A singular idea is an idea “which is intended to represent one thing alone” and is denoted either by a proper noun, like Alexander the Great, or by a common noun applied to one man, for example, this man or that man.
A universal idea is an idea “which is suitable for representing several things individually” whose sign (which is a common noun) can be predicated distributively of individuals, as man [can be predicated] of Peter, Paul, etc.
Nouns which denote a collection [of things], or one thing which is an aggregate of several things, are not properly predicated of individuals and often denote singular complex ideas. Examples are the city of Rome, Alexander’s army, the human race, the world.
Complex ideas are said to have comprehension, which “is a collection of all the simpler ideas which are combined in the complex,” for example, in animal [are contained the ideas of] body, living, and sentient.
Universal ideas are said to have extension, or quantity, which is “a collection of objects which an idea can represent, or [objects] the word for which is predicable individually.”
From what has been said about abstraction, it will be clear that the greater the extension, the less the comprehension, and vice versa.
CHAPTER 47
A universal idea or predicable word has five species: genus, species, differentia, property, and accident.8 They are defined with regard either to ideas or to terms as follows:
| With respect to ideas | With respect to terms |
| 1. A genus is a universal idea representing an object as a thing, which extends to other universal ideas. | 1. A genus is a [word] predicable of several things which differ in kind (specie) in some respect (in quid) “or as a material part of the essence, as animal of man and brute.” |
| 2. A species is “a universal idea representing a thing, which is subordinate to a more general idea,” or [an idea] which applies only to individual things. | 2. A species is “a [word] predicable of several things which are numerically different in some respect (in quid ),” or as the total essence, as man [is predicable] of Peter and Paul. |
| The highest genus is [the genus] “which does not have a more general genus above it,” for example, being. A subaltern is one “which can be a species with respect to a more general [genus].” | |
| The lowest species is [the species] “which covers individuals alone”; a subaltern species can be a genus. | |
| 3. A differentia is “a universal idea which represents a thing modified by an essential primary attribute,” i.e., [an idea] which divides a genus into species, and combines with a genus to constitute a species. | 3. A differentia is “a [word] predicable of several things that differ in species or number, in respect of some quality (in Quale Quid )” or as a formal part of the essence; for when it is added to a genus it completes the essence of a species and its definition. |
| 4. A property is the “universal idea of a thing modified by an essential secondary attribute,” that is, [an attribute] which is contained in the idea of the thing not formally but as a consequence; for instance, being subject to law is a property of man. | 4. A property is “a [word] predicable of several things in respect of a quality necessarily” (in Quale necessario), that is, [an attribute] which belongs to this species, and only this species, and the whole of this species, at all times, or as bound up with its essence. |
| 5. An accident is “the universal idea of a thing modified by a true/true mode,” that is, [a mode] which may be either present or absent. | 5. An accident is “a [word] predicable of several things in respect of a quality contingently” (in Quale contingenter). |
CHAPTER 5
A genus is said to be a logical whole or universal with respect to its species which are logical parts in the division of it. On the other hand a species is said to be a metaphysical whole, with respect to its genus and its differentia, which are metaphysical parts of its essence, but is said to be a physical whole with respect to its integrating parts. For example, (1) animal is the logical whole with respect to man and the brutes; (2) man is the metaphysical whole, or formal [whole], with respect to that which is animal and rational; (3) man is the physical or integral whole with respect to body and soul. The human body is also the integral whole with respect to head, chest, abdomen, limbs, etc., which are the integrating parts.9
N.B. Abstract, absolute, or denominating names of true modes, as well as abstract ideas themselves, may be either genera or species when they represent objects as things, without any distinct or direct idea of the subject, for instance, justice, virtue, and their opposites; true substances regarded as appendices of other things, and their concrete and connotative names, may be differentiae, properties, or accidents, for example, golden, silvery, clothed, shod.
CHAPTER 6
A logical whole, or the extension of an idea, is expressed by a division, which is “the enumeration of the several things contained in the extension of a common idea or name.” These are its rules:
1. “The parts should be so distinct that no single one contains within its own [extension] the extension or part of the extension of another [part].”
2. “The division should be made into the species immediately below.”
3. “The parts should exhaust the thing divided”; or the division should be adequate.
CHAPTER 7
A metaphysical whole, or the comprehension of a complex idea, is expressed by a definition, which is “a statement which explicates the simpler ideas that are combined in a complex [idea].” There are other definitions which are improper, for instance, nominal [definition], which explicates a word, as coelum (“sky”), which is from [Greek] koilon (“hollow”). There is also accidental definition, which explicates modes, causes [and] effects. For example, man is an animal which is featherless, biped, erect, etc.; this constitutes a description. [And] there is physical definition, which explicates natural parts; for instance, man is an animal consisting of an organic body and a soul endowed with reason.
The rules [of definition] are:
1. “Definitions should be short.”
2. “They should be clear.”
3. “They should be adequate,” so that they may be reciprocating, i.e., so that the definition and the thing defined may be mutually predicated of each other distributively.
4. “Avoid metaphors.”
5. “They should consist of the nearest genus and the proper differentia.”10
Categories or predicaments are “a series of ideas or terms arranged by degrees (gradatim) under the same highest genus.” Different authorities give different categories. For Aristotle there are ten: substance, quantity, quality, relation, action, passion, place, time, position, and state.11 He means that every predication or affirmation may be reduced to one of these. If we explain one, the rest will be understood.
These are the substances:12
Hence also that of which something is affirmed or denied in any category should be called a subject.
CHAPTER 8
A term is “a name which signifies an idea or a thing, and which can be the subject or predicate of a proposition”; hence it is called a predicable (categorema).
Other components of terms are jointly predicable (syncategoremata), such as all, no. Some are mixed, such as always, i.e., in all time; no one, i.e., no man; [he] runs, [he] is running.13
An