144
or also
a
is an
property of an object
individual property
so that, for example, there is a length that a given rod has, i.e., the length of that rod
(the property of an object) is that length (an individual property), and there is a reading comprehension ability that a given individual has, i.e., the reading comprehension ability of that individual (the property of an object) is that reading comprehension
ability (an individual property).
Each property of an object identifies an individual property: individual properties
can be handled mathematically, for example by checking which of two lengths is
greater, whereas relations between properties of objects must be investigated empirically. In a complementary way, when a property of an object appears in a formal
relation, such as a mathematical equation or a logical inference, it is the corresponding individual property to which one actually refers. This applies in particular to the
relation of indistinguishability of properties of objects: as already pointed out, the
observation that two properties of objects, P[a i ] and P[a j ], are indistinguishable,
P[a i ] ≈ P[a j ], is interpreted by assuming that P[a i ] and P[a j ] either identify the same
individual property or identify distinct but empirically indistinguishable individual
properties. Since in general it is not possible to ascertain which of these situations
is true, the customary notation P[a i ] = P[a j ] is just a convenient shorthand, acceptable whenever the relation is transitive. (See Sect. 5.2.6 on the implications of this
assumption.)
As discussed in Sect. 2.2.3, comparable individual properties are said to be of the
same kind (JCGM, 2012: 1.2). Kinds of properties are abstract entities that are reified by assuming the existence of corresponding general properties, so that the
adjectives “long”, “heavy”, etc. are replaced by the nouns “length”, “weight”, etc.,
and a relation such as
long a long b
[ ] ≈
[ ]
as in Sect. 5.2.6 is more customarily written as
length a length b
[ ] ≈
[ ]
Each individual property is then an instance of a general property, and two individual properties are comparable only if they are instances of the same general property. Again, the examples are obvious: any given length is an instance of length, any
given reading comprehension ability is an instance of reading comprehension ability, and so on. A second relation of the framework is then
an
is an instance of a
individual property
g eneral property
These relations are depicted in Fig. 6.1.
6 Values, scales, and the existence of properties
or also
a
is an
property of an object
individual property
so that, for example, there is a length that a given rod has, i.e., the length of that rod
(the property of an object) is that length (an individual property), and there is a reading comprehension ability that a given individual has, i.e., the reading comprehension ability of that individual (the property of an object) is that reading comprehension
ability (an individual property).
Each property of an object identifies an individual property: individual properties
can be handled mathematically, for example by checking which of two lengths is
greater, whereas relations between properties of objects must be investigated empirically. In a complementary way, when a property of an object appears in a formal
relation, such as a mathematical equation or a logical inference, it is the corresponding individual property to which one actually refers. This applies in particular to the
relation of indistinguishability of properties of objects: as already pointed out, the
observation that two properties of objects, P[a i ] and P[a j ], are indistinguishable,
P[a i ] ≈ P[a j ], is interpreted by assuming that P[a i ] and P[a j ] either identify the same
individual property or identify distinct but empirically indistinguishable individual
properties. Since in general it is not possible to ascertain which of these situations
is true, the customary notation P[a i ] = P[a j ] is just a convenient shorthand, acceptable whenever the relation is transitive. (See Sect. 5.2.6 on the implications of this
assumption.)
As discussed in Sect. 2.2.3, comparable individual properties are said to be of the
same kind (JCGM, 2012: 1.2). Kinds of properties are abstract entities that are reified by assuming the existence of corresponding general properties, so that the
adjectives “long”, “heavy”, etc. are replaced by the nouns “length”, “weight”, etc.,
and a relation such as
long a long b
[ ] ≈
[ ]
as in Sect. 5.2.6 is more customarily written as
length a length b
[ ] ≈
[ ]
Each individual property is then an instance of a general property, and two individual properties are comparable only if they are instances of the same general property. Again, the examples are obvious: any given length is an instance of length, any
given reading comprehension ability is an instance of reading comprehension ability, and so on. A second relation of the framework is then
an
is an instance of a
individual property
g eneral property
These relations are depicted in Fig. 6.1.
6 Values, scales, and the existence of properties