individual, Englishman is the species, and Man the genus. Taking a wider reach of relations Man may be taken as the species and animal as the genus; in which case, according to the language of the logicians, Englishman is the subaltern species and mammal the proximum genus. In the scale of generalisation the widest in extension is the summum genus; the lowest or narrowest, the infima species; neither of them is absolutely fixed, but both depend upon the extent of the scales. If all things in the universe be taken, still the infima species cannot be determined with rigorous certainty, though being may be regarded as the summum genus. The intension of the summum genus is at a minimum; that of the infima species is at a maximum. Any group of things may be called a genus if it be made up of two or more species. A species is any class which is regarded as forming part of a next larger class. A class may be both genus and species according to its relations. The relations of concepts in a series of extension is also expressed in a different set of terms, as follows: One concept is said to be subordinate to another (which is called its superordinate) when the former is included. within the extension of the latter: two or more concepts are coördinate when each excludes the other from its extension, but both go together to make up the extension of a third to which they are co-subordinate. One concept is said to be co-extensive with another when each has the same number of subordinate concepts with the other. Concepts intersect each other when their spheres of extension intersect, and exclude each other when no part of the one coincides with any part of the other.

§ 6. Classifications in similar manner are made of the attributes which constitute the intension of a general notion. Concepts may be subordinate and superordinate in intension; they may be coördinate, exclusive or intersecting. The remaining three of the five predicables (genus, species, differentia, proprium, accidens) ground their differences upon the intension of concepts. Those attributes which, taken together and added to the intension of the genus form the intension of the species, are termed the differentia. If the concept man includes all that is included in animal and rational besides, the latter is the differentia. Again, those attributes which are common to the whole class, but not necessary to distinguish that class from others, are embraced under the name proprium. That three internal angles

of a triangle. Still again, those attributes which are entirely accidental, which belong to a class but which may, or may not, belong without affecting the other qualities, are characterised by the name accidens. The size of a house is an accident; so is the colour of a horse or dog. Separable accidents are those which are sometimes actually found absent from a class; sitting is a separable accident of the class man; Virgil resides in Rome, states a fact which was a separable accident of Virgil. Virgil was born in Mantua, expresses an inseparable accident of Virgil. Inseparable accidents are those which never are found absent, though, so far as we can judge, they might be, or might have been absent, without altering the class. It may be remarked that the terms genus and species apply equally to divisions in intension. The genus, species, and differentia were considered by the Aristotelian logicians to be of the essence of the subject.

§ 7. A distinction is sometimes drawn which applies to concepts (and which has been extended also to percepts) between First and Second Intentions. A concept which embraces directly particulars of presentative experience, as man, horse, ship, tree, is said to be of the first intention; a concept which by a higher generalisation has first intentions for its proximate particulars and views these intentions in relation to each other, is of the second intention, as genus, species, accident. The distinction has been thus expressed: first intentions are objects in relation to consciousness alone, second intentions are objects in relation to other objects in consciousness.

§ 8. A natural distinction seems to run through concepts, between those which are marked by adjectives generally and those marked by substantives. The concept represented by man is a concept in which the attention is more particularly called to objects in extension, while the attributes connoted by the name are less. prominently before the mind. On the contrary, when the name white is used a concept is evoked in which the intension is the more conspicuous. Of course white has no meaning except with reference to some object, but the object (in extension) is of less moment than the attribute (object in intension). Concepts of the former character may be called Concrete Concepts; those of the latter Abstract Concepts. Examples of the former may be found in any series of concepts in the order of extension. All those given in the series in § 5 are of this class; the latter division is

individual, Englishman is the species, and Man the genus. Taking a wider reach of relations Man may be taken as the species and animal as the genus; in which case, according to the language of the logicians, Englishman is the subaltern species and mammal the proximum genus. In the scale of generalisation the widest in extension is the summum genus; the lowest or narrowest, the infima species; neither of them is absolutely fixed, but both depend upon the extent of the scales. If all things in the universe be taken, still the infima species cannot be determined with rigorous certainty, though being may be regarded as the summum genus. The intension of the summum genus is at a minimum; that of the infima species is at a maximum. Any group of things may be called a genus if it be made up of two or more species. A species is any class which is regarded as forming part of a next larger class. A class may be both genus and species according to its relations. The relations of concepts in a series of extension is also expressed in a different set of terms, as follows: One concept is said to be subordinate to another (which is called its superordinate) when the former is included within the extension of the latter: two or more concepts are coördinate when each excludes the other from its extension, but both go together to make up the extension of a third to which they are co-subordinate. One concept is said to be co-extensive with another when each has the same number of subordinate concepts with the other. Concepts intersect each other when their spheres of extension intersect, and exclude each other when no part of the one coincides with any part of the other.

§ 6. Classifications in similar manner are made of the attributes which constitute the intension of a general notion. Concepts may be subordinate and superordinate in intension; they may be coördinate, exclusive or intersecting. The remaining three of the five predicables (genus, species, differentia, proprium, accidens) ground their differences upon the intension of concepts. Those attributes which, taken together and added to the intension of the genus form the intension of the species, are termed the differentia. If the concept man includes all that is included in animal and rational besides, the latter is the differentia. Again, those attributes which are common to the whole class, but not necessary to distinguish that class from others, are embraced under the name proprium. That three internal angles

of a triangle. Still again, those attributes which are entirely accidental, which belong to a class but which may, or may not, belong without affecting the other qualities, are characterised by the name accidens. The size of a house is an accident; so is the colour of a horse or dog. Separable accidents are those which are sometimes actually found absent from a class; sitting is a separable accident of the class man; Virgil resides in Rome, states a fact which was a separable accident of Virgil. Virgil was born in Mantua, expresses an inseparable accident of Virgil. Inseparable accidents are those which never are found absent, though, so far as we can judge, they might be, or might have been absent, without altering the class. It may be remarked that the terms genus and species apply equally to divisions in intension. The genus, species, and differentia were considered by the Aristotelian logicians to be of the essence of the subject.

§ 7. A distinction is sometimes drawn which applies to concepts (and which has been extended also to percepts) between First and Second Intentions. A concept which embraces directly particulars of presentative experience, as man, horse, ship, tree, is said to be of the first intention; a concept which by a higher generalisation has first intentions for its proximate particulars and views these intentions in relation to each other, is of the second intention, as genus, species, accident. The distinction has been thus expressed: first intentions are objects in relation to consciousness alone, second intentions are objects in relation to other objects in consciousness.

§ 8. A natural distinction seems to run through concepts, between those which are marked by adjectives generally and those marked by substantives. The concept represented by man is a concept in which the attention is more particularly called to objects in extension, while the attributes connoted by the name are less. prominently before the mind. On the contrary, when the name white is used a concept is evoked in which the intension is the more conspicuous. Of course white has no meaning except with reference to some object, but the object (in extension) is of less moment than the attribute (object in intension). Concepts of the former character may be called Concrete Concepts; those of the latter Abstract Concepts. Examples of the former may be found in any series of concepts in the order of extension. All those given in the series in § 5 are of this class; the latter division is

The relation which the two bear to each other may be exhibited in the following table :

Under the concepts man, house, cloud, cloth, we have ranged a vast number of particulars in extension represented by the perpendicular lines. Some of the objects under man agree with certain objects under house, cloud, and cloth in the particular which we term whiteness; their agreement is marked by a cross division. denominated that of white objects; so also are formed the succeeding cross classes, beautiful, dark, etc., indefinitely. The extension of the concept white comprises all white objects, as cloth, cloud, house, man, and so forth; its intension is the attribute whiteness. It will be noticed that abstract concepts are based on single points of community, that is to say, the intension is always taken as one. The intension of magnificent is expressed by magnificence, which is regarded as a single attribute, although it may be analysed and separated into various other attributes, as largeness, beauty, grandeur, sublimity, which enter into it and make up more or less completely its constitution. The concept virtuous has virtue for its intension, which is separable into justice, temperance, honesty, chastity, fortitude, and many others, but is nevertheless taken as a whole and thus regarded as singular.

§ 9. Differences are observable in concrete concepts according as they are composed of individuals which are items of presentative knowledge or of individuals which in their unity are representative; in other words, according as their original proximate components are external realities or unrealities. The concept of a horse in this particular differs from that of a hippogriff; that of a maiden from that of a mermaid. This is a distinction applicable only to the extension of concepts, for no attributes have corresponding external realities. Abstract concepts may include in their extension both real and fictitious particulars; dark-coloured might apply equally to a horse and a hippogriff; so that abstract concepts could not properly be made the subject of a division of the character we are now considering. Some abstract concepts, how