correct. However, one can have different intensities of blue, which can be measured on a continuous scale.

Part I.

I have long thought that the epistemology is the weakest part of Objectivism, and the weakest part of that weakest part is the notion of "unit," which is the heart of Rand's theory of concepts. If her ideas on "unit" fall, so does her theory of concepts.

Rand defines "unit" as follows:

(1) "A unit is an existent regarded as a separate member of a group of two or more similar members. (Two stones are two units; so are two square feet of ground, if regarded as distinct parts of a continuous stretch of ground.)"

As I'll show in finer detail below, there is already a problem with this definition and with the two examples she gives, i.e., two stones and two square feet of ground, each one, in her view, being "two units of something."

Continuing:

Rand asserts that a "unit" is an existent — an existent regarded as a separate member of a group of two or more similar members, but an existent nevertheless. So let us look at how she defines existent:


(2) "The building-block of man's knowledge is the concept of an 'existent', of something that exists, be it a thing, an attribute or an action."

Putting definitions (1) and (2) together, we have:

A "unit" is a thing, an attribute of a thing, or an action performed by a thing.

Before proceeding, I'd like to point out that this is already mistaken.

A "unit" is not a thing; it is not an attribute of a thing; and it is not an action performed by a thing.

Take, for example, a lead ball. "Mass" is certainly one of its attributes. But the unit "1 kilogram" as a way of measuring its mass exists in consciousness, not in the lead ball: without consciousness there might, indeed, be lead balls, but there are no "units". Without consciousness, "lead" exists, but "gram" does not. Without consciousness, "lead" exists, but the unit number — "1" — does not.

Using Aristotle's "Categoriae" as a reference, we can say that a "unit" is not a thing — not a "substance", as Aristotle would have understood that term — but rather, it falls under the category of "relation", and a relation among three things: the "whole" attribute of an entity (i.e., the entity's whole mass, the entity's whole weight, the entity's whole length, etc.); a "part" of that attribute (some division of mass, weight, length, etc.); and the mental act of comparing that PART to the WHOLE by naming the part "1".

So we need three things for a "unit": The whole of some attribute; a part of that attribute; the mental act of mathematically comparing the part to the whole by calling the part "1" plus a name: thus, we have the whole of mass of some entity; we arbitrarily take a part of that whole and call it "1" + the name "gram". We can now use that part to compare to other entities with the same attribute of mass. We have the whole length of something; we arbitrarily take a part of that whole and call it "1" plus the name "inch", and we can use that part for comparison against any other entity that has the whole attribute of length.

The "part-of-the-whole" relation (known in logic as the "partitive relation") is obviously essential to the idea of "unit." All units are, by definition, 1 part of the whole attribute being measured. There's a simple grammatical substitution test one can do to test if something is really a unit: just put it into a partitive phrase with "of" as the preposition linking the antecedent idea (the part) to the consequent idea (the whole). For example

"a gram of mass." (a "gram" is one unit of a whole attribute called "mass")
"a meter of length." (a "meter" is one unit of a whole attribute called "length")
"a gallon of volume." (a "gallon" is one unit of a whole attribute called "volume")
etc.

Of course, we are usually accustomed to substituting the right side of that partitive phrase with the name of the actual substance we are measuring, e.g.,

"a gram of lead"
"a meter of rope"
"a gallon of water"
etc.

But notice, it's not really "lead", per se, that we are comparing to the gram, but rather one of lead's attributes, i.e., mass. So to be a real stickler for precision both grammatical and logical, we ought to say, "a gram of mass of lead," and "a meter of length of rope", and "a gallon of volume of water".

It is, perhaps, all right that we not say this, but we should *think* it, and *mean* it, when we employ the more common constructions of "a gram of lead", etc.

Part II.

Now, if you understand that a unit is always some part of a greater whole attribute that we wish to measure, then it behooves us to ask what, precisely, is the meaning of Miss Rand's assertion that "two stones are two units."

It makes no sense.

"Two grams (of mass) of lead" makes sense, because of the parenthetical "of mass" phrase, which tells us that "gram" is itself a little bit of mass given the label of "1". Remember that the test of "unit-ness" is that partitive phrase — the "of ____". If that phrase cannot be completed intelligibly in a sentence, then the meaning of that sentence has nothing to do with "units". We could even put that sentence into the following form for the sake of consistency with Miss Rand's sentence:

(3) "Two grams (are two units of mass) of lead"


Returning to Miss Rand's assertion, let's see if we can apply the partitive test by putting it into the same form as (3):

(4) "Two stones (of ______) are two units (OF WHAT????)"

A "unit" is always a unit OF SOMETHING.

So if two stones are two units, what are they units OF?

Blank out.

Miss Rand confuses the issue for herself as much as for her readers when she immediately continues that assertion with the following:

"so are two square feet of ground, if regarded as distinct parts of a continuous stretch of ground."

Notice, please, that Miss Rand inadvertently makes use of that partitive construction we saw as necessary to all units: "so are two square feet OF ground." The precise construction, of course, should be, "so are two square feet (OF area) of ground."

Yes, two square feet of area truly are two units of area of ground — and they need not be continuous, by the way: if one square foot is in New York and another square foot is in Beijing, adding the two together still give "two square feet of area".

But "two stones" are not two units OF anything — they're simply "two stones." They would only be two units OF something of there were a unit called "the stone" by which we measure some other entity that had the attribute of "stone."

But "stone" is not an attribute of some other entity; a "stone" — as used by Miss Rand in her assertion — is itself an entity.

There are a number of other problems with Objectivist epistemology, at least as it is expounded in ITOE. I'll mention one more:

A unit OF something (notice again, please, that all-important partitive construction with "of", showing the part-to-whole relation on which the idea of unit logically rests) must comprise the same attribute as the "whole" one is measuring. In other words, a unit of length must itself be a little bit of length; a unit of mass must itself be a little bit of mass; etc.

In ITOE, Miss Rand asserts that the unit of color is the wavelength of light (e.g., the angstrom, which is 1/10^10 meter). Putting aside quantum quibbles regarding whether or not light is a wave, it's obvious that wavelength, or the angstrom, is a unit of LENGTH, not of COLOR. To be a true unit of color, the unit itself must have the attribute of "color", just as a unit of mass (e.g., the kilogram) itself has the attribute of mass. "Length" is not the same attribute as "color" and cannot be used as a unit thereof. The most we can say is that length — specifically, wavelength — seems to CORRELATE with the subjective experience we call color, through a complicated process of perception, physiological processing, and cognitive computation; thus a wavelength of X "correlates" with the subjective experience of a color we recognize as "blue." But the "wavelength" and the "blue" are two completely different things, and the former is not a unit of the latter.