What makes a ball roll?

“What kind of question is that?” you might ask. Isn’t that self-evident? Pushing it or kicking it is the obvious answer. And what makes a ball bounce? Dropping it to the floor or kicking it through the air, obviously. What makes a ball do other strange things, such as deflating? Pricking a ball with a needle would do the trick. But what could possibly make a ball sing? I will return to this question later – although the obvious answer is that balls don’t sing.

I much appreciate David Harriman’s book The Logical Leap, and I appreciate Leonard Peikoff’s lecture series on which the book is based.[1] I know too little about physics or about the history of science to be able to judge the objections that have been raised by John McCaskey; but I do know what makes balls roll and what makes paper burn and many other examples of “first-level generalizations”. I write this mainly to test my own understanding.

Harriman writes:

A toddler, say, pushes a ball and it rolls away. How do we formulate (in adult, conceptual terms) what the child actually perceives here without benefit of language? Here are three formulations: “I rolled the ball by pushing it”; “My pushing it made the ball roll”; “I caused the ball to roll by pushing it”. (The Logical Leap, p. 22.)

Let me take this one step further. The toddler may go to the beach and observe that the ball rolls slower on sand; and he may take the ball into the water and observe that it does not roll at all on water; he has to push it constantly to make it move at all. Does this invalidate his initial generalization? Certainly not! What he has to do with his first “first-level generalization” is merely to modify it in view of the wider context. This is how knowledge grows.

Harriman himself has another example to demonstrate the same point:

A child learns, for example, that pushing a ball makes it roll. Later he discovers that this does not happen if the ball reaches a certain weight, or if it is glued to the floor, or if it is made of iron and sitting on top of a strong magnet. None of this overthrows the initial first-level generalization. On the contrary, the latter is necessary for anyone to consider subsequent qualifications. One cannot reach or validate “Pushing moves a ball only under X conditions” until one has first grasped the elementary fact that “pushing moves a ball”. (P. 20.)

One can take other examples to illustrate the same point. (Of course, they are all very “childish”.) Take the example that fire makes paper burn. The toddler may observe this only to later observe that if one puts a soaking wet newspaper into the fire, it does not catch fire or at least takes longer to catch fire. This does not invalidate the toddler’s knowledge; it expands it; he knows it does not apply the same way to wet paper as it does to dry paper. (The same would go for wood: the dryer the wood, the more easily it catches fire.)

Or take the first-level generalization that water extinguishes fire. It does not take too long to realize that the amount of water and the size of the fire are important factors here. A small fire may be extinguished by a glass of water, but a big fire would not.

Some mistakes may be possible even on this very elementary level. Say the toddler mistakenly makes the generalization that liquid (any liquid) extinguishes fire. He is in for a very unpleasant surprise, if he tries to extinguish a fire with petrol. (Admittedly, this is a rather contrived example.)

But back to the question of singing balls. Balls don’t sing. So what could possibly make it sing? Well, this is what Travis Norsen writes in his Amazon review of Harriman’s book:

But take another example: say, a ball (containing batteries and appropriate electronic circuitry) that, when squeezed, plays a little song. Now, there is some sense in which a child who squeezes this ball and hears the song is perceiving causation: he is perceiving an entity acting in accordance with its identity, and that, according to Objectivism, is what causality is. But here, it seems to me that — unlike the case of the rolling ball — the specific features of its identity which underwrite the action in question are not relevantly available in perception. So presumably it would be wrong for a child to generalize, in this case, to “balls sing when you squeeze them” or just “balls sing” for short.

Is this a valid counter-argument? I don’t think so. It is even more contrived than the petrol example I gave above. Why on earth would anyone construct such a ball (or such an argument, for that matter)? In order to fool little kids into making the false generalization that “balls sing when squeezed”? Well, even if one were to succeed in fooling some kid this way, the kid would soon correct his mistake: he would encounter several balls that don’t sing at all when squeezed, and he would realize this was a very exceptional experience.

I asked Harriman on his blog what he thinks about this counter-example, and he answered:

What would a toddler’s response be to a ball that sings when he squeezes it? The child would laugh with surprise, because he knows that squeezing doesn’t cause singing. Anyone who can’t see the difference between the pushing/rolling example and the squeezing/singing example has spent too much time with professors and not enough time with children.

I agree.

And for another example of what kinds of misunderstanding surround this book, see A Weird Confusion about Concept Formation.


[1]) I have some serious disagreements with Leonard Peikoff, above all his unjust treatment of me. But I have to admit he has done a good job on the issue of induction.

Induction in Economics

A very preliminary remark

The first part of this essay is a Facebook note I wrote some months ago; the second part is added now.

Ludwig von Mises – the “dean of Austrian economics” – maintained that economics is a purely deductive (even “aprioristic”) science, and that induction has no role whatsoever to play in economics. An illustrative quote:

Reasoning is necessarily always deductive. This was implicitly admitted by all the attempts to justify ampliative induction by demonstrating or proving its logical legitimacy, i.e., by providing a deductive interpretation of induction. The plight of empiricism consists precisely in its failure to explain satisfactorily how it is possible to infer from observed facts something concerning facts yet unobserved. (Ludwig von Mises, The Ultimate Foundation of Economic Science, p. 21.)

This view obviously clashes with Objectivism. One may excuse Mises on the grounds that he had no opportunity to read David Harriman’s The Logical Leap, which explains the relationship of induction to deduction. However, Harriman’s book deals only with induction in physics and the closely related subjects of astronomy and chemistry (and in philosophy). So I will make an attempt to apply what Harriman writes to economics. It will be only an attempt.

The basis of induction is sense perception. And what is perceived by the senses are actually some simple and basic causal connections. For example, a toddler may observe that when he puts a newspaper into a fire, it will burn. (If the newspaper is damp, it will burn slower.) If he puts his hand into the fire, it will hurt. If he pours water on the fire, the fire will go out. Etc. (Anyone could find other examples.) What the toddler is actually perceiving is causal connections (“fire causes paper to burn” or “my hand to hurt”, “water causes the fire to go out”). Those generalizations are at the bottom of more advanced identifications of causal connections (such as “gravity is the cause of tides and of many other phenomena”).

Is there a similar perceptual starting point for economics? Are there causal connections in economics that a toddler could see with his own eyes? That is the question I will try to answer.

Every science must start with some basic concepts – and the process of concept formation is an inductive process, while the process of applying a concept, once it has been formed, is a deductive process:

[T]he process of forming and applying concepts contains the essential pattern of two fundamental methods of cognition: induction and deduction.

The process of observing the facts of reality and of integrating them into concepts is, in essence, a process of induction. The process of subsuming new instances under a known concept is, in essence, a process of deduction. (Ayn Rand, Introduction to Objectivist Epistemology, p. 28.)

What concepts are basic in economics? There are many, but two that I can think of off-hand are “money” and “exchange”.

A toddler can form the concept “money” by merely observing coins and/or notes. (He would have to learn from some adult that those mysterious little things are called “money”; and it is hardly immediately evident why both coins and certain pieces of paper are both subsumed under the concept “money”; but he will learn that later on.)

What about “exchange” and its relation to “money”? Well, the toddler may accompany his father (or mother or some adult) to a store and observe that his parent passes a coin or note to the store owner, and that this has the peculiar effect of making the store owner pass a bottle of milk (or whatever) to the parent. He is observing an instance of causation, just like when he observed that fire burns paper (etc). It is still mysterious to him exactly what the causal connection is (does the money cause a bottle of milk to pass over, or is it the bottle of milk that causes money to pass over? It may take the toddler some times to understand that this is a case of “reciprocal causation” – and of course that there are other underlying causes yet to be discovered.)

And I have to stress that this is a very preliminary remark. More work has to be done.

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To show that Mises took a Kantian approach, let me quote the following:

A new epistemology of rationalism aimed at the refutation of this [John Locke’s] integral empiricism. Leibniz added to the doctrine that nothing is in the intellect that had not previously been in the senses the proviso: except the intellect itself. Kant, awakened by Hume from his “dogmatic slumbers”, put the rationalistic doctrine upon a new basis. Experience, he taught, provides only the raw materials out of which the mind forms what is called knowledge. All knowledge is conditioned by the categories that precedes any data of experience both in time and in knowledge. The categories are a priori; they are the mental equipment of the individual that enables him to think and – we might add – to act. As all reasoning presupposes the a priori categories, it is vain to embark upon attempts to prove or to disprove them. (The Ultimate Foundation of Economic Science, p. 11.)

So, for Mises, economics rests upon a priori categories not derived from experience but logically and chronologically prior to experience.

Murray Rothbard is actually better (and closer to Objectivism) on this point:

Most writers on the 1929 depression make the same grave mistake that plagues economic studies in general – the use of historical statistics to “test” the validity of economic theory. We have tried to indicate that this is a radically defective methodology for economic science, and that theory can only be confirmed or refuted on prior grounds. Empirical fact enters into the theory, but only at the level of basic axioms and without relation to the common historical-statistical “facts” used by present-day economists. (America’s Great Depression, p. 81; emphasis added.)

So, in Rothbard’s view, at least the basic axioms of economics are derived from experience; which is actually an advance over Mises.

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PS. I should mention that David Harriman actually takes up the very same objection to induction that Mises writes about. Here is a short quote:

As a rule, the attempt to validate induction has taken the form of attempting to reduce induction to deduction. (The Logical Leap, p. 30.)

The Logical Leap itself is an attempt to validate induction inductively. But I won’t go further into that, because you can always read the book.

Some less preliminary remarks

There is one large difference between the natural sciences (such as physics) and the humanities or social sciences (such as economics). It is not hard to grasp this difference, but it needs to be pointed out.

In the natural sciences, experimentation is crucial. The heroes of natural sciences, such as Galileo and Newton (and later, Faraday and Maxwell) performed lots of experiments. Characteristically, in experimentation, one keeps one factor constant and varies some other factor to note what difference this makes.

But in economics and the other social sciences, there is no such thing as experimentation. This, by the way, is a point that Mises stresses over and over again. But this means that the inductive method Harriman describes in The Logical Leap cannot be “translated” into the social sciences.

(Some people undoubtedly try to make experiments in the social sciences. There is much talk about the “communist” or “Soviet” experiment. But we certainly know today – and should have known from the beginning – that those experiments with human life simply end up in total disaster.)

The only kind of experiments one can do in the social sciences is “thought experiments”. Mises, for example, uses “imaginary constructions” (such as “the static state” and “the evenly rotating economy”.) Those imaginary construction have no counterpart in reality; they are merely used as aids to thought; reality can be compared to those imaginary constructions.

A similar case may be found in George Reisman’s Capitalism. He starts out with the assumption of invariable money, something that simply does not exist in reality. But having analyzed what would happen under invariable money, he then adds in what would happen under a gold standard, and then what happens under fiat money.

The way Mises and Reisman uses this deductive method is perfectly sound. But there is a grave danger with it, if one confuses those imaginary standards with reality or makes them the standard for judging reality. This is most readily seen in the idea of “pure and perfect competition”. There is no such thing in reality; but the adherents of this theory think this is how reality should be and recommend policies on this basis. The result, as I am sure you all know, is antitrust legislation. (The “pure and perfect refutation” of this theory is contained in Reisman’s essay Platonic Competition, included in Capitalism, p. 430ff.)

To summarize, I do not think induction plays the same crucial role in economics as it does in physics. But to say that economics is only deduction (as Mises says when he calls the subject “aprioristic”) is going too far; the simple, basic concepts used in economics have to be formed inductively (if for no other reason because concepts are never formed deductively; they can only be applied deductively).

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Now, there are a couple of schools of economics that claim to be using induction and shun the deductive approach to the subject. The best known of those schools is the “German Historical School”. This school objected to classical economics on the grounds that it was “too abstract”, that the theorems of the classical school were divorced from reality, and that the proper way of approaching the subject was meticulous historical and statistical studies. The proponents of this school are also known as the “socialists of the chair” (“Kathedersozialisten”). The errors of this school are thoroughly dealt with by Menger and Mises (the seminal work on the subject being Menger’s Investigations into the Method of the Social Sciences).

Another such school is the “English Historical School”. With this I am not familiar; but I will quote a couple of lines from Wikipedia on this school to show where it leads:

They rejected the hypothesis of “the profit maximizing individual” or the “calculus of pleasure and pain” as the only basis for economic analysis and policy. They believed that it was more reasonable to base analysis on the collective whole of altruistic individuals. (Italics mine.)

Both those schools actually reject economic science altogether. They do not attempt to ground economic theories in perceptible reality; they aim to replace economic theory with history and statistics. If this is an inductive approach, then it must be an improper form of induction.

To try to integrate economic history with economic theory would be a worthy undertaking. But it would have to consist of applying sound (Austrian or Austro-Classical) economic theory to history, not the other way ‘round.

I will give the last word to Ludwig von Mises (unfortunately, I don’t remember the source for this quote):

Facts don’t speak; they have to be spoken about by a theory.

A Weird Confusion about Concept Formation

(This is another blog post I write mainly to get something off my chest.)

A former friend and “comrade-in-arms” of mine, Henrik Unné, has written an extremely negative review on Amazon of David Harriman’s The Logical Leap. (He has also posted it on his own blog.) The gist of Henrik’s criticism is that Leonard Peikoff and David Harriman have departed from Ayn Rand’s own writings on concept formation. (He draws out some implications of this with regard to the future of the Objectivist “movement”, but for the moment I will focus on the issue of concept formation.)

Here is what Henrik writes:

Ayn Rand stated clearly in her seminal work on Objectivist epistemology – titled Introduction to Objectivist Epistemology – that only concepts of entities could be first-level concepts. There is no way that Ayn Rand can be taken, by anyone who is both honest and can attach meanings to words, to have admitted even the possibility that concepts of actions or concepts of metaphysical abstractions could be first-level concepts.

Yet David Harriman writes, on page 19 of TLL, – “A first-level generalization is one derived directly from perceptual observation, without the need of any antecedent generalizations. As such, it is composed only of first-level concepts; any form of knowledge that requires the understanding of higher-level concepts cannot be gained directly from perceptual data”. Later, on page 22, Dr. Harriman presents a concrete example of a first-level generalization – “A toddler, say, pushes a ball and it rolls away. How do we formulate (in adult, conceptual terms) what the child actually perceives here, without the benefit of language? Here are three formulations: `I rolled the ball by pushing it’; “`My pushing it made the ball roll’; `I caused the ball to roll by pushing it.'”

Now, all this means that Dr. Harriman claims on page 19, that first-level generalizations are composed only of first-level concepts. Yet, on page 22, he claims that “I caused the ball to roll by pushing it” constitutes an example of a first-level generalization. So, according to Dr. Harriman, such concepts as “roll”, “pushing” and “caused”(!) are first-level concepts!

This is a brazen contradiction of a position which Ayn Rand herself took in a question which belongs to the science of philosophy. Ayn Rand was very clear in ITOE – her conviction was that only concepts of entities could be first-level concepts. And Dr. Harriman is equally clear in his book TLL. He holds that even concepts of actions (such as “roll”) and concepts of metaphysical abstractions (such as “caused”) can be first-level concepts.

Well, Dr. Harriman is free to disagree with Ayn Rand on any philosophical issue he wishes to. But then he has no right to call himself an Objectivist any longer. Ayn Rand insisted on her “property right” to the “brand-name” Objectivism. She created Objectivism. Objectivism is her philosophy. Nobody else has a right to call his philosophy “Objectivism” – if is something other than Ayn Rand’s philosophy. Because it is in fact not “Objectivism” if it is something other than Ayn Rand’s philosophy.

The issue here is honesty. If anyone holds a philosophy which is not Ayn Rand’s philosophy, then that philosophy is not Objectivism. And if that person then proceeds to claim that he is an “Objectivist” nevertheless – then he is, strictly speaking, lying (unless he does not know what he is talking about – in which case he is “merely” shooting his mouth off).

Henrik here saddles Ayn Rand with a manifest absurdity. Let me try to explain:

Here is what Ayn Rand actually writes in ITOE:

The first concept man forms are concepts of entities – since entities are the only primary existents. (Attributes cannot exist by themselves, they are merely the characteristics of entities; motions are motions of entities; relationships are relationships among entities.)

In the process of forming concepts of entities, a child’s mind has to focus on a distinguishing characteristic – i.e., on an attribute – in order to isolate one group of entities from all others. He is, therefore, aware of attributes while forming his first concepts, but he is aware of them perceptually, not conceptually. It is only after he has grasped a number of concepts of entities that he can advance to the stage of abstracting attributes and forming separate concepts of attributes. The same is true of concepts of motion: a child is aware of motion perceptually, but cannot conceptualize “motion” until ha has formed some concepts of that which moves, i.e., of entities.

Yes, she says that concepts of entities are the first concepts to be formed by a child. (And I think that anyone who has a toddler of his own can verify that such is the case.) But does she say that only concepts of entities are first-level concepts? No, she does not. All she says is that concepts of attributes, motions and relationships come slightly later. (I believe that a study of language development in children would verify this, too.)

So, what is actually the difference between a “first level” concept and a “higher level” concept? Well, higher level concepts are formed by “abstraction from abstractions”. First level concepts are not – which leaves only one possibility: that they are formed directly from sense perception. Some examples:

With regard to entities, I can simply use Ayn Rand’s own example: One would have to form the concepts “table”, “chair”, “bed” (and, perhaps, some more), before one could form the concept “furniture”. Or one would have to form some concepts like “dog”, “cat”, “horse”, “bird”, “snake”, before one could form the concept “animal”.

What about attributes? One example should suffice: One would have to form the concepts “red”, “blue” “yellow”, “green”, before one could form the concept “color”.

And what about motions? A toddler would first form some concepts like “walking”, “running”, “swimming”, “flying”, “riding” in order to arrive at some higher level concept, such as “transportation” or “locomotion” (or, simply, “motion”).

This is pretty straightforward, don’t you think? But on Henrik’s interpretation of ITOE, a concept like “blue” or “walking” are formed by a process of abstraction from abstractions! I don´t know what to say about this, except that it is ludicrous.

Was Ayn Rand not clear enough in ITOE? The book was written in 1966. How could she possibly have foreseen that such a weird misinterpretation of her words would crop up in 2011?

(David Harriman himself has answered this kind of objection in a blog post called What Do We Mean by “Level” in Epistemology? So perhaps my blog post was unnecessary.)

Update December 2011: Henrik has now removed his post on his own blog, but it is still on Amazon.