The truth or falsehood of all of man’s conclusions, inferences, thought and knowledge rests on the truth or falsehood of his definitions. [IOTE, 49]
Definitions are the guardians of rationality, the first line of defense against the chaos of mental disintegration. [RM, 77]
There is a serious problem with the Objectivist view of definitions that neither Rand nor her followers have ever adequately answered. The truth and falsehood of man's knowledge cannot possibly rest on definitions, because definitions are ultimately circular. One word is merely defined by other words; so that to expect to find truth and rationality in definitions is to expect what can never be found. As Karl Popper explained in The Open Society and Its Enemies:
Since Aristotle, it has become widely known that one cannot prove all statements, and that an attempt to do so would break down because it would lead only to an infinite regression of proofs. But neither he nor, apparently, a great many modern writers seems to realize that the analogous attempt to define the meaning of all our terms must, in the same way, lead to an infinite regression of definitions. The following passage from Crossman's Plato To-day is characteristic of a view which by implication is held by many contemporary philosophers of repute, for example, by Wittgenstein: '. . . if we do not know precisely the meaning of the words we use, we cannot discuss anything profitably. Most of the futile arguments on which we all waste time are largely due to the fact that we each have our own vague meaning for the words we use and assume that our opponents are using them in the same sense. If we defined our terms to start with, we could have far more profitable discussions. Again, we have only to read the daily papers to observe that propaganda (the modern counterpart of rhetoric) depends largely for its success on confusing the meaning of the terms. If politicians were compelled by law to define any term they wished to use, they would lose most of their popular appeal, their speeches would be shorter, and many of their disagreements would be found to be purely verbal.' This passage is very characteristic of one of the prejudices which we owe to Aristotle, of the prejudice that language can be made more precise by the use of definitions. Let us consider whether this can really be done.
First, we can see clearly that if 'politicians' (or anybody else) 'were compelled by law to define any term they wished to use', their speeches would not be shorter, but infinitely long. For a definition cannot establish the meaning of a term any more than a logical derivation can establish the truth of a statement; both can only shift this problem back. The derivation shifts the problem of truth back to the premises, the definition shifts the problem of meaning back to the defining terms (i.e., the terms that make up the defining formula). But these, for many reasons, are likely to be just as vague and confusing as the terms we started with; and in any case, we should have to go on to define them in turn; which leads to new terms which too must be defined. And so on, to infinity. One sees that the demand that all our terms should be defined is just as untenable as the demand that all our statements should be proved.
At first sight this criticism may seem unfair. It may be said that what people have in mind, if they demand definitions, is the elimination of the ambiguities so often connected with words such as 'democracy', 'liberty', 'duty', 'religion', etc.; that it is clearly impossible to define all our terms, but possible to define some of these more dangerous terms and to leave it at that; and that the defining terms have just to be accepted, i.e., that we must stop after a step or two in order to avoid an infinite regression. This defence, however, is untenable. Admittedly, the terms mentioned are much misused. But I deny that the attempt to define them can improve matters. It can only make matters worse. That by 'defining their terms' even once, and leaving the defining terms undefined, the politicians would not be able to make their speeches shorter, is clear; for any essentialist definition, i.e. one that 'defines our terms' (as opposed to the nominalist one which introduces new technical terms), means the substitution of a long story for a short one, as we have seen. Besides, the attempt to define terms would only increase the vagueness and confusion. For since we cannot demand that all the defining terms should be defined in their turn, a clever politician or philosopher could easily satisfy the demand for definitions. If asked what he means by 'democracy', for example, he could say 'the rule of the general will' or 'the rule of the spirit of the people'; and since he has now given a definition, and so satisfied the highest standards of precision, nobody will dare to criticize him any longer. And, indeed, how could he be criticized, since the demand that 'rule' or 'people' or 'will' or 'spirit' should be defined in their turn, puts us well on the way to an infinite regression so that everybody would hesitate to raise it? But should it be raised in spite of all that, then it can be equally easily satisfied. On the other hand, a quarrel about the question whether the definition was correct, or true, can only lead to an empty controversy about words.
Thus the essentialist view of definition breaks down, even if it does not, with Aristotle, attempt to establish the 'principles' of our knowledge, but only makes the apparently more modest demand that we should 'define the meaning of our terms'.
But undoubtedly, the demand that we speak clearly and without ambiguity is very important, and must be satisfied. Can the nominalist view satisfy it? And can nominalism escape the infinite regression?
It can. For the nominalist position there is no difficulty which corresponds to the infinite regression. As we have seen, science does not use definitions in order to determine the meaning of its terms, but only in order to introduce handy shorthand labels. And it does not depend on definitions; all definitions can be omitted without loss to the information imparted. It follows from this that in science, all the terms that are really needed must be undefined terms. How then do the sciences make sure of the meanings of their terms? Various replies to this question have been suggested, but I do not think that any of them is satisfactory. The situation seems to be this. Aristotelianism and related philosophies have told us for such a long time how important it is to get a precise knowledge of the meaning of our terms that we are all inclined to believe it. And we continue to cling to this creed in spite of the unquestionable fact that philosophy, which for twenty centuries has worried about the meaning of its terms, is not only full of verbalism but also appallingly vague and ambiguous, while a science like physics which worries hardly at all about terms and their meaning, but about facts instead, has achieved great precision. This, surely, should be taken as indicating that, under Aristotelian influence, the importance of the meaning of terms has been grossly exaggerated. But I think that it indicates even more. For not only does this concentration on the problem of meaning fail to establish precision; it is itself the main source of vagueness, ambiguity, and confusion.
In science, we take care that the statements we make should never depend upon the meaning of our terms. Even where the terms are defined, we never try to derive any information from the definition, or to base any argument upon it. This is why our terms make so little trouble. We do not overburden them. We try to attach to them as little weight as possible. We do not take their 'meaning' too seriously. We are always conscious that our terms are a little vague (since we have learnt to use them only in practical applications) and we reach precision not by reducing their penumbra of vagueness, but rather by keeping well within it, by carefully phrasing our sentences in such a way that the possible shades of meaning of our terms do not matter. This is how we avoid quarrelling about words.
The view that the precision of science and of scientific language depends upon the precision of its terms is certainly very plausible, but it is none the less, I believe, a mere prejudice. The precision of a language depends, rather, just upon the fact that it takes care not to burden its terms with the task of being precise. A term like 'sand-dune' or 'wind' is certainly very vague. (How many inches high must a little sand-hill be in order to be called 'sand-dune'? How quickly must the air move in order to be called 'wind'?) However, for many of the geologist's purposes, these terms are quite sufficiently precise; and for other purposes, when a higher degree of differentiation is needed, he can always say 'dunes between 4 and 30 feet high' or 'wind of a velocity of between 20 and 40 miles an hour'. And the position in the more exact sciences is analogous. In physical measurements, for instance, we always take care to consider the range within which there may be an error; and precision does not consist in trying to reduce this range to nothing, or in pretending that there is no such range, but rather in its explicit recognition.
Even where a term has made trouble, as for instance the term 'simultaneity' in physics, it was not because its meaning was imprecise or ambiguous, but rather because of some intuitive theory which induced us to burden the term with too much meaning, or with too 'precise' a meaning, rather than with too little. What Einstein found in his analysis of simultaneity was that, when speaking of simultaneous events, physicists made a false assumption which would have been unchallengeable were there signals of infinite velocity. The fault was not that they did not mean anything, or that their meaning was ambiguous, or the term not precise enough; what Einstein found was, rather, that the elimination of a theoretical assumption, unnoticed so far because of its intuitive self-evidence, was able to remove a difficulty which had arisen in science. Accordingly, he was not really concerned with a question of the meaning of a term, but rather with the truth of a theory. It is very unlikely that it would have led to much if someone had started, apart from a definite physical problem, to improve the concept of simultaneity by analysing its 'essential] meaning', or even by analysing what physicists 'really mean' when they speak of simultaneity.
I think we can learn from this example that we should not attempt to cross our bridges before we come to them. And I also think that the preoccupation with questions concerning the meaning of terms, such as their vagueness or their ambiguity, can certainly not be justified by an appeal to Einstein's example. Such a preoccupation rests, rather, on the assumption that much depends upon the meaning of our terms, and that we operate with this meaning; and therefore it must lead to verbalism and scholasticism. From this point of view, we may criticize a doctrine like that of Wittgenstein, who holds that while science investigates matters of fact, it is the business of philosophy to clarify the meaning of terms, thereby purging our language, and eliminating linguistic puzzles. It is characteristic of the views of this school that they do not lead to any chain of argument that could be rationally criticized; the school therefore addresses its subtle analyses exclusively to the small esoteric circle of the initiated. This seems to suggest that any preoccupation with meaning tends to lead to that result which is so typical of Aristotelianism: scholasticism and mysticism.How would Rand have responded to Popper's charge that definitions lead to an infinite regress? While Rand did not specifically address the question, she did leave some hints on how it might be addressed. In my next post, I will examine these hints.