Tom

Quantity and Cognition

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In Introduction to Objectivist Epistemology, Ayn Rand writes (32-33)

Measurement is the identification of a relationship—a quantitative relationship established by means of a standard that serves as a unit.

Measurement is an identification of a quantitive relationships. Does this mean that of relationships that can be measured, they are always quantitative? Are there relationships that cannot be measured?

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In Introduction to Objectivist Epistemology, Ayn Rand writes (32-33)

Measurement is the identification of a relationship—a quantitative relationship established by means of a standard that serves as a unit.

Measurement is an identification of a quantitive relationships. Does this mean that of relationships that can be measured, they are always quantitative? Are there relationships that cannot be measured?

If a thing exists, it has a nature. If it has a nature, it is measurable.There are measurable things we can't measure.

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Measurement is an identification of a quantitive relationships. Does this mean that of relationships that can be measured, they are always quantitative?

Relationships are always quantitative IF you use "quantitative" in the broadest sense. This would include measurements such as "more than" or "less than" and geometrical and topological relationships such as "to the right of," "over," and "inside."

Are there relationships that cannot be measured?

I can't think of any. Can you?

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Relationships are always quantitative IF you use "quantitative" in the broadest sense. This would include measurements such as "more than" or "less than" and geometrical and topological relationships such as "to the right of," "over," and "inside."

What is the "broadest sens" of the word "quantitative"?

ruveyn

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Relationships are always quantitative IF you use "quantitative" in the broadest sense. This would include measurements such as "more than" or "less than" and geometrical and topological relationships such as "to the right of," "over," and "inside."

What is the "broadest sens" of the word "quantitative"?

What I said. "Quantitative" includes degrees of attributes like more or less and geometrical and topological relationships. Can you give an example of ANY relationship that is NOT quantifiable?

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Measurement is an identification of a quantitive relationships. Does this mean that of relationships that can be measured, they are always quantitative?

Relationships are always quantitative IF you use "quantitative" in the broadest sense. This would include measurements such as "more than" or "less than" and geometrical and topological relationships such as "to the right of," "over," and "inside."

Are there relationships that cannot be measured?

I can't think of any. Can you?

Thanks! That's what I thought she meant. And no, I cannot think of any non-measurable relationship.

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The context there (actually p. 13 in 1st ed., p. 7 in 2nd ed.) is that she is focusing on the meaning and process of measurement as such, where you know a measurable relationship exists in simple examples, not an analysis of the concept 'relationship'. This is in anticipation of using the idea of measurement later in discussing concept formation. That discussion isn't about a theory of abstract concepts of relationship and their varieties. In that statement she is referring to any specific measurement of a particular relationship -- not a concept of a kind of relationship -- specifically in the form of the identification of the unit used as the standard of comparison as a 'unit of measurement', and its specific quantitative comparison with the standard. The first of your questions concerns her context there by implication, but the second does not.

For your first question, are measurable relationships quantitative, her position is that all measurements are quantitative (and therefore all measurements of relationships). Later she elaborates that this may be cardinal or ordinal, i.e., 'teleological' as a degree in a graded relationship, as opposed to the cardinatl that you may think of, for example, as an integer quantity of some number of a physical 'unit'. Only cardinal quantities are employed in the early, more simple examples of perceivable units identified through concepts of a low level of abstraction like length or weight.

For your second question, are all relations measurable, in the ensuing discussion she holds that measurement and units are implicit in all conceptualization and therefore all conceptual knowledge and all conceptual identification, which includes concepts of kinds of relationships. To conceptualize some kind of relationship requires at least implicitly the possibility of measurement. No standard or no quantitative comparison means no measurement and therefore nothing to be conceptually identified as a relationship.

So all relationships conceptually identified as such, i.e., referred to by the concept 'relationship', must be measurable in some way, but this may be implicit when you form the concept: you don't consciously go through the process of measurement omission for every concept you form, especially at the lower levels of abstraction. For example you first grasp the concept of length without explicitly going through the process of comparison with a standard, either ordinal -- or when you become more precise, when you can -- cardinal.

The explicity identification of the process of comparison with a unit, such as measuring length, is more advanced than the concept length, and further advanced when you deal explicitly with the conceptualization at higher level abstractions of a 'relationship' as such, as a kind of association between the attribute length and a unit of length employed as the standard. (You identify particular instances of relationships before you integrate them into the concept of that kind of relationship). For the role of 'units' in the omitted measurement process of conceptualization at that higher level of abstraction see the chapter on abstractions from abstractions, but first you need the understanding of what measurement is and its role in first level concepts.

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