145
While such a conceptualization might appear redundant, it is not hard to
show that:
• Properties of objects are not identical to individual properties: properties of
objects are in fact features of objects and as such have a spatiotemporal location
and can be (individual) measurands, and neither individual properties nor general properties share this feature; however, some features, such as being comparable with respect to a given relation, are characteristic of individual properties
and are inherited by properties of objects; for example, we can say that the individual length ℓ 1 is greater than the individual length ℓ 2 if they are identified as the
length of rod a and of rod b, respectively, and rod a has been empirically discovered to be longer than rod b.
• Individual properties are not identical to general properties: individual properties
can be comparable with each other, and general properties do not share this feature; however, some features, such as being a quantitative or a qualitative property and being a physical property or a psychosocial property, are characteristic
of general properties and are inherited by their instances; for example, a given
length is a physical quantity because length is a physical quantity.
This provides a pragmatic justification of the structure illustrated in Fig. 6.1.
2
On this basis, we defer to Sects. 6.5 and 6.6 a more specific analysis about general properties, in particular about their categorization into types, such as nominal
and ordinal. In the sections that follow we continue to develop this framework
grounded on individual properties, by introducing values of properties and first
focusing on values of quantities.
2 A foundational ontology might endeavor to build a framework on properties eventually based on
one entity, from which everything else can be derived (an example of this monism is trope theory;
see Maurin, 2018) or reduced, as nominalism would do by assuming that both individual properties
and general properties are just concepts, and only properties of objects exist outside our minds (see
Sect. 5.3.1). However, this philosophical task has no direct consequences for measurement
science.
Fig. 6.1 Relations between properties of objects, individual properties, and general properties
6.1 Introduction
While such a conceptualization might appear redundant, it is not hard to
show that:
• Properties of objects are not identical to individual properties: properties of
objects are in fact features of objects and as such have a spatiotemporal location
and can be (individual) measurands, and neither individual properties nor general properties share this feature; however, some features, such as being comparable with respect to a given relation, are characteristic of individual properties
and are inherited by properties of objects; for example, we can say that the individual length ℓ 1 is greater than the individual length ℓ 2 if they are identified as the
length of rod a and of rod b, respectively, and rod a has been empirically discovered to be longer than rod b.
• Individual properties are not identical to general properties: individual properties
can be comparable with each other, and general properties do not share this feature; however, some features, such as being a quantitative or a qualitative property and being a physical property or a psychosocial property, are characteristic
of general properties and are inherited by their instances; for example, a given
length is a physical quantity because length is a physical quantity.
This provides a pragmatic justification of the structure illustrated in Fig. 6.1.
2
On this basis, we defer to Sects. 6.5 and 6.6 a more specific analysis about general properties, in particular about their categorization into types, such as nominal
and ordinal. In the sections that follow we continue to develop this framework
grounded on individual properties, by introducing values of properties and first
focusing on values of quantities.
2 A foundational ontology might endeavor to build a framework on properties eventually based on
one entity, from which everything else can be derived (an example of this monism is trope theory;
see Maurin, 2018) or reduced, as nominalism would do by assuming that both individual properties
and general properties are just concepts, and only properties of objects exist outside our minds (see
Sect. 5.3.1). However, this philosophical task has no direct consequences for measurement
science.
Fig. 6.1 Relations between properties of objects, individual properties, and general properties
6.1 Introduction