131
5.2.5 Context dependence of properties
Our analysis of properties and objects is grounded on the basic assumption that
objects can persist in space and time even if one or more of their properties change.
26
In particular, by indexing properties of objects by time instant (so that, for example,
long[a, t] is the property designated by the functor “long” that the object a has at
time instant t), a property-related comparability criterion is given such that, for distinguishable time instants t and t′, it may happen that
long a t long a t
,
,
> @|
> @
c
heavy a t
heavy a t
,
,
> @|
> @
c
/
where ≈ denotes indistinguishability with respect to the given criterion:
27,28
it is a
situation in which the object a has maintained its individuality from t to t′ because
26 For example, on the one hand, at least in the broadly Western tradition, each of us admits our own
persistence in time as individuals even though we change, say, our height and weight and, less trivially, our cognitive abilities. On the other hand, an object can change to another one if one or more of
its properties change, as in the case of an informous amount of clay that is modeled and finally
becomes a jar. An extreme case of the dilemma of the conditions of object persistence is known since
the classical world as the Theseus paradox (see Korman, 2016: 2.4): Does a ship remain the same
even if, one by one, all its wooden boards are substituted? And therefore, is an object characterized
by the matter of which it is constituted, or by its shape? The assumption of some basic persistence is
intrinsic to our concept of object. Even just imagining how to avoid it is challenging. In one of his
tales, “Funes el memorioso” (“Funes the Memorious”), Jorge Luis Borges (1944) tried imagining
what it would be like to avoid it, by telling of an individual of prodigious memory: “In the seventeenth century, Locke postulated (and condemned) an impossible language in which each individual
thing—every stone, every bird, every branch—would have its own name; Funes once contemplated
a similar language, but discarded the idea as too general, too ambiguous. The truth was, Funes
remembered not only every leaf of every tree in every patch of forest, but every time he had perceived
or imagined that leaf.” Compare this with: “All is impermanent, because all is in a state of perpetual
change. A thing does not remain the same during two consecutive ksanas (the ksana being the shortest period of time in Buddhism). It is because things transform themselves ceaselessly that they
cannot maintain their identity, even during two consecutive ksanas” (Nhat Hanh, 1974: p. 35).
27 By acknowledging that time instant is also a property (of the reference system shared by the
considered objects), the condition that t and t′ are distinguishable time instants should be written
as t ≉ t′, not t ≠ t′, thus emphasizing that two time instants could be indistinguishable (because,
e.g., they are within 1 ns of one another and the quality of the available instrumentation is not able
to detect this difference) even though they are not necessarily exactly the same.
28 A relation such that object a at time instant t and object a′ at time instant t′ are indistinguishable
in their being long may be differently interpreted. If objects are considered to be entities with time
instances, then the relation could be written as long[a(t)] ≈ long[a′(t′)] (see Mortensen, 2020: ch.
5). By focusing even more explicitly on objects and considering to be long as a feature of the way
objects are compared, the relation could be written instead as a(t) ≈ long[a′(t′)]. The focus in measurement science on properties—what is measured is the property of an object, not an object per
se—justifies our choice of adopting the form long[a] ≈ long[a′], and possibly its time explicit version long[a, t] ≈ long[a′, t′] whenever appropriate. The alternative position of focusing on objects
is taken in particular in the representational theories of measurement, which usually develop their
formalization on empirical relations among objects; see, e.g., how the concept is introduced in Krantz et al. (1971: p. 8).
5.2 Some clarifications about properties
5.2.5 Context dependence of properties
Our analysis of properties and objects is grounded on the basic assumption that
objects can persist in space and time even if one or more of their properties change.
26
In particular, by indexing properties of objects by time instant (so that, for example,
long[a, t] is the property designated by the functor “long” that the object a has at
time instant t), a property-related comparability criterion is given such that, for distinguishable time instants t and t′, it may happen that
long a t long a t
,
,
> @|
> @
c
heavy a t
heavy a t
,
,
> @|
> @
c
/
where ≈ denotes indistinguishability with respect to the given criterion:
27,28
it is a
situation in which the object a has maintained its individuality from t to t′ because
26 For example, on the one hand, at least in the broadly Western tradition, each of us admits our own
persistence in time as individuals even though we change, say, our height and weight and, less trivially, our cognitive abilities. On the other hand, an object can change to another one if one or more of
its properties change, as in the case of an informous amount of clay that is modeled and finally
becomes a jar. An extreme case of the dilemma of the conditions of object persistence is known since
the classical world as the Theseus paradox (see Korman, 2016: 2.4): Does a ship remain the same
even if, one by one, all its wooden boards are substituted? And therefore, is an object characterized
by the matter of which it is constituted, or by its shape? The assumption of some basic persistence is
intrinsic to our concept of object. Even just imagining how to avoid it is challenging. In one of his
tales, “Funes el memorioso” (“Funes the Memorious”), Jorge Luis Borges (1944) tried imagining
what it would be like to avoid it, by telling of an individual of prodigious memory: “In the seventeenth century, Locke postulated (and condemned) an impossible language in which each individual
thing—every stone, every bird, every branch—would have its own name; Funes once contemplated
a similar language, but discarded the idea as too general, too ambiguous. The truth was, Funes
remembered not only every leaf of every tree in every patch of forest, but every time he had perceived
or imagined that leaf.” Compare this with: “All is impermanent, because all is in a state of perpetual
change. A thing does not remain the same during two consecutive ksanas (the ksana being the shortest period of time in Buddhism). It is because things transform themselves ceaselessly that they
cannot maintain their identity, even during two consecutive ksanas” (Nhat Hanh, 1974: p. 35).
27 By acknowledging that time instant is also a property (of the reference system shared by the
considered objects), the condition that t and t′ are distinguishable time instants should be written
as t ≉ t′, not t ≠ t′, thus emphasizing that two time instants could be indistinguishable (because,
e.g., they are within 1 ns of one another and the quality of the available instrumentation is not able
to detect this difference) even though they are not necessarily exactly the same.
28 A relation such that object a at time instant t and object a′ at time instant t′ are indistinguishable
in their being long may be differently interpreted. If objects are considered to be entities with time
instances, then the relation could be written as long[a(t)] ≈ long[a′(t′)] (see Mortensen, 2020: ch.
5). By focusing even more explicitly on objects and considering to be long as a feature of the way
objects are compared, the relation could be written instead as a(t) ≈ long[a′(t′)]. The focus in measurement science on properties—what is measured is the property of an object, not an object per
se—justifies our choice of adopting the form long[a] ≈ long[a′], and possibly its time explicit version long[a, t] ≈ long[a′, t′] whenever appropriate. The alternative position of focusing on objects
is taken in particular in the representational theories of measurement, which usually develop their
formalization on empirical relations among objects; see, e.g., how the concept
5.2 Some clarifications about properties