Once you had learned to sort what you could see into mental piles called concepts, by learning words and definitions, then were you satisfied? Was that enough? No! You were just getting started.
You had chairs and tables and houses and trees and plates and forks—you had high chairs and big houses and green trees and flat plates, but you did not yet have high and big and green and flat. You could sort out things, but not properties of things. How you learned to sort out properties of things can be shown with the line of squares pictured before:
|n n n n n n n n n n|
Instead of focusing on the similarity, you could focus on the difference. You could treat the difference as if it were a thing: you could sort it into a mental pile with other instances of the same difference. You could pile it into a word and make a concept. The result would be color.
Just as you learned to make a unit by regarding many things as if they were one, so you can learn to regard attributes as if they could exist separately. Then you can sort them out. Once you realize how well that works, you can go on to regard movements of things as if they could exist apart from the moving things. You can form concepts of motion. In the same way, you can sort out relationships.
Something that is bigger than its surroundings may have other differences also, but you can focus on just the size difference, and treat it as if the relationship could be separate from the objects. You mentally separate what cannot be physically separated. You can do the same with shape, texture, position, temperature....
Children delight in playing pretend games. They are learning to act as if this were that. They have not yet been told that mental actions are happening in some other dimension. To them, mental skills are to be tried out and practiced just like any other actions. Acting as if is a way to try out what being Mommy would be like, and also a way to sort out not just objects, but properties of objects, aspects of objects, relationships between objects. They are discovering the power of abstraction.
Reality is always itself. It is not constructed like a connect-the-dots painting, with markings and codings to indicate what to do where. It is as you first saw it: a welter of sights and events with no explanatory announcements. But your consciousness is capable of comparison, which means measurement, which provides the rules for sorting everything out. Imagine the triumph you must have felt when you got your first glimmer of how reality might be sorted out and made manageable. What you got can be characterized by the words as if. Treat a group of similars as if it were a unit. Treat a characteristic as if it were a thing.
F Ouch! That sound hurts the ears. But another sound is hard to hear at all. How do you sort that out mentally? As if to the rescue: you form the concept "loudness." You act as if loudness could exist apart from sound. Then you can make a definition in terms of how strong an impression you get. Then you can act as if the concept could be applied to other things than sound. So you can talk about loud clothing and loud colors.
After a few years of practice, you have as if down pat. You form abstractions, and then you form abstractions from abstractions. You mentally separate gray from a gray object, then mentally separate gray into a black component and a white component, then mentally separate white into all the other colors, then....
Children are busiest learning concrete things and observing events. Adults are concerned largely with abstractions. Can we still find our way back to concrete things and observations? We can, as long as we don't forget what is meant by as if. And we must, or else we will lose the orderliness of keeping reality sorted out. To start thinking of, say, color as actually existing apart from a colored thing, is the same as to start thinking that pretending to be Mommy is the same as being Mommy.
You can pile as if on top of as if until you forget where it all started—with observations of things. It is vital to remember that a conceptual method holds both the object and the attribute equally in mind. A well-trained mind knows, whenever saying as if, to keep a concrete example handy. A good thinker is like a good writer: not, "That's a loud tie," but, "That tie is louder than a giant's sneeze."
Elaborate philosophical rackets have been based on confusing things you see with abstractions you make—as if redness were as concrete as a red apple, or as if a red apple were no more concrete than the idea of redness. Love is supposedly an illusion because you can't put it on the table and photograph it. Fear supposedly hobbles you just like chains do. Knowledge supposedly is impossible because you can't sort out things from your ideas of things.
In fact, there is nothing confusing or mystical about it. Metaphysics says that our senses give us the means to perceive the reality we live in. Epistemology says that our conceptual faculty gives us the means to sort out the reality we live in, so that we turn confusion into knowledge. One of the methods we use is the mental trick called abstraction. We act as if properties of things and relationships among things were themselves things. Then we can sort them out using the conceptual method. It is simple enough for a two-year-old to master. If a twenty-year-old philosophy student is confused, that is the result of bad teaching, not unknowable reality.
Abstraction as a mental method is like dynamite as a mechanical method: its tremendous power must be directed lest it do damage rather than good. Here is an example of abstraction exploding into chaos:
"Number is therefore simply the unity of the synthesis of the manifold of a homogeneous intuition in general, a unity due to my generating time itself in the apprehension of the intuition."
That was written two centuries ago by confused philosopher Immanuel Kant in a book called Critique of Pure Reason (N.K.Smith translation, P.184). How would we go about looking for reality in such gibberish? By looking for a connection to some real thing. There it is, buried in the middle: the pronoun my. He is referring to things I do. I number. I intuit. I synthesize. I apprehend. I generate time. He treats these things as if they could be separated from me, which allows him to sort them out in various ways and look for relationships among them. Then he makes his mistake: he forgets the as if. He forgets that he is dealing with abstractions rather than objects. He attributes causality to an abstraction. He abstracts from an abstraction of an abstraction, and then pretends to see causal connections among the abstractions. To show that one of these abstractions is "due to" another requires more than juggling words in the air; it requires observation and description of the real thing behind the abstractions—me.
A toddler plays with blocks—sorting them this way and that, building them up and knocking them down. It is a learning process. Then the toddler becomes a babbler, playing with words—combining them this way and that, building phrases and trying out sentences. It is a learning process. We indulge it. We smile at children's nonsense because we know that playing with words is part of learning to use words. As the child matures, standards rise; indulgence declines. As an adult, I cannot expect people to take word eruptions seriously. I can use abstractions to discover new relationships, but I must not neglect to verify the discoveries by observing not just the abstractions but the real objects behind the abstractions. I cannot go directly from as if to it is; I must go back from abstraction to physical reality, where it really is.
In the beginning, I observe similarity and figure out the rules. Then I can use those rules, based on measurement omission, to sort out everything I see, and everything I do. By treating things I do as if they could exist separately from me, I can form concepts of mental actions. I can talk about thinking, feeling, apprehending. I can ask how to synthesize, how to number, how to time. What I cannot do is turn as if back on itself. I cannot form a group of abstractions and then make valid declarations about the abstractions as if describing things I see. That would be like trying to sit down not on a chair but on the word "chair."
A pile of chairs in a warehouse is there before you. Take a chair off the pile, and sit on it. The concept "chair" piles all possible chairs into your mind. Take an abstract chair off this abstract pile, and think about it as much as you want. But don't try to sit down on it, or else you'll get bruises and ridicule. If you declare yourself a genius, you might avoid the ridicule, but not the bruises.
Presumably, in the quotation, Kant is trying to talk about numbers. If we were to trace his airy abstractions back to reality, we might notice that his sentence is a description of counting. Imagine, for example, how I would go about "generating time." I would say: "One, two, three, four, five, six...."
To make numbers, you abstract from various piles of similar things, not the contents of the pile, but the quantity of things in the pile. You treat the quantity as if it could be separated from the piles. You define it by pointing at the piles. "There's one; there's two; that's three; that's four." Or, you can count off on your fingers. When you get to the number of fingers on your hands, that's a good place to abstract from the abstraction. Define twenty as two tens, thirty as three tens, etc.
No wonder kids love to count. It is perfect practice for keeping straight the endless layers of abstraction which make the conceptual method able to encompass the universe in a flash. It gives kids a view of the open-endedness of the method. By adding layers of abstraction, you can go on counting indefinitely. If you can mentally handle two things as if they were one, then you can handle two zillion things as if they were one.
Kant's reckless—or tricky—use of the as if method is an example of what Ayn Rand calls floating abstraction. If I say "240 plus 380 equals 620," that is an abstract statement, firmly grounded in reality. Because we all use the same numbering system, we can easily trace the abstractions back to their origin in objects. When Kant talks about "homogenous intuition," however, the reader is left to guess how to trace the abstractions to an origin. The abstractions float free. Something I do, or might do, is being treated as if it could be separated from me—but what? If you are inclined to shrug at the question, note where Kant's reliance on floating abstraction took him: he classified all of reality as unknowable.
Perhaps when you were starting out in life, things were so confusing as to seem unknowable—until you noticed similarity, your first glimpse of relationship and therefore order. You figured out how to use similarity when you got the idea of making units. Then you discovered that this as if method of abstraction could be applied in many ways to help you deal with reality. How you learned to extend it to inference is something we can learn by looking more closely at the kind of comparison called measurement.
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