Measurement omission

Measurement omission is the mental operation by which a group of similar units is integrated into a concept: the distinguishing characteristic is retained and its particular measurements are dropped, on the principle that they must exist in some quantity but may exist in any. Objectivism treats it as the specific mechanism that makes an open-ended abstraction possible from a finite number of observations.

“The basic principle of concept-formation (which states that the omitted measurements must exist in some quantity, but may exist in any quantity) is the equivalent of the basic principle of algebra, which states that algebraic symbols must be given some numerical value, but may be given any value.”
   ~ Ayn Rand, "Concept-Formation", Introduction to Objectivist Epistemology

The operation

Take the concept "table". Its units share a distinguishing characteristic: a flat level surface with supports, serving a particular function. They differ in height, width, weight, colour, material and number of legs.

Forming the concept keeps the first and drops the second — not by forgetting the measurements, and not by averaging them, but by declining to specify them. What results is a single mental unit that applies to:

• every table anyone has seen,
• every table anyone will build,
• and every table nobody will ever build,

because nothing in the concept commits to a height, and any height will do. This is the algebraic analogy Rand drew. Writing x does not mean the value is unknown or unimportant; it means the statement holds whatever the value turns out to be.

Why the theory needs it

The problem measurement omission solves is the oldest one in the theory of concepts: how a finite mind, having observed a handful of things, can form an idea that covers an unlimited number it has not observed.

• Intrinsicism answers that the mind perceives a universal, which relocates the problem rather than solving it.
• Nominalism answers that no such idea is formed — the word is a label applied by habit — which makes classification arbitrary and cannot say why some groupings work.
• Objectivism answers that the mind performs a definite operation on facts it has observed. The similarity is real and quantitative; omitting the quantity while keeping the characteristic yields an abstraction that is open-ended because nothing in it excludes any measurement.

The operation is only stateable because measurement has been analysed first, and because similarity has been defined as the relationship between existents possessing the same characteristic in differing degree. See Concept formation and Conceptual Common Denominator.

Range, not blankness

Some concepts omit measurements entirely; others retain a range. "Table" places no upper bound on height in the abstract, but a structure a hundred feet tall could not serve the function, so the function itself sets limits. Concepts of value work similarly: the standard is a purpose, and the omitted measurements are bounded by what serves it.

What is never retained is a specific value. A concept that fixed one would name a particular rather than a kind.

Common misunderstandings

• That measurements are taken and then thrown away. Nothing is measured. The claim is that the characteristics are measurable — that they vary in degree along a dimension — which is what makes omitting them a definite act rather than vagueness.
• That the concept is an average or a composite image. A mental picture of a typical table is not the concept. The concept has no height at all, which is why it covers heights no picture could.
• That measurement omission is a description of introspection. Few people report doing this consciously. It is an account of what the process must be for the result to be valid, not a report of what it feels like.
• That it makes concepts vague. The opposite: it is what lets a concept be exact about what it includes while being silent about what does not matter. Vagueness would be failing to identify the distinguishing characteristic at all.

See also

• Concept · Concept formation · Unit · Measurement
• Conceptual Common Denominator · Crow-epistemology · Unit-economy
• Existents · Identity · Objectivity · Induction
• Nominalism · Realism · Intrinsicism · Invalid Concept
• Introduction to Objectivist Epistemology — the primary source

Discussion

• Attribute vs quality
• A criticism of Objectivist epistemology
• Objectivist epistemology and metaphysics

References

• Rand, Ayn. "Cognition and Measurement" and "Concept-Formation", Introduction to Objectivist Epistemology. The Objectivist, 1967.
• Peikoff, Leonard. Objectivism: The Philosophy of Ayn Rand, chapter 3.