Differences, Similarities, and the Unit-perspective
As far as we know, other animals lack concepts, and even the ability to form them. While they have their own ways to perceive the world (some snakes see through processing infrared light, for instance), as we do, they cannot do anything more with their perceptions than act on them. Using sight and hearing, a lion can hunt and kill its prey, but cannot do something that we do all the time: in general, other animals cannot organize their perceptual field, the objects they deal with every day.
Animals notice that things around them exist and act in certain ways, but they cannot reach the next step: the recognition of similarities and differences among the identities of things. We’re able to notice that some things are completely different from each other. Birds have the characteristic of flight, but trees do not; we see objects in colors and shapes, but our thinking about our own thoughts lack such features; some things in the universe are life-forms, but other things possess no life processes. In observing the world, we can’t help but notice the plethora of features and characteristics that objects have (or don’t have).
However, we’re not restricted to only noting differences amongst things. We can also notice the ways in which things are similar, or are less different, in comparison with other things. In realizing that some things are alive and some things aren’t, we can then relate these living things as having a certain attribute in common, namely “life.” Some animals have legs and can run, making them similar in comparison to, say, snakes or snails that cannot run.
These two facts, our noticing of differences and similarities, points to another significant fact about the human mind: we’re able to group or classify things according to shared characteristics (flying, color, weight, speed, etc.), considering them as units or members of a group of similars. This is the “unit-perspective,” which Rand insists is the key or beginning of the conceptual level of consciousness.
A unit is an “existent regarded as a separate member of a group of two or more similar members.” [ItOE, p. 6] While perception allows us to become aware of certain characteristics of objects around us, such as appearing or feeling like they possess a certain length or a rough surface, the unit-perspective allows us to be aware of things as existing in certain relationships with other things due to their characteristics, whether the things being compared are different from or similar to each other. (I’ll note that the concept unit doesn’t apply only to perceptual objects, such as balls and dogs. Political systems and scientific theories can be units too, in relation to the concept theory for instance, but it’s important to realize here that our first units are of perceptual objects.)
As I said in part 1, concepts are things that relate certain knowledge as applying to a plethora of things that we’ve grouped together. Such a phenomena as a concept would be impossible if we didn’t group things together in the first place, if we didn’t regard things as units. Of special significance is the fact that, without a unit-perspective, we would not be to “count, measure, identify quantitative relationships [such as some object weighing 10 pounds]; [we] could not enter the field of mathematics.” [OPAR, p. 76]
This seeming coincidence is, as Rand argues, actually the means by which we can understand the connection between concept-formation and mathematics, and thus understand the nature of concepts themselves. “The process of concept-formation is, in large part, a mathematical process.” [Introduction to Objectivist Epistemology, p. 7]
The point of the next section is to see why that is.
Measurement, and Measurement-omission
To truly understand concepts, we need to understand the mathematical idea of measurement, both what it is and the reason why we measure things.
In Rand‘s definition, measurement, “is the identification of a relationship--a quantitative relationship established by means of a standard that serves as a unit.” [Ayn Rand Lexicon entry: Measurement] Typically, measurement involves two things--the thing being measured, and the other thing which acts as the standard of measurement. By taking a foot as a standard of “length,” for instance, we can compare/measure other objects with it and determine if they are longer or shorter. A foot is itself a unit of length, so it can be used to measure other units of length and give us knowledge about certain attributes, specifically information about the magnitudes of various objects, whether of large or small magnitude. A similar process occurs when measuring weight, density, volume, time, and other units of measurements.
What’s important here is that the real purpose of measurement isn’t to simply relate objects that we deal with in everyday experience, but to expand the range of what we can consider and learn about beyond the perceptual level, beyond individual feet, or seconds which we can count. We can observe something that weighs one gram, for instance, but we can’t comprehend the weight of the Earth by merely looking at it; instead, we need to compare it to other objects that we can weigh and form new standards of measurement, such as a kilogram, which we can relate to a perceptual unit (the gram). Our perceptual field is the foundation and standard, and we relate our more sophisticated and abstract measurements to units that we can perceive with only our senses.
A similar thing happens when dealing with objects classed under a concept; the objects have the same characteristic (as we realize from observation), but differ in the exact quantities of these characteristics. Two birds may have the same characteristic “flight,” but may differ in certain quantities relating to flight, such as how high they can fly, how swift, how fast they can take off from the ground, and so on (for a striking comparison, look at eagles versus flamingos). Correspondingly, this will lead to differences in our measurements of these quantities. The world, we realize, is filled with objects which have the same characteristics, but differ in various ways in regard to the particular quantities of such characteristics or features, and our measurements will differ when relating these objects to our units of measurement.
To form concepts, we retain the characteristic, but omit our measurements of the various quantities of things’ characteristics. To form the concept flight, we specify the relevant characteristics (a self-propulsion through a certain medium, pushing against the force of gravity, etc.), but omit/not specify the particular measurements of these characteristics (for instance, the kind of atmosphere, the speed of propulsion, the instruments being used to fly, the amount of gravity being counter-acted). We must be careful to recognize that in “omitting” measurements, we’re not pretending that they don’t exist: without measurements, there is no one relating the quantities of things, and thus no comparisons which would lay the groundwork for forming a given concept. Instead, the “principle is: the relevant measurements must exist in some quantity, but may exist in any quantity.” [Ayn Rand Lexicon entry: Concept-Formation]
This “some-but-any” principle, known formally in Objectivism as “measurement-omission,” is the process of abstraction. Omitting the particular measurements from our consideration of a given characteristic is the same process as abstracting a feature from the particular circumstances we observed it in (or originally thought about it being in). In omitting measurements, we’re able to determine the characteristics that a group of things have in common (or do not), and thus apply knowledge gained about this characteristic to all the instances or particulars included in the (future) concept, regardless of any irrelevant circumstances or measurements carried out.
Thus, we come to Rand’s definition of the concept concept, and simultaneously a single-sentence summary of her theory of concepts. A concept, in her definition, is “a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted.” [Ayn Rand Lexicon entry: Concepts]
Now that we’ve discussed the nature of abstraction, we can learn about how concepts are completed, which is the purpose of the third (and final) part of this series.