128
all are designated by predicates with either one or two or more arguments, respectively. For example, ordering is a relation between pairs of objects—if a is less than
a′ then order(a, a′) = true (more usually written as a < a′)—and betweenness is a
relation between triples of objects—if a is greater than a′ and less than a″ then
between (a, a′, a″) = true (more usually written as a′ < a < a″). In this sense any
physical quantity that is relative to a reference system is a relation, as is the case,
e.g., of the speed of an object, which is not a property of the object but a relation
between the object and the system in reference to which speed is considered. Hence,
according to this terminology, while has_a_given_length is a property that an object
can have, has_a_given_speed is a relation, e.g., has_a_given_speed(rod a, reference system b).
21
This distinction is not usually maintained in measurement science, in which the
terms “property” and “quantity” are usually applied both to what would be considered properties and relations in formal logic. For a property to change it is then
sufficient that one object, to which the property applies, changes.
22
We accept this terminological custom here, and—consistently with the current
edition of the VIM (JCGM, 2012: 1.1)—use the term “property” for relations as
well.
23
With this convention, the difference between properties in the sense of formal logic and properties in the sense of measurement science can be analyzed.
21 This is what the Galilean relativity principle asserts. According to Einstein’s relativity theory, the
length of a body observed from a frame of reference in motion with respect to the body depends on
the relative velocity of the two systems: in this view length is also a relation. Moreover, even in
classical physics is_1.2345_m_long(a) could be reinterpreted as the relation is_1.2345-fold_
long(a, s) between the object a and any measurement standard s which materializes the metre:
from this perspective, all ratio properties treated in measurement are relations.
22 This avoids the need of specifically dealing with the so-called Cambridge changes, “such as
when I change from having ‘non-brother’ true of me to having ‘brother’ true of me, just when my
mother gives birth to a second son”, the problem being of course that “it might seem faintly paradoxical that there need be no (other) changes in me (height, weight, colouring, memories, character, thoughts) in this circumstance” (Mortensen, 2020: ch. 2). Consider an example closer to our
context, like
is at a distance of
f rom
a
b
_ _ _
_ _ .
_ _
1 2345 m
body ,reference
true
If instead we assumed that the property is
is at a distance of
f rom reference b
a
_ _ _
_ _ .
_ _
_
_
1 2345 m
body
true
then changes of the position of b would need to be considered also as changes of a property of
a, even though a itself did not move.
23 Sometimes the term “attribute” is used to encompass properties and relations. This was the
choice of the second edition of the VIM, which defines <(measurable) quantity> as an “attribute of
a phenomenon, body or substance that may be distinguished qualitatively and determined quantitatively” (ISO et al., 1993: 1.1).
5 What is measured?
all are designated by predicates with either one or two or more arguments, respectively. For example, ordering is a relation between pairs of objects—if a is less than
a′ then order(a, a′) = true (more usually written as a < a′)—and betweenness is a
relation between triples of objects—if a is greater than a′ and less than a″ then
between (a, a′, a″) = true (more usually written as a′ < a < a″). In this sense any
physical quantity that is relative to a reference system is a relation, as is the case,
e.g., of the speed of an object, which is not a property of the object but a relation
between the object and the system in reference to which speed is considered. Hence,
according to this terminology, while has_a_given_length is a property that an object
can have, has_a_given_speed is a relation, e.g., has_a_given_speed(rod a, reference system b).
21
This distinction is not usually maintained in measurement science, in which the
terms “property” and “quantity” are usually applied both to what would be considered properties and relations in formal logic. For a property to change it is then
sufficient that one object, to which the property applies, changes.
22
We accept this terminological custom here, and—consistently with the current
edition of the VIM (JCGM, 2012: 1.1)—use the term “property” for relations as
well.
23
With this convention, the difference between properties in the sense of formal logic and properties in the sense of measurement science can be analyzed.
21 This is what the Galilean relativity principle asserts. According to Einstein’s relativity theory, the
length of a body observed from a frame of reference in motion with respect to the body depends on
the relative velocity of the two systems: in this view length is also a relation. Moreover, even in
classical physics is_1.2345_m_long(a) could be reinterpreted as the relation is_1.2345-fold_
long(a, s) between the object a and any measurement standard s which materializes the metre:
from this perspective, all ratio properties treated in measurement are relations.
22 This avoids the need of specifically dealing with the so-called Cambridge changes, “such as
when I change from having ‘non-brother’ true of me to having ‘brother’ true of me, just when my
mother gives birth to a second son”, the problem being of course that “it might seem faintly paradoxical that there need be no (other) changes in me (height, weight, colouring, memories, character, thoughts) in this circumstance” (Mortensen, 2020: ch. 2). Consider an example closer to our
context, like
is at a distance of
f rom
a
b
_ _ _
_ _ .
_ _
1 2345 m
body ,reference
true
If instead we assumed that the property is
is at a distance of
f rom reference b
a
_ _ _
_ _ .
_ _
_
_
1 2345 m
body
true
then changes of the position of b would need to be considered also as changes of a property of
a, even though a itself did not move.
23 Sometimes the term “attribute” is used to encompass properties and relations. This was the
choice of the second edition of the VIM, which defines <(measurable) quantity> as an “attribute of
a phenomenon, body or substance that may be distinguished qualitatively and determined quantitatively” (ISO et al., 1993: 1.1).
5 What is measured?