Ayn Rand & Epistemology 36

Analytic-Synthetic Dichotomy 9: Thinking in Essentials Redux. Peikoff resumes his jihad against nominalism with the following bit of libelous persiflage:

On a rational view of definition, a definition organizes and condenses — and thus helps one to retain — a wealth of knowledge about the characteristics of a concept's units. On the nominalist view, it is precisely this knowledge that is discarded when one defines a concept: as soon as a defining characteristic is chosen, all the other characteristics of the units are banished from the concept, which shrivels to a mere definition. For instance, as long as a child's concept of "man" is retained ostensively, the child knows that man has a head, two eyes, two arms, etc.; on the nominalist view as soon as the child defines "man," he discards all this knowledge; thereafter, "man" means to him only: "a thing with rationality and animality." [IOTE, 104]

Note the complete absence of empirical examples to support Peikoff's contentions: which nominalists, after all, believe the people discard knowledge after defining words? Is it too much to ask for names, followed by documented evidence? This absence of evidence is not only intentional, but necessary: there can be no examples because it's unlikely any nominalist ever held the position attributed them by Peikoff in this passage. What Peikoff and other Objectivists still can't seem to grasp is that definitions define words, not concepts. The definition explains how a particular word is to be used. It gives the meaning of the word in different terms. Neither Rand nor Peikoff ever bothered to provide evidence for the assertion that definitions organize and condense knowledge about the characteristics of a concept's units. Since definitions only express the same meaning in different words, they add no knowledge about external matters of fact (other than knowledge about word usage).

Rand & Human Nature 9

Denial of Jealousy. From a naturalist point of view, it is difficult to escape the view that man is a product of an evolutionary process, and that this process plays an important part in the development of man's character. Since a species, if it is to survive, must both reproduce and care for its offspring, it is likely that the process of evolution will favor those individuals who have a strong predisposition to reproduce and bestow care upon their progeny. Hence the near universality of both sexual desire and jealousy.

In comparing Rand's view of human nature with what we find in the study of actual human beings, the astute observer can hardly fail to notice the degree to which Rand has stripped away everything she found annoying in man. In distinguishing all those elements that separated man from the animals, Rand, in effect, implicitly suggests that man is not essentially an animal. His animalistic characteristics are mere accidents. Man's essence is his "reason" and his volition. These elements supercede the natural or animalistic characteristics. Man has no "instincts" or innate predispositions, only such acquired dispositions as he imbibes from the people around him or his own thinking. Although it is unlikely that Rand would have ever (à la William Jennings Bryan) explicitly denied that man was a mammal, her philosophy, at times, seems to blissfully evade this palpable fact. Indeed, in some ways, this evasion is worse than an outright denial. Bryan, because of his belief in the myth of original sin, could at least be brought to recognize those actual characteristics which human beings share with animals. Rand, on the other hand, saw such characteristics (provided they were not merely physical) as defects acquired through evasion and lack of focus, rather than intregal aspects of a functioning animal.

Objectivism & Politics, Part 38

Natural disasters and state assistance. Does the government have a role in helping people whose homes have been destroyed or severly damaged in a natural disaster? I was reminded of this issue by a 6.5 earthquake that hit this last weekend just twenty miles from where I live, knocking over bookshelves and CD racks. As natural disasters go, this one was very minor—hardly even worth troubling about. But it could easily have been much worse. Forty miles to the south three massive plates come together, creating tensions that could spill over into moster quakes. Twenty years ago the area generated a 7.0 quake; yet it is fully capable of generating quakes comparable to the Anchorage and Indian Ocean quakes.

The destructive capacity of nature is immense. Whether it's earthquakes, tornadoes, hurricanes, tsunamis, volcanic eruptions, floods, these events can devestate entire communities. Yet oddly, Rand and her disciples have very little to say about these "Black Swan" events (to borrow Nassim Taleb's terminology). One could imagine Rand criticizing the mere mention of them as evincing a "malevolent" sense of life. After all, they don't happen all that often: so why dwell on them?


Although they are not an everyday occurence (at least in any given locality), nonetheless they do happen; and most people have a fairly strong conviction that the government has a role in assisting the victims of catastrophic natural disasters. Claiming the state has no role is a hard sell. Why should the state do nothing? It is precisely in a catastrophic disaster that collective action governed by strong leadership becomes advantageous. To oppose such action appears to be mere obstinacy, with neither wisdom nor good sense in support of it.

It is here that Rand's principle-centric approach gets her into trouble. Principles, for Rand, are invioble "absolutes." Only an individual suffering from an "anti-conceptual mentality" would approve of violating a principle. Yet this view of things presupposes an orderly, linear, "logical" universe; it assumes that the non-linear, the disorderly, the non-logical either doesn't exist or is "non-essential." Such assumptions, however, go against facts that confront us in everyday life and in history. As Nassim Taleb reminds us, "the world is more nonlinear than we think, [or] than scientists [and Rand] would like to think.... Linear relationships are truly the exception; we only focus on them in classrooms and textbooks because they are easier to understand." Principles that work fine under ordinary circumstances often break down under exceptional circumstances. Hence wisdom counsels flexibility. When confronted by a rare, extremely impactful event, the individual may need to improvise. Obstinacy on behalf of one's principles, far from being a mark of intelligence and "rationality," merely demonstrates an inability to adapt to new circumstances.

The Cognitive Revolution & Objectivism, Part 11

Conclusion. Having briefly run through some of the major challenges posed by the Cognitive Revolution to orthodox Objectivism, a recapitulation of the main points would be in order.

1. Rand's blank slate view of human nature, particularly her denial that human choice (i.e., free will) is not "saddled with tendencies," is not a plausible position.

2. There is no compelling evidence to support Rand's assertion that emotions are a product of an individual's premises.

3. The Randian view that nothing gets in the "subconscious" without first being in the consciousness is grossly implausible, and about as scientifically creditable as the view that the earth is flat.

4. Rand greatly exaggerates the role that consciousness plays in concept-formation, leading her to place far too much importance on definitions and other trappings of formalized, conscious thinking.

5. Wittgenstein's "family resemblance" theory of concept demonstrates the poverty of Rand's classical view of concepts.

6. Rand's view that "Reason is man's only means of grasping reality and acquiring knowledge" is falsified by the overwhelming evidence for intuitive forms of thinking (such as Oakeshott's "practical knowledge"), which do not use "reason."

7. Rand's view that "Emotions are not tools of cognition" are falsified by cutting edge research by neuroscientist Antonio Damasio.

8. Rand's belief that epistemological truth is best attained through introspection is refuted by the view, common in the cognitive science world, that "unconscious thought is 95 percent of all thought." Introspection, then, would only have access to 5 percent of thought! Not a good vantage point for understanding human cognition!

9. Since most of human thought is hidden from introspection, anyone who claims to understand cognition from their introspective observations is talking through their hat; and any epistemology found on such slim pickings must, ipso facto, be largely speculative. This is the major problem with Randian epistemology. It is mostly speculative, rather than empirical and scientific. Rand is not an authority on human cognition. Cognitive scientists, who study human cognition empirically, using scientific methods of research and the rigorous system of peer review to catch errors, are likely to know a great deal more about cognition than Rand.

10. The cognitive unconscious and the important role of tacit, intuitive knowledge constitutes a huge blow to foundationalism, which is so central to Objectivism, particularly to the Objectivist theory of history. Non-verbal forms of knowledge, which form a critical component of human knowledge, cannot be proved or validated or deduced from axioms or from basic truths.

Having refuted the worst of Rand's epistemological pretensions, we can now examine some of the other parts of her system with greater depth and insight. Among the many lessons that can be drawn from the Cognitive Revolution, perhaps the most important has to do with the inevitable conflict between Objectivist methodology on the one hand and the understanding of human nature on the other. Human nature is a family resemblance concept which is partially based on tacit, intuitive knowledge. Consequently, no detailed and practically effective understanding of human nature can be achieved through the sort of "reason" based essentialism advocated by Rand. The Objectivist definition of man as a "rational animal" provides no real insight into human nature and could not be used as a reliable guide in predicting how people are likely to behave in a given situation. There are individuals in politics, in business, in law enforcement, in the criminal underworld who are very savvy at guessing the probable behavior of strangers in special circumstances. This knowledge is very useful and gives them an advantage in the competition for preeminence in society.

An Objectivist critique of Popper examined

Nicholas Dykes' critique of Popper, linked by the poster Ian, while not as bad as most such Rand-inspired criticisms, does have its share of serious problems.

Dykes begins his critique by complaining about Popper's tone of assurance.

One thing which is quite certain is that Popper wrote with absolute assurance of his own rectitude, as I think the quotations in this paper reveal. For all his belittlement of knowledge and certainty, I have never read anyone who wrote so many books all imbued with such conscious certainty and authority— the authority of one who knows.

Dykes appears to be annoyed by the fact that Popper never prefaces all his remarks with the phrase I suppose or I conjecture. Of course, it would be very tedious to proceed in this way. Dykes also takes Popper to task for declaring "I am not a belief philosopher. I do not believe in belief" while at the same time refusing, in other places in his work, to stop using the phrase I believe to state one of his positions. Here Dykes shows himself deaf to the ambiguity of language. Popper's phrase "I don't believe in belief" plays on two senses of the word belief to make a point. In the first sense of the term Popper is using it to describe certain belief, in the second, the sort of conjectural belief Popper supported. In other words, Popper is simply saying that he doesn't believe (in the conjectural sense of the term) in certainty.

Dykes unquestioningly accepts the Platonic view that equates knowledge with certainty, asserting that all denials of certainty are "self-contradictory," because "in the absence of certain knowledge one is either forced into a position involving some kind of unfounded conviction, belief or faith, or into scepticism." Says who? Dykes here make use of an oft-repeated Objectivist fallacy: the either-or fallacy, where we are given the choice between the Objectivist position and several unappetizing alternatives. But who says that the only alternative between certain knowledge is unjustified belief and skepticism? What about probable knowledge? What about degrees of reliability? If one knowledge claim can be regarded as superior to another, isn't that good enough for practical purposes?

Some of Dykes criticisms demonstrate a lack of familiarity with Popper's ideas. He accuses Popper, for instance, of refusing "to have anything to do with definitions." This is an exaggeration. Popper accepted scientific, or nominalistic, definitions; he simply has no use for essentialist definitions — another matter entirely. I can find no evidence that Dykes understands this distinction, or has any idea why essentialist definitions, and the scholastic mythology that has grown-up around them, deserve the criticism and scorn Popper directed at them.

Dykes essay particularly flounders when he attempts to explode Popper's critical rationalism by associating it with the views of Kant and Hume. He repeats the Objectivist canard that Hume's "whole argument" is in conflict with the Law of Identity. Alas, this misses the point entirely. Hume's argument is not directed at the Law of Identity, but at our knowledge of specific identities. How do we know which attributes of an object are constant and which are not? This is not a question which the Law of Identity can answer. Reminding ourselves that objects have identities is nothing to the purpose if we don't know, or can't be sure, what those identities are.

Dykes is equally clueless when it comes to Kant. Because Popper believed that all observations are "theory impregnated," Dykes assumes that Popper regards all theories as prior to experience, and even wonders whether Popper is "asking us to accept that the heliocentric theory came before observation of perturbations in planetary orbits?" Again, however, Dykes has missed the point. When Popper asserts that observations are "theory-impregnated" he is merely noting how hopeless it would be for an empty mind, bereft of any presuppositions or "theories," to make sense of observations. As Kant put it, "Thoughts without content are empty, intuitions [i.e., sense experiences] without concepts are blind." Regardless of whatever confusions and pendantries Kant may have stumbled into trying to elucidate this paradox in the Critique of Pure Reason, the principle itself constitutes one of the seminal insights of epistemology, easily corroborated by common experience and scientific investigation. I wonder if Dykes has any familiarity, let alone understanding, of it. Or does he believe that facts can be understood without any prior theories at all? Hardly a plausible position, if so. After all, how can a blank mind ever make neither heads nor tails of the bewildering complexity of sense experience, without at least some prior heuristic to guide it? It can't. So some measure of theory does appear to precede fact. How, then, on a realist framework, are we to account for this? Popper at least deserves credit for taking this issue seriously and trying to provide a non-idealist, non-Kantian solution to it. Since Dykes does not even appear to grasp that this is what Popper is attempting to do, his criticism is worthless. One cannot effectively criticize what one doesn't understand.

And that seems to be the over-riding problem of Dykes critique. His understanding of the problems Popper attempts to solve is minimal, at best. His attachment to Randian categories of interpretion has rendered him hopelessly naive in the face of problems originally posed by Hume and Kant and later elucidated by Pierce, Santayana, Popper and Polanyi. His outlook is still trapped in the scholasticism of Plato and Aristotle.

Aristotle's "Secret Revolt" Against Reason

"...every discipline, as long as it used the Aristotelian method of definition, has remained arrested in a state of empty verbiage and barren scholasticism...." - Karl Popper

In her effort to rebuild philosophy anew, free from the influence of the modern post Kantian philosophy she despised, Ayn Rand chose to rehabilitate Aristotle's original methodology as the basic OS on which she was to run her shiny new Objectivism software. Aristotle, with his fundamental role in formalising logic, plus his interest in the natural world, must have seemed like the ideal partner for her ambition of healing the breach between empiricism and rationalism which had first been opened by the skeptical enquiry of David Hume.

Unfortunately, Rand's decision turned out to be what I conjecture to be her most profound mistake. Rand did not realise how deeply Aristotle's method was already a part of her hated modern philosophy; how, with its emphasis on definitions and "true" meanings(what Rand called "checking your premises"), it diverted debates over real problems into fruitless arguments over mere words; arguments, as it turns out, that cannot be logically resolved. It matters not a whit whether Rand applied Aristotle's essentialism at the "epistemological" level rather than the "metaphysical" level - the logical issues are the same.

The result is that her philosophy has followed the same path as those who also adopted the Aristotelian method lock stock and barrel; into unproductive scholasticism, full of sterile schisms and, despite unprecedented levels of publicity for a philosopher, a startling lack of intellectual, aesthetic, or political progression. In true scholastic fashion, this lack of progress stands in inverse proportion to the huge amount of sheer verbiage Objectivism generates. It can produce any number of works allegedly defining art - "What Art Is" - yet despite all this huffing and puffing over preliminaries, can't seem to produce much in the way of actual art. It will spend countless hours discoursing on the vital importance of epistemology to the survival of the human race; but, in 40 years, has not gone any further in developing it than Ayn Rand's "Introduction." As Karl Popper puts it, it leads to "always sharpening one's pencil, and never writing anything." Such are the hidden consequences of the Aristotelian method.

The inescapable logical problems with Aristotle's definition-based methodology, and its subtly deleterious influence, are not widely discussed in general philosophical circles, and are almost completely unknown in Objectivism. Given what I view as its importance, to philosophy in general and Objectivism in particular, I present the most simple and thorough criticism of this silently destructive methodology that I know of: Karl Popper's "Two Kinds of Definition" (adapted from Chapter 11 of his brilliant "The Open Society and Its Enemies"). Enjoy.

(Warning: Long post. And don't let its length let you miss Greg's recent interesting discussion of the basic differences between Rand and Nietzsche below)


TWO KINDS OF DEFINITION
By Karl Popper

"The chief danger to our philosophy, apart from laziness and woolliness, is scholasticism, . . . which is treating what is vague as if it were precise...." - F. P. Ramsey

The problem of definitions and of the 'meaning of terms' is the most important source of Aristotle's regrettably still prevailing intellectual influence, of all that verbal and empty scholasticism that haunts not only the Middle Ages, but our own contemporary philosophy; for even a philosophy as recent as that of L. Wittgenstein suffers, as we shall see, from this influence. The development of thought since Aristotle could, I think, be summed up by saying that every discipline, as long as it used the Aristotelian method of definition, has remained arrested in a state of empty verbiage and barren scholasticism, and that the degree to which the various sciences have been able to make any progress depended on the degree to which they have been able to get rid of this essentialist method. (This is why so much of our 'social science' still belongs to the Middle Ages.) The discussion of this method will have to be a little abstract, owing to the fact that the problem has been so thoroughly muddled by Plato and Aristotle, whose influence has given rise to such deep-rooted prejudices that the prospect of dispelling them does not seem very bright. In spite of all that, it is perhaps not without interest to analyse the source of so much confusion and verbiage.

Aristotle followed Plato in distinguishing between knowledge and opinion. Knowledge, or science, according to Aristotle, may be of two kinds - either demonstrative or intuitive. Demonstrative knowledge is also a knowledge of 'causes'. It consists of statements that can be demonstrated - the conclusions - together with their syllogistic demonstrations (which exhibit the 'causes' in their 'middle terms'). Intuitive knowledge consists in grasping the 'indivisible form' or essence or essential nature of a thing (if it is 'immediate', i.e. if its 'cause' is identical with its essential nature); it is the originative source of all science since it grasps the original basic premisses of all demonstrations.

Undoubtedly, Aristotle was right when he insisted that we must not attempt to prove or demonstrate all our knowledge. Every proof must proceed from premisses; the proof as such, that is to say, the derivation from the premisses, can therefore never finally settle the truth of any conclusion, but only show that the conclusion must be true provided the premisses are true . If we were to demand that the premisses should be proved in their turn, the question of truth would only be shifted back by another step to a new set of premisses, and so on, to infinity. It was in order to avoid such an infinite regress (as the logicians say) that Aristotle taught that we must assume that there are premisses which are indubitably true, and which do not need any proof; and these he called 'basic premisses'. If we take for granted the methods by which we derive conclusions from these basic premisses, then we could say that, according to Aristotle, the whole of scientific knowledge is contained in the basic premisses, and that it would all be ours if only we could obtain an encyclopaedic list of the basic premisses. But how to obtain these basic premisses? Like Plato, Aristotle believed that we obtain all knowledge ultimately by an intuitive grasp of the essences of things. 'We can know a thing only by knowing its essence', Aristotle writes, and 'to know a thing is to know its essence'. A 'basic premiss' is, according to him, nothing but a statement describing the essence of a thing. But such a statement is just what he calls a definition. Thus all 'basic premisses of proofs' are definitions.

What does a definition look like? An example of a definition would be: 'A puppy is a young dog.' The subject of such a definition sentence, the term 'puppy', is called the term to be defined (or defined term); the words 'young dog' are called the defining formula. As a rule, the defining formula is longer and more complicated than the defined term, and sometimes very much so. Aristotle considers the term to be defined as a name of the essence Of a thing, and the defining formula as the description of that essence. And he insists that the defining formula must give an exhaustive description of the essence or the essential properties of the thing in question; thus a statement like 'A puppy has four legs', although true, is not a satisfactory definition, since it does not exhaust what may be called the essence of puppiness, but holds true of a horse also; and similarly the statement 'A puppy is brown', although it may be true of some, is not true of all puppies; and it describes what is not an essential but merely an accidental property of the defined term.

But the most difficult question is how we can get hold of definitions or basic premisses, and make sure that they are correct - that we have not erred, not grasped the wrong essence. Although Aristotle is not very clear on this point, there can be little doubt that, in the main, he again follows Plato. Plato taught that we can grasp the Ideas with the help of some kind of unerring intellectual intuition; that is to say, we visualise or look at them with our 'mental eye', a process which he conceived as analogous to seeing, but dependent purely upon our intellect, and excluding any element that depends upon our senses. Aristotle's view is less radical and less inspired than Plato's, but in the end it amounts to the same. For although he teaches that we arrive at the definition only after we have made many observations, he admits that sense experience does not in itself grasp the universal essence, and that it cannot, therefore, fully determine a definition. Eventually he simply postulates that we possess an intellectual intuition, a mental or intellectual faculty which enables us unerringly to grasp the essences of things, and to know them. And he further assumes that if we know an essence intuitively, we must be capable of describing it and therefore of defining it. (His arguments in the Posterior Analytics in favour of this theory are surprisingly weak. They consist merely in pointing out that our knowledge of the basic premisses cannot be demonstrative, since this would lead to an infinite regress, and that the basic premisses must be at least as true and as certain as the conclusions based upon them. 'It follows from this', he writes, 'that there cannot be demonstrative knowledge of the primary premisses; and since nothing but intellectual intuition can be more true than demonstrative knowledge, it follows that it must be intellectual intuition that grasps the basic premisses.' In the De Anima, and in the theological part of the Metaphysics, we find more of an argument; for here we have a theory of intellectual intuition - that it comes into contact with its object, the essence, and that it even becomes one with its object. 'Actual knowledge is identical with its object.')

Summing up this brief analysis, we can give, I believe, a fair description of the Aristotelian ideal of perfect and complete knowledge if we say that he saw the ultimate aim of all inquiry in the compilation of an encyclopaedia containing the intuitive definitions of all essences, that is to say, their names together with their defining formulae; and that he considered the progress of knowledge as consisting in the gradual accumulation of such an encyclopaedia, in expanding it as well as in filling up the gaps in it and, of course, in the syllogistic derivation from it of 'the whole body of facts' which constitute demonstrative knowledge.

Now there can be little doubt that all these essentialist views stand in the strongest possible contrast to the methods of modern science. (I have the empirical sciences in mind, not perhaps pure mathematics.) First, although in science we do our best to find the truth, we are conscious of the fact that we can never be sure whether we have got it. We have learnt in the past, from many disappointments, that we must not expect finality. And we have learnt not to be disappointed any longer if our scientific theories are overthrown; for we can, in most cases, determine with great confidence which of any two theories is the better one. We can therefore know that we are making progress; and it is this knowledge that to most of us atones for the loss of the illusion of finality and certainty. In other words, we know that our scientific theories must always remain hypotheses, but that, in many important cases, we can find out whether or not a new hypothesis is superior to an old one. For if they are different, then they will lead to different predictions, which can often be tested experimentally; and on the basis of such a crucial experiment, we can sometimes find out that the new theory leads to satisfactory results where the old one breaks down. Thus we can say that in our search for truth, we have replaced scientific certainty by scientific progress. And this view of scientific method is corroborated by the development of science. For science does not develop by a gradual encyclopaedic accumulation of essential information, as Aristotle thought) but by a much more revolutionary method; it progresses by bold ideas, by the advancement of new and very strange theories (such as the theory that the earth is not flat, or that 'metrical space' is not flat), and by the overthrow of the old ones.

But this view of scientific method means that in science there is no 'knowledge', in the sense in which Plato and Aristotle understood the word, in the sense which implies finality; in science, we never have sufficient reason for the belief that we have attained the truth. What we usually call 'scientific knowledge' is, as a rule, not knowledge in this sense, but rather information regarding the various competing hypotheses and the way in which they have stood up to various tests; it is, using the language of Plato and Aristotle, information concerning the latest, and the best tested, scientific 'opinion'. This view means, furthermore, that we have no proofs in science (excepting, of course, pure mathematics and logic). In the empirical sciences, which alone can furnish us with information about the world we live in, proofs do not occur, if we mean by 'proof' an argument which establishes once and for ever the truth of a theory. (What may occur, however, are refutations of scientific theories.) On the other hand, pure mathematics and logic, which permit of proofs, give us no information about the world, but only develop the means of describing it. Thus we could say (as I have pointed out elsewhere ): 'In so far as a scientific statement speaks about reality, it must be falsifiable; and in so far as it is not falsifiable, it does not speak about reality.' But although proof does not play any part in the empirical sciences, argument still does; indeed, its part is at least as important as that played by observation and experiment.

The role of definitions in science, especially, is also very different from what Aristotle had in mind. Aristotle taught that in a definition we have first pointed to the essence - perhaps by naming it - and that we then describe it with the help of the defining formula; just as in an ordinary sentence like 'This puppy is brown', we first point to a certain thing by saying 'this puppy', and then describe it as 'brown'. And he taught that by thus describing the essence to which the term points which is to be defined, we determine or explain the meaning of the term also.

Accordingly, the definition may at one time answer two very closely related questions. The one is 'What is it?', for example 'What is a puppy?'; it asks what the essence is which is denoted by the defined term. The other is 'What does it mean?', for example, 'What does "puppy" mean?'; it asks for the meaning of a term (namely, of the term that denotes the essence). In the present context, it is not necessary to distinguish between these two questions; rather, it is important to see what they have in common; and I wish, especially, to draw attention to the fact that both questions are raised by the term that stands, in the definition, on the left side and answered by the defining formula which stands on the right side. This fact characterizes the essentialist view, from which the scientific method of definition radically differs.

While we may say that the essentialist interpretation reads a definition 'normally', that is to say, from the left to the right, we can say that a definition, as it is normally used in modern science, must be read back to front, or from the right to the left; for it starts with the defining formula, and asks for a short label for it. Thus the scientific view of the definition 'A puppy is a young dog' would be that it is an answer to the question 'What shall we call a young dog?' rather than an answer to the question 'What is a puppy?' (Questions like 'What is life?' or 'What is gravity?' do not play any role in science.) The scientific use of definitions, characterized by the approach 'from the right to the left', may be called its nominalist interpretation, as opposed to its Aristotelian or essentialist interpretation. In modern science, only nominalist definitions occur, that is to say, shorthand symbols or labels are introduced in order to cut a long story short. And we can at once see from this that definitions do not play any very important part in science. For shorthand symbols can always, of course, be replaced by the longer expressions, the defining formulae, for which they stand. In some cases this would make our scientific language very cumbersome; we should waste time and paper. But we should never lose the slightest piece of factual information. Our 'scientific knowledge', in the sense in which this term may be properly used, remains entirely unaffected if we eliminate all definitions; the only effect is upon our language, which would lose, not precision, but merely brevity. (This must not be taken to mean that in science there cannot be an urgent practical need for introducing definitions, for brevity's sake.) There could hardly be a greater contrast than that between this view of the part played by definitions, and Aristotle's view. For Aristotle's essentialist definitions are the principles from which all our knowledge is derived; they thus contain all our knowledge; and they serve to substitute a long formula for a short one. As opposed to this, the scientific or nominalist definitions do not contain any knowledge whatever, not even any 'opinion'; they do nothing but introduce new arbitrary shorthand labels; they cut a long story short.

In practice, these labels are of the greatest usefulness. In order to see this, we only need to consider the extreme difficulties that would arise if a bacteriologist, whenever he spoke of a certain strain of bacteria, had to repeat its whole description (including the methods of dyeing, etc., by which it is distinguished from a number of similar species). And we may also understand, by a similar consideration, why it has so often been forgotten, even by scientists, that scientific definitions must be read 'from the right to the left', as explained above. For most people, when first studying a science, say bacteriology, must try to find out the meanings of all these new technical terms with which they are faced. In this way, they really learn the definition 'from the left to the right', substituting, as if it were an essentialist definition, a very long story for a very short one. But this is merely a psychological accident, and a teacher or writer of a textbook may indeed proceed quite differently; that is to say, he may introduce a technical term only after the need for it has arisen.

So far I have tried to show that the scientific or nominalist use of definitions is entirely different from Aristotle's essentialist method of definitions. But it can also be shown that the essentialist view of definitions is simply untenable in itself. In order not to prolong this discussion unduly, I shall criticize two only of the essentialist doctrines; two doctrines which are of significance because some influential modern schools are still based upon them. One is the esoteric doctrine of intellectual intuition, and the other the very popular doctrine that 'we must define our terms', if we wish to be precise.

Aristotle held with Plato that we possess a faculty, intellectual intuition) by which we can visualize essences and find out which definition is the correct one, and many modern essentialists have repeated this doctrine. Other philosophers, following Kant, maintain that we do not possess anything of the sort. My opinion is that we can readily admit that we possess something which may be described as 'intellectual intuition'; or more precisely, that certain of our intellectual experiences may be thus described Everybody who 'understands' an idea, or a point of view, or an arithmetical method, for instance, multiplication, in the sense that he has 'got the feel of it', might be said to understand that thing intuitively; and there are countless intellectual experiences of that kind. But I would insist, on the other hand, that these experiences, important as they may be for our scientific endeavours, can never serve to establish the truth of any idea or theory, however strongly somebody may feel, intuitively, that it must be true, or that it is 'self-evident'." Such intuitions cannot even serve as an argument, although they may encourage us to look for arguments. For somebody else may have just as strong an intuition that the same theory is false. The way of science is paved with discarded theories which were once declared self-evident; Francis Bacon, for example, sneered at those who denied the self-evident truth that the sun and the stars rotated round the earth, which was obviously at rest. Intuition undoubtedly plays a great part in the life of a scientist, just as it does in the life of a poet. It leads him to his discoveries. But it may also lead him to his failures. And it always remains his private affair, as it were. Science does not ask how he has got his ideas, it is only interested in arguments that can be tested by everybody. The great mathematician, Gauss, described this situation very neatly once when he exclaimed: 'I have got my result; but I do not know yet how to get it.' All this applies, of course, to Aristotle's doctrine of intellectual intuition of so-called essences, which was propagated by Hegel and in our own time by E. Husserl and his numerous pupils; and it indicates that the 'intellectual intuition of essences' or 'pure phenomenology', as Husserl calls it, is a method of neither science nor philosophy . (The much debated question whether it is a new invention, as the pure phenomenologists think, or perhaps a version of Cartesianism or Hegelianism, can be easily decided; it is a version of Aristotelianism.)

The second doctrine to be criticized has even more important connections with modern views; and it bears especially upon the problem of verbalism. 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). 14 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.

Let us consider briefly how these two typical results of Aristotelianism have arisen. Aristotle insisted that demonstration or proof, and definition, are the two fundamental methods of obtaining knowledge. Considering the doctrine of proof first, it cannot be denied that it has led to countless attempts to prove more than can be proved; medieval philosophy is full of this scholasticism and the same tendency can be observed, on the Continent, down to Kant. It was Kant's criticism of all attempts to prove the existence of God which led to the romantic reaction of Fichte, Schelling, and Hegel. The new tendency is to discard proofs, and with them, any kind of rational argument. With the romantics, a new kind of dogmatism becomes fashionable, in philosophy as well as in the social sciences. It confronts us with its dictum. And we can take it or leave it. This romantic period of an oracular philosophy, called by Schopenhauer the 'age of dishonesty', is described by him as follows: 'The character of honesty that spirit of undertaking an inquiry together with the reader, which permeates the works of all Previous philosophers, disappears here completely. Every page witnesses that these so-called philosophers do not attempt to teach, but to bewitch the reader.'

A similar result was produced by Aristotle's doctrine of definition. First it led to a good deal of hairsplitting. But later, philosophers began to feel that one cannot argue about definitions. In this way, essentialism not only encouraged verbalism, but it also led to the disillusionment with argument, that is, with reason. Scholasticism and mysticism and despair in reason, these are the unavoidable results of the essentialism of Plato and Aristotle. And Plato's open revolt against freedom becomes, with Aristotle, a secret revolt against reason.

As we know from Aristotle himself, essentialism and the theory of definition met with strong opposition when they were first proposed, especially from Socrates's old companion Antisthenes, whose criticism seems to have been most sensible. But this opposition was unfortunately defeated. The consequences of this defeat for the intellectual development of mankind can hardly be overrated.

- Karl Popper, 1945