In her great book Introduction to Objectivist Epistemology, Ayn Rand committed a fallacy that has taken me years to identify.
It is a fallacy that prevented her observing the variations that can occur in a concept.
Before stating that fallacy, here is what she herself said will happen with an uncorrected falsehood:
Observe that the history of philosophy reproduces—in slow motion, on a macrocosmic screen—the workings of ideas in an individual man’s mind. A man who has accepted false premises is free to reject them, but until and unless he does, they do not lie still in his mind, they grow without his conscious participation and reach their ultimate logical conclusions. A similar process takes place in a culture: if the false premises of an influential philosopher are not challenged, generations of his followers—acting as the culture’s subconscious—milk them down to their ultimate consequences.
The Ayn Rand Letter Vol. III, No. 10 February 11, 1974 Philosophical Detection–Part II
What false premises are there in ITOE? Only one: the idea that concepts, in the field of cognition, perform a function similar to that of numbers in mathematics.
Ayn Rand sets out her analogy here :
Since concepts, in the field of cognition, perform a function similar to that of numbers in the field of mathematics, the function of a proposition is similar to that of an equation: it applies conceptual abstractions to a specific problem.
A proposition, however, can perform this function only if the concepts of which it is composed have precisely defined meanings. If, in the field of mathematics, numbers had no fixed, firm values, if they were mere approximations determined by the mood of their users—so that “5,” for instance, could mean five in some calculations, but six-and-a-half or four-and-three-quarters in others, according to the users’ “convenience”—there would be no such thing as the science of mathematics.
Yet this is the manner in which most people use concepts, and are taught to do so.
Above the first-level abstractions of perceptual concretes, most people hold concepts as loose approximations, without firm definitions, clear meanings or specific referents; and the greater a concept’s distance from the perceptual level, the vaguer its content.
P 75 Introduction to Objectivist Epistemology 8. Consciousness and Identity
What function does a number perform in mathematics? A number is a fixed quantity represented by a symbol of fixed value. There are no variants of a number and thus the meaning of its symbol does not change. It functions as a constant.
However, the meaning of a concept’s symbol varies. The number “5” cannot mean “five in some calculations, but six-and-a-half or four-and-three-quarters in others”—Ayn Rand is quite right about that. But the word “man” can mean “men, women and children” in some propositions, “an adult male” in others and “a chess piece” in others.
This fact wipes out Ayn Rand’s analogy, however you explain the phenomenon.
I say a word’s meaning changes because there are variants of the concept it represents. But even if you argue, as Harry Binswanger does, that a word stands for a number of different concepts, the similarity to a number is lost. A number does not stand for several different quantities.
Now, it may well be that only one meaning of a word—one form of a concept—is objectively appropriate to a given context.
But if you start insisting that a concept and a number perform the same function, your idea of a concept is likely to harden to the point where you miss the wide variations possible in its form.
That is a recipe for dogmatism.
Copyright © 2016 Tom Minchin
Footnote:
If concepts are the variables of cognition, what are the constants? Perceptions.
Have you ever asked why more people can drive a car than can engage in an abstract discussion? Both activities require reason.
But in driving, people are dealing direct with reality via their perceptions. Perceptions (assuming an intact and non-substance affected brain) do not vary between people. Conceptions do. So the scope for mistakes is vastly less with perception.
It isn’t that people can’t deal with abstractions successfully. They can. It is just harder because there are so many variables to consider. Everyone knows what an oncoming car means. It is not so easy to know what someone else means by an abstraction.
It is not a good solution to declare that concepts have a single meaning and proceed to assert what that is. It is much better to recognize variability and get to learn what the other person means, even if you then persuade them that their variant of the concept is invalid or not appropriate to the context.
But then again, they might persuade you.
© Tom Minchin August 12 2017
Second footnote
Ayn Rand’s great insight about concepts is that they are used as the algebraic, not the numeric symbols of cognition. As she wrote in chapter 2 of ITOE:
a concept is used as an algebraic symbol that stands for any of the arithmetical sequence of units it subsumes.
To give an example, the concept “cat” can refer to any particular cat, past, present or future despite the fact that each of them may differ widely in their measurements, i.e., quantitatively.
My discovery is that a concept isn’t just used as a symbol for units that can vary in quantity. It is used as a symbol for units that can vary in quality. A unit of the concept “cat” may be a feline… or a jazz musician.
To give a more abstract example, the concept “compromise” can stand for units that are qualitatively very different. A compromise can be a positive phenomenon or a negative one, depending on which variant of the concept you’re talking about. It can be a legitimate adjustment of competing claims or the unilateral surrender of a principle. Either is a valid form of the concept, but their units are radically different.
Everyone agrees that a word can vary in its meaning. But it can do so for only one reason: the concept it represents can vary qualitatively.
How is that possible? Isn’t a concept an entity with a fixed nature? That’s certainly the conventional wisdom. But is it right?
It’s time to take a much deeper look at what a concept is. We will do so in the next article.
© Tom Minchin August 16 2017