We've traced the steps from cognitive self-regulation to measurement omission to abstraction to concept formation. We've watched the perceptual infant become a conceptual toddler, learning a method capable of sorting all of reality into orderly groups. At this time in your life you began doing something that many people consider mysterious at any time. You began making projections. "If I tell Mommy that Daddy said yes, then she'll say yes." How did you learn to do that?
A more fundamental question is: When did you start drawing conclusions of any kind? The answer is: even before you started making concepts. To sort variegated blocks into piles is a process of drawing conclusions. It is implicit identification. "This one belongs in this pile. That one belongs over there." Sorting out reality means classifying everything into concepts, which means deciding what goes where. The fundamental conclusion is identification—deciding what goes where.
In the idea of drawing conclusions lies the crux of mental action. We watch a dog bark at a stranger, and we casually assume that the dog drew a conclusion about the stranger. This leads us to pretend that the honey bee and the humming bird draw conclusions about flowers. But we balk at saying that an ant draws conclusions about cooperation, or that the cockroach decides to check in at the Roach Motel. That's because it is obvious that ants and roaches lack the equipment to draw conclusions. So do dogs.
When Ayn Rand identified measurement omission as the base of similarity, she explained something that has been noted for thousands of years: that the kind of comparison called measurement is fundamental to the way we handle reality. It is fundamental not just to the kind of decisions called identification, but also to the kind of decisions called inference.
To measure is to quantify difference between similars. It combines counting with comparing. I've got two sticks. This one is twice as long as that one. So the shorter stick is my standard which I'll use as a unit, called a "stick". Now the other one is two sticks long. Wait! There's a better way. Make the length of my foot a standard unit, and compare both sticks to that. One stick is a foot and a half long; the other is three feet. I can improve further on that by agreeing to use a standard foot-long stick called a ruler. Then I can mark off any number of smaller units on the ruler, and use it to measure all kinds of similar things. For example, my thumb.
My thumb measures a little less than an inch wide. How much less? Well, the division is not marked on the ruler, but if it were marked it would be half way between the last eighth-inch mark and the inch mark. So, by extrapolation, my thumb is a sixteenth of an inch short of an inch wide. I might say, "I guess it's about fifteen sixteenths of an inch." However, my method is not guess but logic. I used logic to fill in the missing division. Can I use logic if I run out of ruler?
How high is the room? Well, it's a lot more than my ruler. If I put the foot-long ruler against the wall four times, it would be half way to the ceiling. So the room must be eight feet high. Hey! I didn't run out of ruler at all; I created an abstract ruler—an as if ruler—eight feet long.
The child makes piles of similar things, then learns to do the same mentally by using words. That's learning to make concepts. The child measures things using physical scales, which leads to the idea of making measurements in the mind, using mental scales. How would you create a mental scale?
I dropped something. It broke. When you drop things, they break. That generalization was my first standard for breakability. Then I dropped something else. It did not break. Now I had a mental measuring stick: from non-breakable to breakable. Eventually, I have a mental arrangement of things on a breakability scale. It is not an open-ended scale. It is a scale with limits, and a few general divisions. Now we can ask: by what process do I decide where a new thing fits on the breakability scale?
The answer is extrapolation. I use the standards I've developed to infer how breakable the new thing is. My purpose is to avoid finding out the hard way: by breaking it. I conclude how to avoid breaking it by figuring out where it belongs on my mental measuring stick of breakability. I use past experience and the rules of similarity to fill in missing details. I handle new things by seeing how they fit in with old things.
If I know that you are six feet tall, then I can infer the height of the room without needing a ruler at all. Knowledge of your relationship to the standard is enough. The room is a third higher than you, or eight feet.
Can you look at a teacup and infer the capacity of an odd-shaped swimming pool? No, because the rules of similarity are violated: there is no conceptual common denominator; the range is too different. Nor could you infer the capacity of the pool by comparing it to the size of the lawn around it; area and capacity are not commensurable. There's no mystery, of course: the capacity is less than a lake, and more than a hot tub. By making whatever measurements are possible, you could narrow down to a useful extrapolation. You could, for example, infer how much chlorine you need for purification.
Will Mom say yes when I ask to go swimming? Well, she said yes before—that's one limit. She also said no before—the other limit. There are divisions between the limits: no-unless, maybe, yes-if, and the dreaded "we'll see." There are observed conditions corresponding to these divisions; I can make a scale of conditions. By comparing the present conditions to the scales, I can infer Mom's answer. Then I can try to influence the answer by influencing the conditions. I need to perfect this new method, because throwing tantrums won't work forever.
When I project Mom's answer, I am not making a psychic divination. I have integrated observed possibilities into a scale. I know the limits, and respect them. I do not want to be random; I want to avoid being random. I have no wish to venture into unknown territory, but only to locate conditions within a known range.
To emphasize that inference is never a venture beyond the limits, we can consider inferring the size of the universe. Of course, if the universe means all that exists, then the answer is easy: it has all the size there is. But we can get around that by thinking only of the "known universe," which is an as if universe we can imagine standing outside of and measuring. And that's the point: we imagine standing outside of it, or traveling through it to a limit. We imagine a limit, and try to locate the limit on some standard.
Since the conceptual method encompasses all of reality at all times, it can never run out of ruler. Extrapolation is never a grope, never a squint into the void. It finds new divisions within an area of knowledge. This is the crucial essence of inference: it is conceptual. It is contained within a context. It is not a wild leap, but a conceptual refinement. It is not speculation, but image enhancement.
There is a method of improving the picture on some expensive television sets that uses extrapolation in a direct way. It compares two neighboring bits of information, and then inserts between them a tiny extra bit of picture which is mathematically half way between the two. The image is enhanced by inferring what was beyond the system's ability to record. Your mind does the same thing better. When you see a door frame or a telephone pole on TV that looks wavy, you infer the truth so fast you hardly notice the glitch. A black and white picture gives shades of gray, and lets you infer the whole color scheme.
Still, some view inference as groping in the dark for unexplainable inspiration—in other words, as guessing. To them, it will remain a mystery. Others view inference as elaborating the obvious—as second-guessing. To them, it will remain an annoyance. In fact, it is a process which was dawning on you at the ripe age of two—a process of using the rules of similarity to fill in missing details. You dropped a glass from shoulder height, and it broke. Then you dropped one from waist high, and it did not break. What conclusion did that suggest about dropping a glass from knee high, and from overhead?
One reason inference is considered magical is that it depends on logic. How can we claim that a toddler knows the rules of logic? The answer is that logic is simply another way of looking at the process we've been describing: the process of sorting things out.
When a child is sorting blocks into piles, physical reality keeps things orderly. You can put a block into the wrong pile; you can change a block from one pile to another; but you cannot put a block into two piles at the same time. Logic is recognition of the fact that you cannot put one object in two piles at the same time. Or, in Ayn Rand's more elegant words, it is the art of non-contradictory identification.
From this angle, it's easy to see that logic is not just the conceptual method done right; it is inherent in doing the conceptual method at all. To identify is to assign a classification—this is that. You can refuse to classify in three ways: deny that this exists, deny that it is classifiable, or declare it that and also not that at the same time. Then you are left with no method of sorting out the complexities of life.
F An anti-logician could say, "I deny that A is A—I deny Aristotle's Law of Identity—but I can still sort things out." But this is obvious nonsense. How do you sort out things which do not have identity?
F Or the anti-logician could say, "I deny Aristotle's Law of the Excluded Middle—things are not either-or—I declare that some things cannot be classified." But that is assigning things to a classification called "unclassifiable." What Aristotle excluded was a pretended middle ground between putting something in a pile and not putting it in the pile. If a child sorting blocks refuses to touch some blocks because they look icky, then at the end, one of the piles on the table will be a pile of icky blocks.
F Or the anti-logician could say, "Do I contradict myself? Very well, then, I contradict myself. To hell with Aristotle's Law of Non-contradiction." This is an honest expression of hatred for the very idea of sorting out reality, of classifying, of living conceptually. It is based on a misunderstanding: nobody says you can't refuse to sort things out, but only that you won't like what happens after that.
Usually, of course, contradictions are presented in ways not so obvious. Logicians devise elaborate rules and procedures for finding hidden contradictions. Some imitate mathematics. Diagrams and symbols cover textbook pages. However, nobody should be intimidated; the purpose of even the most elaborate logical system is simply to make hidden contradictions stand out. It's like learning a complex system to improve memory or reading speed: the learning time is made up by increased power and precision from then on.
A child sorting blocks would not think of putting one block into two piles at once, because there would be no purpose to it; nothing would be accomplished. Later, when the child has learned to do the same thing mentally, then the temptation might develop to fool people by seeming to identify one thing two different ways at once—perhaps to keep Mommy and Daddy both happy at once, or get off the hook for something, or get admired for cleverness.
One way of pretending to sort a block into two piles at once would be to switch it from pile to pile faster than the eye could see. This is the method most used by politicians. You may call your money pay, but politicians call it income, revenue, investment, taxes, and many other things in quick succession. It is being rapidly switched between two mental groups: yours and mine. A blatant use of the switch happened some years back, when the U.S. Dollar was thought weak. "Your Dollar is absolutely sound," said a Government Official, "because it is backed by the assets of every person in the country."
Another way of hiding a contradiction is called equivocation. This is a favorite of the confidence man. "I didn't lie; the check is in the mail; I just didn't say who it's addressed to." Enemies of business declare that there is no difference between "economic power" and police power. Advocates of socialized medicine declare that there is no difference between paying for an operation with your own money, and paying for it with other people's money.
In sorting blocks, this would be done by pushing two piles together and declaring them one pile. "There's no real difference between square and round, so all these blocks are the same." That would be an obvious refusal to sort things out. Doing the same thing mentally is not so obvious, and it can happen in two ways: ignoring a difference, or failing to notice a difference. Complex reality is not as easy to sort out as blocks, so mistakes happen.
When we look at conceptualizing from the standpoint of logic, in other words, we see a principle. Failures of the sorting process come about in two ways: error, and evasion. An error is a failure to note a significant difference. An evasion is a refusal to do so. We'd better take a closer look at that.
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