A predicate which coincides both in extension and intension with its subject is exactly what is meant by a definition. One which coincides in extension without coinciding in intension, that is, which applies to the same things without expressing the whole meaning, of the subject, is what is known as a Proprium or Peculiar Property.
If, on the other hand, the two terms are not co-extensive, the predicate must either partially coincide in intension with the subject or not. [Footnote: The case could not arise of a predicate which was entirely coincided in intension with a subject with which it was not co-extensive. For, if the extension of the predicate were greater than that of the subject, its intension would be less, and if less, greater, in accordance with the law of inverse variation of the two quantities (§ 166).] This is equivalent to saying that it must either state part of the definition of the subject or not. Now the definition is made up of genus and difference, either of which may form the predicate: but as the two are indistinguishable in relation to a single subject, they are lumped together for the present purpose under the one head, genus. When the predicate, not being co-extensive, is not even partially co-intensive with its subject, it is called an Accident.
§ 340. Proprium, it will be seen, differs from property. A proprium is an attribute which is possessed by all the members of a class, and by them alone, e.g. 'Men are the only religious animals.'
§ 341. Under the head of definition must be included all propositions in which the predicate is a mere synonym of the subject, e.g. 'Naso is Ovid,' 'A Hebrew is a Jew,' 'The skipper is the captain.' In such propositions the predicate coincides in extension with the subject, and may be considered to coincide in intension where the intension of both subject and predicate is at zero, as in the case of two proper names.
§ 342. Designations and descriptions will fall under the head of 'proprium' or peculiar property, e.g. 'Lord Salisbury is the present prime minister of England,' 'Man is a mammal with hands and without hair.' For here, while the terms are coincident in extension, they are far from being so in intension.
§ 343. The term 'genus' must be understood to include not only genus in the accepted sense, but difference and generic property as well.
§ 344. These results may be exhibited in the following scheme—
Predicate
___________________|______________
| |
Coextensive with not
the subject coextensive
________|_________ _____|________
| | | |
Co-intensive not partially not at all
with the subject cointensive cointensive [Greek: sumbubekós]
[Greek: òrismós] [Greek: îdion] [Greek: génos] Accident
______|_____ ______|_____________ |________________
| | | | | | | |
Defini- Synonym Designa- Descrip- Peculiar Genus Differ- Generic
tion tion tion Property ence Property
§ 345. Thus Aristotle's four heads of predicables may be split up, if we please, into nine—
1. Definition \
> [Greek: òrismós].
2. Synonym /