127
There is an ambiguity about the very concept that an object does not have a property. For example, if we consider now the object water a″ = the water in a given
glass, should we simply accept that
is longer than one metre water a
_
_
_
_
cc
false
despite its obvious difference with the previous case? Hence the problem arises of
maintaining a distinction between the case of objects that do not have a property P
#
but could have it and the case of objects that even in principle cannot have a property P
#
. This is based on the idea that only in the first case can P
#
be experimentally
assessed on the object, and thus that the second case would be better reported as
is longer than one metre water a
_
_
_
_
cc
undefined
We can account for this difference by restricting the application of each property P
#
to a given set of objects, called the domain of P
#
. Hence the object screw a′ belongs
to the domain of the property is_longer_than_one_metre, and does not have the
property, whereas the object water a″ does not belong to the domain of the property,
because trying to assess whether some amount of water in a glass is longer than one
meter is meaningless. The distinction between physical properties and psychosocial
properties is then usually and first of all a distinction of domain: a rod has no reading comprehension ability (the domain of reading comprehension ability does not
include rods), and a company has no length (the domain of length does not include
companies). In summary, for each property P
#
the set of objects is split into three
subsets: the subset of objects that actually have P
#
, the subset of objects that may
have P
#
but do not actually have it, and the subset of objects that cannot have P
#
. The
identification of the domain of a property, i.e., the union of the first two subsets, can
be considered an essential component of knowledge of that property.
20
5.2.3 Properties and relations
In the philosophical tradition, and again in formal logic in particular, a distinction is
also maintained between properties and relations, where the former are features of
(i.e., apply to) single objects and the latter are features of two or more objects, and
20 If the position is assumed that every predicate designates a property (in the sense of formal
logic), things can become tricky. Consider, e.g., the predicate “is a length”: if is_a_length(a) = true,
then it is because a is a property, and it is in fact a length. The domain of is_a_length is then a set
of properties—so that is_a_length(a given rod) is undefined, not false—and is_a_length is a higher
order property, i.e., a property of properties. It is doubtful that such kinds of properties can be
assessed via empirical interactions (on the other hand, is_a_quantity is an example of a secondorder property, which instead admits an empirical validation—see the related discussion in Sect.
6.3.2).
5.2 Some clarifications about properties
There is an ambiguity about the very concept that an object does not have a property. For example, if we consider now the object water a″ = the water in a given
glass, should we simply accept that
is longer than one metre water a
_
_
_
_
cc
false
despite its obvious difference with the previous case? Hence the problem arises of
maintaining a distinction between the case of objects that do not have a property P
#
but could have it and the case of objects that even in principle cannot have a property P
#
. This is based on the idea that only in the first case can P
#
be experimentally
assessed on the object, and thus that the second case would be better reported as
is longer than one metre water a
_
_
_
_
cc
undefined
We can account for this difference by restricting the application of each property P
#
to a given set of objects, called the domain of P
#
. Hence the object screw a′ belongs
to the domain of the property is_longer_than_one_metre, and does not have the
property, whereas the object water a″ does not belong to the domain of the property,
because trying to assess whether some amount of water in a glass is longer than one
meter is meaningless. The distinction between physical properties and psychosocial
properties is then usually and first of all a distinction of domain: a rod has no reading comprehension ability (the domain of reading comprehension ability does not
include rods), and a company has no length (the domain of length does not include
companies). In summary, for each property P
#
the set of objects is split into three
subsets: the subset of objects that actually have P
#
, the subset of objects that may
have P
#
but do not actually have it, and the subset of objects that cannot have P
#
. The
identification of the domain of a property, i.e., the union of the first two subsets, can
be considered an essential component of knowledge of that property.
20
5.2.3 Properties and relations
In the philosophical tradition, and again in formal logic in particular, a distinction is
also maintained between properties and relations, where the former are features of
(i.e., apply to) single objects and the latter are features of two or more objects, and
20 If the position is assumed that every predicate designates a property (in the sense of formal
logic), things can become tricky. Consider, e.g., the predicate “is a length”: if is_a_length(a) = true,
then it is because a is a property, and it is in fact a length. The domain of is_a_length is then a set
of properties—so that is_a_length(a given rod) is undefined, not false—and is_a_length is a higher
order property, i.e., a property of properties. It is doubtful that such kinds of properties can be
assessed via empirical interactions (on the other hand, is_a_quantity is an example of a secondorder property, which instead admits an empirical validation—see the related discussion in Sect.
6.3.2).
5.2 Some clarifications about properties