122
While all this could well be taken for granted, the structure of the relations among
these entities is important for a measurement-oriented ontology and epistemology
of properties. Starting from the uncontroversial assumption that individual properties (ii)
13
are instances of general properties (i) (so that for example, any given mass
is an instance of mass, i.e., more customarily and trivially, any given mass is a
mass), we acknowledge that individual properties are entities which need to be
somehow identified in order to be handled, and in particular to be compared with
each other. On this basis we develop here two basic arguments.
First, individual properties (ii) are identified as properties of objects (iii) or as
values of properties (iv), so that for example a given mass can be identified as the
mass of a given object a or as x kg for a given nonnegative number x, as it is explicit
in the case of the Basic Evaluation Equation. In fact, properties of objects and values of properties are complementary modes of identification of instances of general
properties: by identifying a mass as the mass of a given object a, the reference is to
the object a that bears that mass; if a mass is instead identified as x kg for a given
nonnegative number x, the reference is to an element of the structure that, via the
choice of a mass unit and the construction of its multiples, includes all masses.
14
Figure 5.2 summarizes the relations among these kinds of entities, and highlights
the pivotal role of individual properties in the conceptual framework we are devel13 The label “(ii)” refers to the four assertions immediately above, and similarly for the labels
below.
14 It is not controversial that individual properties are instances of general properties, but there is a
delicate ontological issue about how properties of objects and values of properties are related to
individual properties (see also the discussion in Sect. 5.3.1). With the aim of remaining as independent as possible of ontological presuppositions, we only assume that properties of objects and
values of properties identify individual properties.
Fig. 5.2 Graphical representation of the relations among the four kinds of entities related to
properties
5 What is measured?
While all this could well be taken for granted, the structure of the relations among
these entities is important for a measurement-oriented ontology and epistemology
of properties. Starting from the uncontroversial assumption that individual properties (ii)
13
are instances of general properties (i) (so that for example, any given mass
is an instance of mass, i.e., more customarily and trivially, any given mass is a
mass), we acknowledge that individual properties are entities which need to be
somehow identified in order to be handled, and in particular to be compared with
each other. On this basis we develop here two basic arguments.
First, individual properties (ii) are identified as properties of objects (iii) or as
values of properties (iv), so that for example a given mass can be identified as the
mass of a given object a or as x kg for a given nonnegative number x, as it is explicit
in the case of the Basic Evaluation Equation. In fact, properties of objects and values of properties are complementary modes of identification of instances of general
properties: by identifying a mass as the mass of a given object a, the reference is to
the object a that bears that mass; if a mass is instead identified as x kg for a given
nonnegative number x, the reference is to an element of the structure that, via the
choice of a mass unit and the construction of its multiples, includes all masses.
14
Figure 5.2 summarizes the relations among these kinds of entities, and highlights
the pivotal role of individual properties in the conceptual framework we are devel13 The label “(ii)” refers to the four assertions immediately above, and similarly for the labels
below.
14 It is not controversial that individual properties are instances of general properties, but there is a
delicate ontological issue about how properties of objects and values of properties are related to
individual properties (see also the discussion in Sect. 5.3.1). With the aim of remaining as independent as possible of ontological presuppositions, we only assume that properties of objects and
values of properties identify individual properties.
Fig. 5.2 Graphical representation of the relations among the four kinds of entities related to
properties
5 What is measured?