xxxii
Fig. 3.1 A black box model of the empirical behavior of
a measuring instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Fig. 3.2 A visual metaphor for precision, trueness, and accuracy;
note that precision is independent of the presence
of the bull’s-eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Fig. 3.3 The basic components of measurement uncertainty
as related to the abstract structure of measurement
(in the case of quantities) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Fig. 3.4 The broad context of measurement (in the case of quantities) . . . . . . 61
Fig. 4.1 A comparison between communication/transmission
(black box (a) and open box (b) models) and measurement
(black box (c) and open box (d) models, as elaborated
from Fig. 2.10) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Fig. 4.2 A simple framework for mapping conceptual perspectives
on measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Fig. 4.3 The starting point: the Euclidean position in the framework . . . . . . . . 96
Fig. 4.4 The first transition: the Galilean position in the framework . . . . . . . . 96
Fig. 4.5 The second transition: the representational position
in the framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Fig. 4.6 The possible third transition in the framework . . . . . . . . . . . . . . . . . 100
Fig. 4.7 A “lens” representation of the role of models
in producing measurement results . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Fig. 5.1 Graphical representation of the relations among
object-related entities, such as the mass of some given
object, and value-related entities, such as x kg for
some given positive number x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Fig. 5.2 Graphical representation of the relations among
the four kinds of entities related to properties . . . . . . . . . . . . . . . . . . 122
Fig. 5.3 Graphical representation of the relations between
objects, properties, and their concepts . . . . . . . . . . . . . . . . . . . . . . . . 124
Fig. 5.4 The semiotic triangle (as in Fig. 2.1) applied to
properties in the sense of formal logic . . . . . . . . . . . . . . . . . . . . . . . . 126
Fig. 6.1 Relations between properties of objects, individual
properties, and general properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Fig. 6.2 Constructing values of quantities: first step
(quantity-related comparison) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Fig. 6.3 Constructing values of quantities: second step
(quantity- related concatenation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Fig. 6.4 Constructing values of quantities: third step
(quantity-related comparison with an object calibrated
with respect to a reference quantity) . . . . . . . . . . . . . . . . . . . . . . . . . 153
Fig. 6.5 The comparison of the length L[b] with the lengths marked
on the rod a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
List of Figures
Fig. 3.1 A black box model of the empirical behavior of
a measuring instrument . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Fig. 3.2 A visual metaphor for precision, trueness, and accuracy;
note that precision is independent of the presence
of the bull’s-eye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Fig. 3.3 The basic components of measurement uncertainty
as related to the abstract structure of measurement
(in the case of quantities) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Fig. 3.4 The broad context of measurement (in the case of quantities) . . . . . . 61
Fig. 4.1 A comparison between communication/transmission
(black box (a) and open box (b) models) and measurement
(black box (c) and open box (d) models, as elaborated
from Fig. 2.10) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Fig. 4.2 A simple framework for mapping conceptual perspectives
on measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Fig. 4.3 The starting point: the Euclidean position in the framework . . . . . . . . 96
Fig. 4.4 The first transition: the Galilean position in the framework . . . . . . . . 96
Fig. 4.5 The second transition: the representational position
in the framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Fig. 4.6 The possible third transition in the framework . . . . . . . . . . . . . . . . . 100
Fig. 4.7 A “lens” representation of the role of models
in producing measurement results . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Fig. 5.1 Graphical representation of the relations among
object-related entities, such as the mass of some given
object, and value-related entities, such as x kg for
some given positive number x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Fig. 5.2 Graphical representation of the relations among
the four kinds of entities related to properties . . . . . . . . . . . . . . . . . . 122
Fig. 5.3 Graphical representation of the relations between
objects, properties, and their concepts . . . . . . . . . . . . . . . . . . . . . . . . 124
Fig. 5.4 The semiotic triangle (as in Fig. 2.1) applied to
properties in the sense of formal logic . . . . . . . . . . . . . . . . . . . . . . . . 126
Fig. 6.1 Relations between properties of objects, individual
properties, and general properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Fig. 6.2 Constructing values of quantities: first step
(quantity-related comparison) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
Fig. 6.3 Constructing values of quantities: second step
(quantity- related concatenation) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Fig. 6.4 Constructing values of quantities: third step
(quantity-related comparison with an object calibrated
with respect to a reference quantity) . . . . . . . . . . . . . . . . . . . . . . . . . 153
Fig. 6.5 The comparison of the length L[b] with the lengths marked
on the rod a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
List of Figures