174
At least two positions are possible. According to one, NOIR is about assignments of
informational entities to objects: nominal, for example, is a feature of the way
numerals (in Stevens’ lexicon, i.e., “names for classes”, Stevens, 1946: p. 679) are
assigned to individuals with respect to their blood type. This is how Stevens introduced it, thus considering blood type evaluated on a scale that is nominal. According
to another position, NOIR is about the properties themselves: nominal, for example,
is a feature of blood type. This is how, for example, the VIM uses it, thus considering
blood type to be a nominal property. Hence given a Basic Evaluation Equation such as
blood type individual x A in the ABOsystem
[
]=
being nominal is considered to be either
34
• a feature of the evaluation that produces the equation, according to the first position, or
• a feature of the general property that is involved in the equation, according to the
second position.
By interpreting them in a representational context, Michell presents these two positions as being about internal and external representations, respectively (Michell,
1999: pp. 165–166, from which the quotations that follow are taken—for consistency, everywhere the term “attribute” used by Michell has been substituted with
“property”). According to Michell, an internal representation
occurs when the [property] represented, or its putative structure, is logically dependent
upon the numerical assignments made, in the sense that had the numerical assignments not
been made, then either the attribute would not exist or some component of its structure
would be absent.
Thus, it is internal to the evaluation. An external representation is instead
one in which the structure of some [property] of the objects or events is identified independently of any numerical assignments and then, subsequently, numerical assignments are
made to represent that [property]’s structure
where the adjective “external” is explained by Michell as the hypothesis that the
property
exists externally to (or independently of) any numerical assignments, in the sense that even
if the assignments were never made, the [property] would still be there and possess exactly
the same structure.
Thus, it is external to the evaluation. In summary (Giordani & Mari, 2012: p. 446),
• an internal representation is an evaluation that induces a structure, whereas
• an external representation is an evaluation that preserves a structure.
34 We are not concerned here with whether the general property applies to single entities or to pairs,
triples, etc. of them, and therefore whether—in the traditional terminology—it is a property or a
relation (see Sect. 5.2.3).
6 Values, scales, and the existence of properties
At least two positions are possible. According to one, NOIR is about assignments of
informational entities to objects: nominal, for example, is a feature of the way
numerals (in Stevens’ lexicon, i.e., “names for classes”, Stevens, 1946: p. 679) are
assigned to individuals with respect to their blood type. This is how Stevens introduced it, thus considering blood type evaluated on a scale that is nominal. According
to another position, NOIR is about the properties themselves: nominal, for example,
is a feature of blood type. This is how, for example, the VIM uses it, thus considering
blood type to be a nominal property. Hence given a Basic Evaluation Equation such as
blood type individual x A in the ABOsystem
[
]=
being nominal is considered to be either
34
• a feature of the evaluation that produces the equation, according to the first position, or
• a feature of the general property that is involved in the equation, according to the
second position.
By interpreting them in a representational context, Michell presents these two positions as being about internal and external representations, respectively (Michell,
1999: pp. 165–166, from which the quotations that follow are taken—for consistency, everywhere the term “attribute” used by Michell has been substituted with
“property”). According to Michell, an internal representation
occurs when the [property] represented, or its putative structure, is logically dependent
upon the numerical assignments made, in the sense that had the numerical assignments not
been made, then either the attribute would not exist or some component of its structure
would be absent.
Thus, it is internal to the evaluation. An external representation is instead
one in which the structure of some [property] of the objects or events is identified independently of any numerical assignments and then, subsequently, numerical assignments are
made to represent that [property]’s structure
where the adjective “external” is explained by Michell as the hypothesis that the
property
exists externally to (or independently of) any numerical assignments, in the sense that even
if the assignments were never made, the [property] would still be there and possess exactly
the same structure.
Thus, it is external to the evaluation. In summary (Giordani & Mari, 2012: p. 446),
• an internal representation is an evaluation that induces a structure, whereas
• an external representation is an evaluation that preserves a structure.
34 We are not concerned here with whether the general property applies to single entities or to pairs,
triples, etc. of them, and therefore whether—in the traditional terminology—it is a property or a
relation (see Sect. 5.2.3).
6 Values, scales, and the existence of properties