Measurement Omission

Abstraction near measurement yeilds the following from the Objectivism CD-ROM:

Prof. A: So the Aristotelians thought there really was an attribute of blueness as such—like a kind of little banner sticking up from blue objects saying “blue.” Whereas the Objectivist position is that there is a Conceptual Common Denominator uniting a red and two blues, and that the two blues are close together on the measurement range within that Conceptual Common Denominator, and that all the different shades of blue can be integrated because they fall within that range.

AR: Exactly

If this is the correct interpretation, then I suppose this is why I find her claims so unsatisfying. Why use the phrase “measurement-omission” rather than “abstraction” if all she claims is that mathematics is the science of reasoning about certain features of object(s), while omitting others?

ITOE appendix : “Abstraction as Measurement Omission”

Edit: Just saw Weaver titled his quote as such…

I think I can summarize this succinctly. Kronecker was a jerk, but he was right. Cantor’s theories are interesting, but they aren’t cut out for dealing with things that actually exist.

Measurement may be defined abstractly as: the process of relating an observed value to a known (and commensurable!) value (the unit of value employed as the basis of measurement).

Note that by nature a value MUST be unitized, i.e., it must be a definite definite quantity along a specific spectrum of possible outcomes (thus QM insistence on observables expressed as linear operators, with the eigenvalues determining the spectrum of possible outcomes of measurement).

Note also that the observer’s focus determines the unit of comparison, and one only needs to consider those facts about an entity that are relevant to the given context considered. So, if one is only interested in color of things, then the rest of their properties can be excluded from consideration as irrelevant.

An actual entity has multiple observable properties, each with a specific unit; the nature of the entity can be described as the integrated set of observations of its properties and functions. So, e.g., shape is no problem, it just requires observation of multiple properties to pin down … and one of those properties is the topology of the shape itself (topological forms are the available observables).

So, measurement omission is the basis of conceptualization because it is not the actual value of measurement(s) that determines the entity’s type/class; and emergent or unknown properties are no problem either … at a higher order, the determination of a given entity’s type, in terms of its known properties, does not preclude the discovery of other properties with experience. The type itself is an observable and evolves over time (concepts are contextual). In a sense, relative to the set of all observable properties of an entity, one’s focus on a specific subset of properties involves measurement omission, yes; but it also involves property omission, because one must winnow out irrelevancies even in cases where one knows in principle all the properties of an entity. For example, the fact of a person’s gender is not relevant when considering their character – in the context of assessing character, we not only omit measurements (e.g., of one’s actions), we also ignore properties that are irrelevant.

So, concepts in all their glory come from measurement omission applied to similar entities; but the measurements one focuses on and omits are also a matter of choice, i.e., the observer’s context masks out only the known properties relevant to current consideration.

Finally, notice that the notion of class type in object oriented software languages provides a convenient and accurate means to represent a concept. Conceptual hierarchies can be directly and reliably modeled as object oriented class hierarchies. And, when one decides to add another property to one’s concept of a given class of entities, then one need only add another member variable to the corresponding OOP class type.

Now this is interesting. I’ll be starting a thread on that soon.

Cheers.

  • ico

Note also that the observer’s focus determines the unit of comparison, and one only needs to consider those facts about an entity that are relevant to the given context considered. So, if one is only interested in color of things, then the rest of their properties can be excluded from consideration as irrelevant.

(snip)

So, concepts in all their glory come from measurement omission applied to similar entities; but the measurements one focuses on and omits are also a matter of choice, i.e., the observer’s context masks out only the known properties relevant to current consideration.

I think the measurements ommited can properly be a matter of choice while using a given concept in certain situations, but when forming the concept the rules are more rigid. If measurements are ommited willy nilly in the formation of a given concept epistemological chaos would ensue. “Package deals”, invalid concepts and so on.

Also, there are many situations when using a concept (such as “engaged”) is not proper without refrerence to a specific context. In that case, in order to properly use the concept the measurements ommited are not a matter of arbitrary choice.

Also, there are many situations when using a concept (such as “engaged”) is not proper without refrerence to a specific context. In that case, in order to properly use the concept the measurements ommited are not a matter of arbitrary choice.

A word is not a concept. The same word can be used to reference many different concepts. The context of the sentence determines the concept that is being referenced by the word. But that has no impact on the underlying structure or formation of concepts.

A word is not a concept. The same word can be used to reference many different concepts. The context of the sentence determines the concept that is being referenced by the word. But that has no impact on the underlying structure or formation of concepts.

A word that doesnt represent a concept would be a sound, not a word. I think youre saying the same thing that I did in sentences 2 and 3, I said “using a concept (word) is not proper without referrence to a specific context”. This obviously is not the case with every word, but the example I gave “engage” is a “package deal” in sentences like “after the war is over, the U.S. should remain engaged with middle eastern countries”. Are you saying when using and forming concepts, which particular measurements are ommitted is not important to the structure and formation of the concept? All Im saying is that it is.

I think of ‘measurement’ in this context as the contingent element of a concept as it relates to the retained characteristics of that concept.

So, however a given characteristic can differ, while remaining what is is as per the definition of the concept, is what the measurement captures.

Spatially, ‘measurement’ refers to this element. And spatial concepts are easy to grasp, but not all concepts are spatial, and not all ‘omitted measurements’ are spatial or scalar measurements.

I think the measurements ommited can properly be a matter of choice while using a given concept in certain situations, but when forming the concept the rules are more rigid. If measurements are ommited willy nilly in the formation of a given concept epistemological chaos would ensue. “Package deals”, invalid concepts and so on.

Also, there are many situations when using a concept (such as “engaged”) is not proper without refrerence to a specific context. In that case, in order to properly use the concept the measurements ommited are not a matter of arbitrary choice.

Excellent!

One must distinguish between constructing a concept, and using it (e.g., for the purpose of relating measurements of its properties).

Fully agree: concept formation does not follow rationally from arbitrary focus, nor haphazard measurement omission. That sounds more like an Epicurean recipe for evasion.

My point is that, with rational focus, it is possible to choose which properties are relevant in a given inquiry, which I think you also agree.

Cheers.

  • David