Beyond Objectivism—Measurement

[Before I describe the second question in this series, I must make one important comment. This series addresses Ayn Rand's philosophy of Objectivism. Except for the specific issues I raise, that philosophy is to be regarded as correct and the basis of all discussion. Neither the questions or discussion will be understood outside the context of that philosophy. If you wish to participate in these discussions, it is assumed you are already familiar with Objectivism, or are willing to make yourself familiar with those aspects of Objectivism pertinent to the discussion.]

The Universal Concept

In the previous article I suggested Ayn Rand's definition of a concept really only pertained to universals, but that there are also particular concepts. This article addresses another issue with Rand's definition of concepts, the issue of measurement.

Here is her definition again:

A concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted.

The question of measurement is a very large one, and this issue could (and will be, eventually) addressed from that aspect, but I've promised to make these articles as short as possible, and will take a different approach and address the problems with the concept of measurement itself in another article.

It may seem like a digression here to mention something which is admittedly only a surmise on my part, but you will see the relevance. I think Ayn Rand was thinking primarily about concepts of physical existents, those things we directly perceive, when she developed her definition. If the definition were only for concepts of physical existents, the "measurement omitted," idea works perfectly. In fact, however, most of our concepts are not of physical existents, but of events, relationships, and attributes (because there are more of those than there are physical existents); but even those are not the most of our concepts. Most of our concepts are of or about other concepts.

The definition works so long as the concepts are for cars, houses, tables, and toys. It does not work when the concepts are for verbs, smallpox, yesterday, and man-made. What is the distinguishing attribute of verbs that the particular measurement of is omitted. What attribute of "verbs" is measurable and what is the unit of measure?

[Note: I've collected over some time a list of concepts that just cannot be made to fit the "measurement omitted" formula. Here are some examples of some of those kinds of concepts: logic, preposition, beer, cheese, milk (is 'goats' a different measure than 'cows'?), brother, uncle, history, man-made, concept, memory, cough, blink, malaise, smallpox, cancer, ethics, politics, value, aesthetics, fruit, quality, example, satirical, mysterious, pregnant, alive, dead, true, false.]

The Appeal

The appeal of Rand's definition of concepts is its simplicity and comprehensiveness. It is exactly what a good definition should be. The measurement idea is especially appealing because, at first blush, it seems to cover everything.

It is, in fact, a kind of rationalism; one I call the Pythagorean fallacy, after the belief of the Pythagoreans that everything could be reduced to numbers (read measurement). Many Objectivists are so allured by this tempting rationalism (the belief that reason alone, without evidence, can determine truth), they go to great lengths to rationalize the measurement aspect of Rand's definition of concepts. It is their attempt to save it.

Saving It

There is another reason Rand's definition is so appealing. It is so close to the truth it seems, on examination, almost intuitively true. It is obvious that what makes things the same kind of things is the fact they have the same attributes. A thing's attributes, after all, are what make it what it is. It is also obvious, if one is honest in their examination, that measurement just does not apply to the vast majority of our concepts. So how can this gloriously insightful definition be saved?

Here's how. ... Well you know I'm not going to tell you, but I will give you a hint. Measurement itself is only a quality, an attribute. Physical things which are identified by a universal concept all have some specific essential or (necessary or distinguishing), attribute(s), but different non-essential (possible) attributes like the "measurement" of one of their attributes.

Here's a second hint. We have two spheres. They are both units of the concept sphere. In every geometrical manner of measurement they are identical. They have the same weight, size, and material. In the physical world, such perfect identity is difficult to imagine, even if the spheres are very precisely made ball bearings. So make the two spheres electrons. What is it that differentiates between them? It is not possibly a measurement of any common attribute.

Can you save Rand's definition?

[For the correct definition of a concept, see "Epistemology, Concepts" in the Autonomist Philosophy series.]