; the intermediate genera, each one of which is under a different highest genus; the genera that are cognate species; and the intermediate genera that are species under different intermediate genera, all of which ascend ultimately to one highest genus. The question “What is it?” is thus not solely about the individual but also may be about a fi nal species and an intermediate species. So responding with either a proximate or remote genus is like responding to our question, “What is the palm?” with “It is a tree and a plant,” or asking “What is a tree?” and getting in response “It is a plant” or “It is a body.” The same holds for the rest of the species.

10. Difference. The difference is a simple universal that allows one to distinguish each of the cognate species in a substance from the species that shares its genus. For a thing may be distinguished from another thing not in its substance but in one of its characteristics, like distinguishing one garment from another in that one is white and the other is red. A thing may also be distinguished from another thing in its substance, like distinguishing felt from palm fi ber, and distinguishing one garment from another in that one is of linen and the other of cotton or wool. So the simple universal by means of which one distinguishes the substance of one species from another that shares its proximate genus is the difference. It is obvious that when [a species] is distinguished in its substance from its cognate species, it is distinguished from every species other than it. Other names should be used when one species is distinguished from another not in its substance [but by a characteristic].

11. Genus and difference are common in that each one of them indicates the very being and substance of the species. However, while the genus indicates the sub- stance that the species has in common with another or what makes its substance similar to another, the difference indicates the substance by which the species is distinct from another or what makes its substance distinct and separate from another. Or, [expressed differently], the genus indicates each of the species under it [but not] what is unique to each, whereas the difference indicates what is unique to the substance of each one. Thus, when we ask about a given species “What is it?” and we are informed about its genus, we are not satisfi ed without seeking to learn what distinguishes it from the other [species] that share that genus. [We do this] by adding the specifying question “What kind?”1 _{to the genus of that species. We do not think we yet know the species}

1 Here in Arabic, the discussion concerns the particle ayy, which does not have an immediate equivalent in English, and reducing it to the simple question word “Which?” does not seem to satisfy the requirements of logical division being discussed here.

suffi ciently when [122] we know what is common to it and another species, but only if in addition to that we also know what is proper to it alone. For example, we ask, “What is the palm?” and the response is “It is a tree.” We are not satisfi ed without asking “What kind of a tree?,” thereby seeking to learn what distinguishes the palm, in its substance and very being, from the other species common to the genus that encompasses it and others.

12. By way of summary, it is only ever to a universal by which we know the species in a nonspecifi c way that we add the query “What kind?” Sometimes that universal is the most general one to describe that species, like “What kind of a thing is the palm?” or “What kind of a being is the palm?” For “thing” and “being” are the most general things possible for describing an individual or a species. Sometimes [that universal] is the closest genus in proximity; other times it is very close in proximity, for example, “What kind of a body is the palm?” or “What kind of a plant is the palm?” or “What kind of a tree is the palm?” The proper response to these questions is the difference.

13. When the genus connected to the “What kind?” query is near to the species we want to know about, it is then proper to respond with a difference that belongs to that species and that distinguishes it in substance from its cognate species. Usually the proper response to this question in most things is not just the difference but also the genus of that species as restricted by its difference. For example, we ask “What is the palm? and we are told “It is a tree,” and we ask next “What kind of a tree?” and the response is “It is a tree that bears dates.” Or we say, “What kind of a garment is the cloak?” and the response is, “It is a garment made of wool”; so “cloak” is its genus and “made of wool” is its difference, its genus having been restricted by it. So we make the response to the query “What kind?” the genus of that species as restricted by its difference. With that, we deem we have learned a suffi cient and thorough amount about that species in itself, as the genus restricted by the difference is the defi nition of the species about which we asked fi rst “What is it?” and second “What kind?”

14. The fi rst part of the defi nition of every species is its genus and the second part is its difference, which is what completes its defi nition and what constitutes it, since it provides knowledge of it by means of what is proper to it in its substance. The difference is related to the species; so it is said to be a difference belonging to the species that constitutes its defi nition. The difference is also related to the genus of that species; so it is said to be a difference belonging to that genus because it restricts and complements it. The genus is complemented by differences in one of two ways. Either (1) it is restricted by contrary and contradictory differences in a sentence to which the disjunctive particle is added. For instance, we say, “The garment is made either of wool or of linen or of cotton,” and “The body either takes nourishment or does not take nourishment.” This is division of genus by differences. Or (2) it is complemented by a series of differences with neither contradiction nor the disjunctive particle. For instance, we say, “A garment of wool, a garment of cotton, and a garment of linen,” and “A body that takes nourishment, and a body that does not take nourishment.”

This type of complement is the response to the question “What kind?” and by means of it defi nitions of species that are under that genus are acquired.

15. In most cases the genus complemented by the difference [123] has a name that is equivalent to it for the purposes of signifying. They both point to one thing and one meaning, so that thing is a species that has a defi nition and a name. But it is not inconceivable for there to be a genus accompanied by a difference, but there is no name whatsoever in that particular language to serve as its equivalent for signifying, in which case that is a defi nition of the species with no name, for example, “the body that takes nourishment; for that has no name to serve as its equivalent for signifying. So the defi nition of that species serves instead of its name in all places that the name would be used.

16. The very differences by which the genus is divided complete the defi nitions of the species under it. This is why the division of the genus by differences ends ulti- mately at the species that are under it, since once the disjunctive particles are removed, the defi nitions of the species appear. Every intermediate genus contains a difference that constitutes it and another difference that divides it. For example, “animal” is an intermediate genus constituting “sentient,” since it is the last part of its defi nition, because the defi nition of “animal” is “a body that seeks nourishment and is sentient,” and it is divided into “rational” and “nonrational” when the disjunctive particle is added to it. Every difference constituting a given species divides the genus of that species, and whatever divides a given genus constitutes a species under that genus. Now clearly the highest genus cannot have a difference constituting it but only dif- ferences that divide it, while the fi nal species cannot have differences dividing it but only differences that constitute it, and fi nally each one of the intermediary species has one difference that constitutes it and other differences that divide it.

17. Now when the genus combined with the query “What kind” is remote from the species about which we seek information, the proper response should be a differ- ence that constitutes the species closest to that genus, and so is complemented by it and so produces a defi nition of a proximate genus below the fi rst genus to which we had connected the query “What kind?” Then the query should also be added to this second genus, the response then being a difference constituting the species closest to this second genus, thereby also producing a defi nition. If that genus is the same as the species about which we seek information, then we have ended at what we sought. But if that defi nition is more general than the species sought, then that also is one intermediary species closer in proximity to the species sought, and the query “What kind?” is added to it, and the response is a difference complementing that third genus. You continue in this sequence until the combination of the difference now serving as response and all that came before it is equivalent to and coextensive with the species for which information was sought.

18. For example, we ask “What is man?,” and it is said “Man is a certain body”; so we ask “What kind of a body?” to which the proper response is, “He is a body that seeks nourishment.” From that is produced “a body that seeks nourishment.” Now that is a defi nition of a species more proximate to body but still more general

than man; so we ask, “What kind of a body that seeks nourishment?” and the response is [124] “One that is sentient.” So the response produces “He is a body that seeks nourishment and is sentient.” Now this is the defi nition of animal, since it is the same as [saying “animal”], and had we been seeking the meaning of animal, then we would have arrived at our goal and been fi nished with the questioning. However, since animal is more general than man, which is our goal, we need to add again the query “What kind?” and so we say, “What kind of a body that seeks nourishment and is sentient is he?” and the response is, “He is rational.” Now we have “He is a body that seeks nourishment and is sentient and is rational,” which we fi nd coextensive with and the same as “Man.” One arrives at what was sought by following this order and sequence, that is, the sequence proper to the “What kind?” questioner and his respondent.

19. In response to the question “What kind?” we arrive at an intermediary species that has no name, in other words, when we fi nd a genus complemented by a