Concepts – formed or found?

The other day I found the following in a debate on Facebook:

Forming new concepts requires the active, volitional use of measurement-omission (remember that forming concepts is literally a volitional, not automatic process).

This was part of an answer to the following paragraph from David Kelley’s book The Contested Legacy of Ayn Rand: Truth and Toleration in Objectivism:

If someone claimed to have evidence against the law of non- contradiction, we could be sure in advance that the evidence is mistaken. If that law is not an absolute, then there is no such thing as evidence, truth, or facts. One cannot claim to know that a principle presupposed by any possible knowledge is false. Suppose, by contrast, that we found certain concepts to which the theory of measurement-omission seemed inapplicable. Here we could not take the same approach. Because the theory explains so much, we would not give it up lightly. We would first try to show that the evidence is mistaken. But we could not be certain of this in advance, as we were with the law of non-contradiction. As an inductive hypothesis about the functioning of a natural object—the human mind— the theory of measurement-omission is open to the possibility of revision in the same way that Newton’s theory of gravity was. And the same is true for the other principles of Objectivism. [My italics.]

And here is the full rejoinder:

I’d like to ask him how on earth would he “find” (pay attention to his wording, he doesn’t say “form”, he says “find”) any concept to which measurement-omission “doesn’t apply”.

Does he think that one learns about measurement-omission and goes about in life trying to “see how it fits” with already formed concepts? As if it was some hypothetical prediction that for confirmation requires us to go around and try to make it “fit in” with concepts out there in nature??

If that’s what he thinks, he’s utterly wrong. Forming new concepts requires the active, volitional use of measurement-omission (remember that forming concepts is literally a volitional, not automatic process) . We might even say that it’s presupposed by all subsequent forming (not finding) of concepts, just as he says it’s not.

Now, let me see if I can get heads or tails of this controversy.

The picture I get is David Kelley – or anybody who has read Introduction to Objectivist Epistemology – facing a bunch of scattered concepts. He picks one of them up and says: “This concept must have been formed by measurement omission.” He does the same with a second and a third and a forth and an n-th concept and says the same. But since every language contains literally millions of concepts (or words denoting concepts), it is hard to be sure that one will not encounter some concept that is formed by another method than measurement omission.

The upshot of this is that David Kelley does not know how to form concepts, since he has never formed one himself. He merely investigates concepts formed by others. With regard to concept formation, he is an abject second-hander. Ayn Rand had to tell him how concepts are formed.

But aren’t we all in the same predicament as Kelley here? None of us knew about measurement omission until we read ITOE. (If you did know, raise your hand and go to the head of the class.)

Speaking for myself. I have no slightest recollection of how I formed my first concepts as a young child. This may be because I, like David Kelley, is an abject second-hander with regard to concept formation, but somehow, I doubt it. (Again, raise your hand if you aren’t, and go to the head of the class.) Nevertheless, I managed to become quite proficient in Swedish (and fairly proficient in English). I learned and came to use one concept after another without giving a single thought to the measurements I omitted; and I did it quite effortlessly.

Now recall the first quote I gave:

Forming new concepts requires the active, volitional use of measurement-omission (remember that forming concepts is literally a volitional, not automatic process). [Emphasis added.]

How on earth did I learn to speak and write, if I did not actively and volitionally omit measurements? Yet, this very text proves that I did learn to speak and write.

One striking feature of man’s language development is the immense speed with which a child learns his first language – and also, how fast it moves from one level of abstraction to the next. Just one example:

Very young children do not use pronouns like “I” – they refer to themselves by their given name. But this is a very short transitional stage. And if you study children, you can certainly find more examples of this. (For example, using Ayn Rand’s own example, how long does it take for a child to move from the first level concepts “table”, “chair”, “bed”, etcetera, to the second level concept “furniture”?)

Learning a second language later in life (or a third or an umpty-first) takes more of a conscious, volitional effort. It takes more time. Some people do it with greater ease than others, but no one does it as easily as they learn their first language. Again, taking myself as an example, I took English for eight years in school; but those eight years did not make me master the language. If I master it now, it is because I have read many books in English, I have lived among English speaking people, I have written quite a lot in English, and I have made translations from English into Swedish. Now I know English well enough to see the shades of difference between English and Swedish.[1]

(I also took German, French, Latin and ancient Greek in school, and later I learned a smattering of Spanish. But I certainly do not master those languages. It is a matter of actually using the languages.)[2]

But back to measurement omission.

That concepts are formed by some characteristics being retained and others omitted is not new with Ayn Rand – what is new is that it is specifically measurements that are omitted. The “pre-Randian” idea is that the essential characteristics are retained and the non-essential or accidental ones are omitted. “Essential” here means those characteristics that make a thing what it is and separates it from all other things.

Take for example the concept “coffee”[3]. What are the essential characteristics of coffee? Well, its color – black or dark brown –, its taste – which distinguishes it from tea, milk, sugar, etcetera –, and the fact that you have to make it by pouring water, preferably boiling water.[4] What is omitted are such things as whether the beans were grown in Brazil or some other country (on the principle that they have to be grown somewhere but may be grown anywhere, within certain climatological limits). We also omit that some people take it straight, while others add sugar, milk or cream: it is still coffee, although the color may change. But the only measurement omitted is whether it is strong, weak, or something in-between.

But on Ayn Rand’s theory, only the strongness/weakness of the coffee would be significant. Or?

Let us see how Ayn Rand derives her theory:

Let us now examine the process of forming the simplest concept, the concept of a single attribute (chronologically, this is not the first concept that a child would grasp, but it is the simplest one epistemologically) – for instance, the concept “length”. If a child considers a match, a pencil and a stick, he observes that length is the attribute they have in common, but their specific lengths differ. The difference is one of measurement. In order to form the concept “length”, the child’s mind retains the attribute and omits its particular measurements. Or, more precisely, if the process were identified in words, it would consist of the following: “Length must exist in some quantity, but may exist in any quantity. I shall identify as ‘length’ that attribute of any existent possessing it which can be quantitatively related to a unit of length, without specifying the quantity.”

But no child goes through this rigmarole – certainly not with every new concept it forms or encounters. Ayn Rand, of course, is aware of this, so she continues:

The child does not think in such words (he has, as yet, no knowledge of words), but that is the nature of the process which his mind performs wordlessly. And that is the principle which his mind follows, when, having grasped the concept “length” by observing the three objects, he uses it to identify the attribute of length in a piece of string, a ribbon, a belt, a corridor or a street. (ITOE, p. 11 in the expanded second edition.)

Fair enough. But how could this wordless process (which I think would take place in a split second[5]) be an active, volitional process, requiring some conscious effort – as my first quote suggests?

Chronologically, this is not the first concept a child learns (or forms, or grasps). Children learn the names (or forms or grasps the concepts) of entities first. And I think a child would learn (form, grasp) the concepts “long” and “short” before the slightly more abstract “length”.[6]

But one thing should be noted: “length” is itself a measurement concept. So of course measurements are omitted when it is formed. What else is there to omit?

But Ayn Rand’s theory is that this applies to all concepts. Her next example, with which you are certainly familiar, is the concept “table”. This is formed by noticing its shape: “a flat, level surface and support(s)”. But is “shape” a measurement? Well, one could say that a common rectangular table has four side and four corners, a triangular table has three sides and three corners, and a circular or oval table has only one side and no corners at all. And most tables have four legs or supports, but they may actually have any number of legs/supports without ceasing being tables. Tables are also distinguished from other objects by their function: “to support other, smaller objects”, but it does not matter what number of other objects.

There are countless concepts to which measurement omission certainly applies. Take emotions: the concept “anger” covers everything from mild irritation to complete rage; the concept “fear” everything from mild nervousness to dreadful anxiety, etcetera. Or take thought processes: one may think hard about a subject or barely give it a thought. Love and hatred may be more or less intense; friendships more or less close; and you may think of more examples (many, or just a few).

Or take social (or political) systems: capitalism is characterized by private property, socialism by public property. But since, in today’s world, we have neither, but mixed economies of various mixtures, there is a graduated scale from “pure capitalism” to “pure socialism”, and we speak of more or less capitalism, more or less socialism.

Now some cases that at first glance appear to be hard:

“Here” and “now”, “there” and “then” are concepts that nobody has the slightest difficulty understanding.[7] But those are either–or concepts: an event happens here and now, or it happens there and then; there is no third possibility. So unless you count “one” and “zero” (or “yes” and “no”) as a measurement, there seems to be no measurements omitted or retained.

Concepts are often compared to file folders. Ayn Rand herself writes:

Concepts represent a system of mental filing and cross-filing, so complex that the largest electronic computer is a child’s toy by comparison. (ITOE, p. 69.)

The idea is that once you encounter (for example) horses, you make a file folder marked “horse” (or “häst”, “Pferd”, “cheval”, etc., depending on your native language). All the information you will ever acquire about horses then gets stuffed into this folder. If you are a hippologist, or work professionally with horses, the folder will be quite voluminous; but – since the folder is mental – there are no physical limitations to be considered. Everything that has ever been known, or will ever be known, about horses will fit into the folder. And the folder, or concept, itself will remain the same.

Now you encounter mules, so a new folder will be created. But, since quite a lot of what we know about horses and donkeys will also apply to mules, information will be copied from their folders and stuffed into the “mule” folder. And now you encounter centaurs (highly unlikely in real life, but they exist in mythology): you will copy information from the “horse” folder and the “man” folder and stuff it into this new folder.

Neither, since the folders are mental, does it pose any problem to stuff the folders into larger folders, such as “mammal” or “animal” or “organism” or “entity”.

And an orderly filing system means an orderly mind; a filing system in disarray means a mind in disarray.

But what about the folders marked “here” and “now”? Everything that happens at some point happens here and now, so those folders would literally contain everything. Or else, those folders would be immediately emptied and all their content moved over to the opposite folders, those marked “there” and “then” – and then, those folders would literally contain everything.

But having given it some further thought (and after a good night’s sleep), I came up with the following:

When I say “here”, I can mean: here, in front of my computer (as opposed to the bedroom, the living room, the kitchen or the bathroom); or here, in my apartment (as opposed to the street outside), or here in town (as opposed to out of town), or here in Sweden (as opposed to all other countries) or here on earth. Or even here in the Solar System, here in the Milky Way, here in the universe. (Only in this last case, there is no “there” to oppose it, since there is nothing outside the universe.)

Similarly with “now”. I could mean now, this moment, or now, today, this week, this year, this century.[8]

Another hard case I thought about is prepositions. Expressions like “the cup is on the table” or “I am sitting in the room” appear to be either–or propositions: either the cup is on the table, or it is not. But what is omitted here is where on the table the cup is situated, and where in the room I am sitting. It has to be somewhere, but it may be anywhere. “To” and “from” have to be to or from somewhere, but may be to or from anywhere. “Above” and “below” do not specify the distance, but it has to be some distance. (And you can go through the rest of the prepositions yourself.)

Another hard case it interjections. What measurements do we omit, when we say “ouch!” or “hooray!” or greet someone with a “hello”. I really don’t know. But Ayn Rand states:

Every word we use (with the exception of proper names) is a symbol that denotes a concept, i.e. that stands for an unlimited number of concretes of a certain kind. (ITOE, p. 10.)

Every word, mind you. And interjections are not proper names!

Concepts perform the function of condensing information. So it may be said that “ouch!” condenses the information “it hurts”, “hooray!” condenses “I have achieved a value and fell happy about it”, and that “hello” condenses “I have recognized you and want to communicate this fact to you”. But where are the measurements omitted? Or are we to call it a measurement omitted that we have to say “hello” to some person, but may say it to any person?

And what about conjunctions – words that join clauses together in a sentence? I see no measurement in the word (or concept) “that”; all the measurements are in the clauses joined together. And what about the infinitive mark – “to” in English? It merely serves to indicate that the verb that follows is in the infinitive form. There is no “more or less” involved here. And what about the definite and indefinite articles?[9]

Verbs (which denote concepts of actions/motions or states) do involve measurements omitted – for example, “walk”, “run”, “swim”, “fly”, which do not specify the speed; or “sit”, “stand”, “lie”, which do not specify the length of time. But what about auxiliary verbs – such as “do” in this very paragraph[10], or “have” in “I have said it before”, or “is” in “he is running” – which perform only a grammatical function?

And do those words – that have a merely grammatical function and have no meaning outside their grammatical context – stand for concepts? Well, Ayn Rand said that every word (except proper names) stands for a concept. But – as Craig Biddle has pointed out – “Ayn Rand said” is not an argument.

The upshot of all this is that “measurement omission” is virtually self-evident with a concept like “length” (or “width” or “weight”), which is already in itself a measurement concept. But it becomes harder and harder with other concepts, and with some concepts it is virtually impossible.

And finally: If measurement omission is “active and volitional”, then what about all those millennia that have passed from pre-historic times, when the first man formed the first concept, up to 1966–1967, when ITOE was first published? Everybody who has formed (or grasped or learned) a concept would simply know what had been going on – so why did Ayn Rand have to write a book about it? It would be like writing a treatise on how children learn to walk – interesting, but it would add very little to our knowledge.

Ayn Rand was not the first one to write about concepts, but she was the first one to give serious attention to the formation of concepts. At least, to my knowledge.[11]

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More on concept formation in What comes First, the Concept or the Word? Or search the tag concept formation. Scandinavian speaking readers may also read Vad ska vi med begrepp till? (i.e. What are Concepts For?).


[1] One such difference is that we do not use the expression “make heads or tails of”; we use expressions such as “make some sense of”. For other examples, see my blog post on the subject.

[2] There are some people – comparatively very few – who speak around thirty or more languages fluently. One of them was HS Nyberg, who was a professor of Semitic languages at the University of Uppsala. He was reportedly speaking 28 different languages – until somebody reported that he also spoke Yiddish to his barber. Another one was Ferdinand de Saussure, the famous linguist. A third one was another Swedish linguist, Björn Collinder, who was a professor of Finno-Ugric languages. And I once met a person, who is not famous and whose name I have forgotten, who told me that if he spent two weeks in a foreign country, he managed to learn the language. To me, who can only master two languages, this sounds like magic. But there has to be an explanation of the phenomenon, although I don’t know it.

[3] I thought of this when I poured my first mug of coffee this morning (or early afternoon, rather). If you drink tea, it would not change much.

[4] I have never tried making coffee by pouring cold or lukewarm water; but something tells me it is not advisable.

[5] I assume it is instantaneous or almost instantaneous, because if a child goes through this procedure with every new concept he encounters, he would not have the time to learn very many concepts, and language development would be very slow, which it certainly is not.

[6] I think this can be verified by closely studying the language development of children.

[7] An exception is St. Augustine, who famously claimed that as long as he does not think about time, he understands it, but as soon as he starts thinking about it, or explaining it, he has no clue. (Book 11 in Confessions.)

[8] St. Augustine, by the way, got into his trouble with time by only considering the fleeting moment as “now” – a “now” that immediately passes into the past..

[9] Some languages, like Latin, do not even have those parts of speech. “To be” in Latin is just “esse”, and Latin makes no distinction between “a house” and “the house”. Ancient Greek at least has a definite article. But the modern languages with which I am familiar do have them.

[10] The “do-construction”, by the way, does not exist in other languages than English. The “have-construction”, on the other hand, is common to many languages. Latin and ancient Greek don’t have them, but use inflections instead.

[11] Plato had the idea that our concepts are recollections of a former existence in the “world of forms”. Aristotle, I believe, was the father of the distinction between “essential” and “accidental” characteristics. The medieval scholastics did write about concepts, and so did John Locke. Immanuel Kant merely pressed all concepts into his scheme of twelve categories. But no philosopher before Ayn Rand, as far as I know, addressed the issue of how concepts are actually formed.

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Implicit versus Explicit Knowledge

A Facebook note I wrote in August 2010.

I don’t know if this is of general interest; it is about my own personal struggle with some issues in Objectivism. Those who already have a perfect understanding of Objectivism might think I’m just stupid.[1]

I have a question: does “implicit knowledge” qualify as knowledge?

To give an example: the axioms of “existence” and “consciousness” are implicit in all knowledge. A child possesses this implicit knowledge from the day it is born. But he cannot express it in explicit terms until much later. The axiom of “identity” (which is actually a corollary of “existence”) is soon learned by a baby: he cannot help noticing that everything around him “is what it is and not something else” or that “everything that exists has a specific nature”. But the child cannot express this knowledge in those slightly ponderous terms. So: is it really knowledge at this early state?

Another example is concept-formation. I have been struggling lately with a puzzle: ITOE is not – or, at least not primarily – about how concepts should be formed, but about how concepts are actually formed. They are formed by observing similarities and differences between various entities, attributes and actions, and then by omitting the specific measurements (on the principles that those measurements must exist in some quantity, but may exist in any quantity).

That is pretty straightforward, so (you may ask) what is the problem here?

Well, I have tried to introspect, because if this is how concepts are formed, I should have some recollection that confirms the theory. But I don’t. I cannot remember having formed any concepts as child, much less then that I formed them by a process of measurement omission. Still, I do have concepts, and I actually (most of the time, at least) use them correctly. But I simply do not remember how I formed them in the first place. Did I form them myself, or did I simply take over concepts formed by others? (And then, how did those others – my parents and other adults – get their concepts?)

And I might ask any of you: do you actually remember how you formed your first concepts in your own early childhood?

Now, there are a couple of reasons why this recollection is so hard. One is that a man’s memory doesn’t reach that far into the past. This may vary from individual to individual – but who has clear memories from before two years of age? But the process of concept-formation and of learning one’s language begins already before this age.

But there is another reason that is perhaps even more important: consider how fast a child actually learns to speak. It does not take the child long to learn literally hundreds, maybe thousands of words (all of them standing for concepts) and to integrate them into sentences, expressing thoughts. This is very different to the fairly slow process of later in life learning a foreign language. How is it possible for a small child to painstakingly go through the process of measurement omission for each and every one of those hundreds, maybe thousands, of concepts? That is the question I asked myself without being able to supply a satisfactory answer. (I even, at one point, thought that this was “the final refutation of Objectivism”).

But, in fact, my doubts were unfounded.

No, children do not consciously and explicitly go through this painstaking process. It takes place implicitly, wordlessly and largely automatically. What Ayn Rand does in ITOE is, metaphorically speaking, putting the process under a magnifying glass.

To go back to the original question: does this implicit knowledge (with regard to both axioms and concept-formation) qualify as knowledge? The best way to put it is that it is not knowledge, but rather the starting point of knowledge.

Or is this simply unnecessary hair-splitting?

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The comments I got were fairly good, so I will quote some of them.

Carl Svanberg: What about the knowledge of how we form concepts? Is this implicit knowledge? Here I think it depends on whether you make a distinction between a skill and knowledge. You can know how to do things without being able to explain why it works. I know how to use a computer, but do not ask me to explain how the computer works because that is beyond me. I know how to cook food, but do not ask me to explain the chemistry, because that is also beyond me. I know how to use my hands, but do not ask me to explain how the consciousness, the brain, the nerves all interact and make my arms move like I want them to when I want them to. Obviously that is way beyond me as well. You can probably think of many other examples of your own.

I think this is a valid distinction. Another example is a child learning to walk. The child, of course, knows nothing of the mechanics of walking (or crawling or running); it is in the same position as the proverbial humble-bee who does not know that humble-bees cannot fly and doesn’t bother; it just flies, nevertheless.

Likewise, a small child learns the skill of talking and of thinking (inasmuch as thinking requires words) without first reading Introduction to Objectivist Epistemology in order to learn how to talk and to think.[2]

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Magnus Kempe: I think there are several distinct issues involved in your questions.

The one aspect I’m currently interested in is how a toddler is forming concepts. My 18-month daughter has recently started to use the word “sock” to designate “things we put on feet” – i.e. both what we think of as socks and shoes. She also recognizes and points at “bug” – little things that crawl or fly (and which adults try to keep out of the house? she’s a keen observer). In both cases, she’s perceived similarities (shapes, sizes, our actions with them) and differences (bugs are not large and don’t bark, nor do they belong to our supply of food; socks don’t fit on the head, nor do we drink from them) and she’s omitting a wide range of attributes or their measurements. She doesn’t know she’s doing that, but she knows what a “sock” or “bug” are. Soon enough, she’ll build on these concepts – she already knows “ant” as a species of “bug”– and she may even leave behind the first concept she formed so she can use more specific and delineated ones. None of her current knowledge is explicit; she’s not yet able to reflect on her conscious processes, but it’s still knowledge. To grasp axiomatic knowledge requires advanced generalizations and specializations, as well as introspection –so it remains implicit until all necessary epistemological steps are complete (I’m curious to see how many years it will take). […]

As a side note, learning a foreign language (as an adult) is not primarily a task of concept-formation, but understanding and automating: new words/symbols/sounds for already known concepts, somewhat different grammar rules, and idiomatic expressions. It’s not similar to how a child develops to understand the world and think.

Thanks for those observations, Magnus!

One thing I am interested in is how early in life concept-formation starts. Some years ago, I had a discussion with an Objectivist who was a grandmother [Ellen Moore]; and she told me that her grandchild at the age of 10 months could point to a dog and say “daw”. Earlier, I had thought that concept-formation starts approximately at the age of 2, when children utter their first primitive sentences. But obviously, it starts earlier than that. (Since I have no children of my own, I haven’t been able to study this in detail.)

We’ve strived to record our observations every day. I’m convinced she was forming concepts within months of birth, but it’s hard to tell what’s going on inside their mind for the first few months… We’re raising her bilingually[3] so we’ve noticed some developments and events that would possibly escape observers of a monolingual infant. I’ll try to add some notes from my records tomorrow.

I suspect that the lack of recall of memories before about 3 years old has something to do with a transition in how our mind holds concepts when we start to develop abstractions from abstractions. Until then conceptualization is intimately tied to perceived entities and their visible actions, they may not involve a visual-auditory symbol.

Thanks again, Magnus. Yes, what happens with a bilingually raised child is really interesting. They have to form (or grasp) the same concepts in two languages. And they would have to learn, at a very early stage, all the subtle differences in grammar between two languages.[4]

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Another thing that is largely implicit is the “choice to live”. You may remember this quote from “Galt’s speech”:

My morality, the morality of reason, is contained in a single axiom: existence exists – and in a single choice: to live. The rest proceeds from these.

But, except in the rare case of considering suicide and refraining from it, the “choice to live” is an implicit choice.

To take a mundane example: choosing to have breakfast in the morning. One does not explicitly go through the following reasoning: “Well, do I want to live today? Yes, I do. What do I have to do to remain alive till the evening? Well, I do need to eat something; otherwise I’ll starve. And since it is still morning, I’ll start with having breakfast.” Such thoughts are implicit in the choice to have breakfast; but one does not have to repeat them to oneself every morning.

One can make up more dramatic examples. One that I have used myself is this: You’re driving your car, and suddenly you encounter a ravine. You immediately put the brakes on. Obviously, the implicit premise behind this is that you don’t want to die. But equally obviously, you don’t go through a whole chain of reasoning, starting with the question: “Do I want to live or die?” If you did, it would be too late to put the brakes on, when you have reached the end of the reasoning![5]

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Bob Gifford: Regarding remembering how you formed concepts, have you formed any concepts recently? I mean, is it necessary to remember childhood experiences to see the measurement-omitted process work? As we go on learning, isn’t that process still going on? Part of the problem at this point is the question of measurement, I mean that in most higher level concepts, which is what intelligent, rational adults would be mostly focused upon, what the measurement is would not be obvious. You would have to dig a little, but if the concept was valid, it would be there somewhere.

The amazing thing about AR is that when she was asked about how she formed concepts she thought about it briefly and gave this answer (as I remember the story). She not only quickly recognized what she was doing but what that meant. That was the clarity of her mind.[6]

Well, I have a confession to make: I haven’t formed a single concept on my own in my whole life. I have merely taken over concepts already formed by others. Yet, I have a vast vocabulary or words, standing for concepts, in two languages (Swedish and English).

But I don’t think this is a problem for Ayn Rand’s theory of concept formation. Grasping a concept already formed by others cannot be too different from forming a totally new concept.

One of my Swedish friends [Filip Björner] recently suggested an exercise in forming a new concept. The example he chose was “blankcoin”, meaning simply a coin that is blank. But I rejected this on two counts:

  1. This “new concept” is merely a combination of two old concepts that I already understand perfectly well (“blank” and “coin”).
  2. The concept “blankcoin” is totally useless. It wouldn’t enhance my understanding of economics (or any subject) one bit.

Consider: The function and value of a coin has nothing whatsoever to do with whether it is smooth or rough to the touch. It has everything whatsoever to do with two things:

  1. The metal content of the coin. Gold, silver, copper or iron? How many carats of gold? And, of course, how large or small is the coin?
  2. The relation between the value of the coin and the value of what one wishes to exchange it for.

As Ayn Rand writes:

concepts are not to be multiplied beyond necessitynor are they to be integrated in disregard of necessity. (ITOE, p. 72.)[7]

There is no necessity about the concept of “blankcoin” (or the corollary concept of “roughcoin”) – except the alleged necessity of teaching me how to form concepts.

New concepts are formed from time to time, but they are formed by geniuses. For example, Newton had to form the concept “gravity” in order to arrive at his theory of universal gravitation. And one example from Ayn Rand (there are certainly more) is the concept “second-hander”. This, of course, uses the old concepts of “second” and “hand”; but it is still a new concept that does enhance our understanding of “what makes people tick”.

Bob Gifford: I understand your feeling that you have never formed a new concept in your life, I have felt the same way. But I don’t think it really is an issue of originality or creativity. If your knowledge is valid, that is, if you can relate it to reality, then you have personally formed those concepts and they are all new to you. It is true that for a child there may be some first time stuff, but even then, the child is learning from his parents and other people. No, if you learned a concept and integrated it into your knowledge, meaning that you have knowledge of the real world, then you have formed the concept and you have used the measurement-omitted technique. […] When you find two instances of something, important or not, make a concept, give it a name, and enjoy the experience.

I see nothing I could dispute in this comment.[8] A concept, of course, is new to the child when he grasps it. And that concept-formation is speeded up by learning from parents and other adults is a point mentioned in ITOE:

… a child does not have to perform the feat of genius performed by some mind or minds in the prehistorical infancy of the human race: the invention of language … (P. 19.)

And yes, at least two instances are needed to form a concept. In the unlikely case of a child having observed only one table, it would stand in his mind as a proper noun (“the Table”). Or take a more likely case: a child grows up in a town and has as yet no experience of other towns, or cities, or villages. In this case, he would form a proper name, “the Town” and only later proceed to form the concept “town” and distinguish it from “city” and “village”.

By the way, in the Appendix to ITOE Ayn Rand mentioned that the concept “God” (in monotheistic religions) is not even an “invalid concept”, since there is only one of them. So I thought of calling this, not an “invalid concept” but an “improper proper name”. But this is more in the nature of joke. It follows, of course, that in order to form the concept “god”, you have to be a polytheist.

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Jakob Meijling: One more thing. How does the omitting of measurements work? It works by subtraction. A child forms concepts by identifying objects and having these objects named by an adult. The child tries to memorize the name of the object. Every time a similar object is identified by the same name by the adult, the child will add this to the “concept folder” in the relevant part of the brain, and notice the differences. The differences will then be omitted, leaving only the significant characteristics needed for the concept. And this “subtraction process” will go on until your brains stop working, and you die. You can experience this process anywhere: seeing new designs at a furniture trade fair; watching birds or cars or typefaces; visiting a foreign country where all artifacts look slightly different from at home.

I’m not sure I understand this. Do you mean that the differences are subtracted? Then this is just another way of saying they are omitted. For example: A child observes two tables that are different in size; then this difference in size is omitted when the concept is formed. Or one table has a round surface, the other a square surface; then this difference in shape is omitted. Or one table has four legs and the other three legs; then the number of legs is omitted. What is retained is what makes it a table: “a flat, level surface with support(s), intended to support other, smaller objects”.

It is indeed just another way of saying they are omitted, but it says something about the process. When adults form concepts consciously, they will omit the irrelevant characteristics by logic; a child will add tens and hundreds of instances of e.g. a table, and slowly arrive at the clear concept, without ever stating explicitly what Ayn Rand did.

OK, I get it.

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Time to stop wrecking my brain on this issue and think about something else.

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See also What Comes First, the Concept or the Word? and Two Observations on Definitions.


[1] Tongue in cheek.

[2] This paragraph of course is jocular.

[3] Magnus is fluent in Swedish, English and French.

[4] Once (a very long time ago) I lived in an English-speaking community in Copenhagen. The children went to Danish schools and had no difficulty switching between English and Danish. A couple of them had German and French parents, and they easily switched between all three languages.

[5] The point I mention here is taken up by Tara Smith in Viable Values, p. 105.I quote her in my own blog post The Choice to Live. Apart from that, I have not seen it discussed by Objectivists.

[6] The story is at the tail end of the Appendix to ITOE (p. 307).

[7] Ayn Rand calls this an ”epistemological razor”. It of course bears resemblance to “Occam’s razor” – the difference being that Occam said that “entities should not be multiplied beyond necessity”. For example, one should not assume there is such an entity as God, if one can explain the world without him. (This, however, is hardly an example that Occam himself gave.)

On a more personal level, I have invented an entity called “the girl in the closet”, who is supposed to perform the household chores for me and my lady-friend. So if the bed isn’t made, or the potatoes not peeled, I blame this entity, when the simple explanation is that I was absent-minded and forgot all about it,

[8] Except that he calls it a feeling. It wasn’t a feeling, it was a thought.

What Comes First, the Concept or the Word?

Words stand for concepts. Typically, nouns stand for entities or things; adjectives for attributes or properties; numerals (of course) for numbers (ordinal or cardinal), verbs for motions, actions or states, prepositions for relationships.

Often, a noun also stands for an attribute, but then it is typically formed from an adjective – e.g., “length” from “long”, “breadth” from “broad”, “happiness” from “happy”, etc.

Pronouns are replacement words, replacing either a noun or an adjective. For example, if I say “he”, it stands for the person I am talking about, etc.

Some verbs are auxiliary – like “do” in “do you agree?” or “I do not think so”, or “have” in “what have you done?” or “what has happened?”. In this case, the verb has only a grammatical function.[1]

Adverbs, I would say, stand for modifications, qualifications or specifications – for example, the word “typically” above, which modifies the thoughts I was expressing. Or the difference between “I stand” and “I stand here”, “It happens” and “It happens now”, which specifies the standing and the happening. (There may be some better way to describe adverbs, but this is the best I can think of for the moment.)

And many adverbs are formed from adjectives, like “typically” and “happily”, etc.[2]

Conjunctions are concepts of relationships among thoughts (here, I merely quote Ayn Rand’s definition).

What about interjections, such as “ouch” or “hooray”? What do they stand for? My best guess is that they stand for some kind of evaluation. We say “ouch” to something we don’t like, and “hooray” to something we like quite a lot.

Of course, this was an extremely rudimentary grammar lesson.

In what order does a child form those concepts?

I think it is obvious that concepts of entities (represented by nouns) come first; then probably concepts of attributes (represented by adjectives) and concepts of motions or states (represented by verbs). Certainly, they come before pronouns. A young child beginning to speak does not refer to him- or herself as “I”, it uses its name. “I”, meaning “the person speaking”, and “you”, meaning “the person spoken to” are really a fairly high level of abstraction. Yet, it does not take long for a child to progress from using its name to saying “I”.

Now to the question in the blog post title.

Ayn Rand’s idea (if I have understood it correctly) is that a child perceives two of more concretes (two or more tables, two or more dogs or whatever), notices that they are similar and that they are different from other concretes, and then forms the concept “table, “dog” or whatever. But in order to retain the concept, the child has to choose a word to denote the concept. Thus, the child forms the concept and then, to complete the process, makes up a word for the concept.

But does it make up the word?

Then how come that a child born into an English speaking environment invariably choose the words “table” and “dog” for those concepts, while I, who was born In Sweden, chooses the words “bord” and “hund”, and a French child chooses “chien” for “dog”? (The French word for “table” is the same, although pronounced differently.) A German child says “Hund” for “dog”, and “Tafel” for “table”.

Now, I must have misrepresented Ayn Rand when saying the child “makes up” the words, because it clearly does not. It uses the words already existing in its own language.

But then one may still ask the question whether the concept actually comes before the word or after. Does the child form a concept “table” (for example) and then asks its parents “What is this called?”? Or does it hear the word “table” uttered by some parent or grown-up and then figure out what it stands for?

Well, both those possibilities are possible.

A child learns his first language partly by imitation. But it is not passive imitation. If it were, the child would be a parrot, not a human.

Now I will quote Ayn Rand:

Even though a child does not have to perform the feat of genius performed by some mind or minds in the pre-historical infancy of the human race: the invention of language – every child has to perform independently the feat of grasping the nature of language, the process of symbolizing concepts by means of words.

This is true for both the possibilities mentioned above.

Why do I bother to think about this?

Well, I do not remember the period in my childhood when I learned to speak (I do not think anyone remembers that far back). Thus, I do not remember forming any concepts or choosing words to symbolize them. I did not think I formed any concepts on my own; I thought I was merely taking over (in some second-hand fashion) concepts that had already been formed by others. And I did not think other people are much different from me in this regard. So I drew the conclusion that children do not actually form concepts; they are merely taking over concepts already formed. They do, however, have to grasp those concepts independently. And this grasping of concepts has to be done by the same process as originally forming them.

But I think the Ayn Rand quote above nails the issue.

And somebody must have been the first man (or woman) to form the first concept and give it a name. Somebody must have been the first to put a simple sentence together. Somebody must have been the first to add a subordinate clause to a sentence.

But how this came about, we can only speculate. It is peering into the pre-historical past.

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Another observation is how extremely fast a toddler learns his first language. I have blogged about this too, but in Swedish.


[1]) There are other words that have only a grammatical function. One example is “to” in “to be”, “to talk”, “to run”, etc. It is an “infinitive marker” and only tells that the next word is the infinitive form of the word. I may write about such words later on.

[2]) On adverbs, see also What did Ayn Rand Know about Adverbs?

What Concepts Are First Level?

(A fairly unnecessary blog post.)

A while ago I wrote a blog post called A Weird Confusion About Concept Formation (a blog post that shouldn’t be necessary, except for the fact that someone was confused about it). Someone claimed that only concepts of entities are “first level” concepts, and that concepts of attributes, motions and relationships must be “higher level” concepts. (He even invoked Ayn Rand’s authority for this view, but that was based on a misreading of her.) But in fact, a first level concept is simply one that can be formed from direct sense experience, and that is certainly the case of many concepts of attributes, motions and relationships as well.

To repeat this point with slightly different words, a simple way to determine whether a concept is first level or higher level is to ask oneself: can the concept be defined ostensively, i.e. by simply pointing to an instance of the concept?

Certainly, simple concepts like “table”, “chair”, “bed”, etc. can be defined ostensively, while “furniture” or “object” cannot. (For simplicity’s sake I am using Ayn Rand’s own examples, but you can make up your own examples, if you like.)

But this is as true about simple attributes as about simple entities or objects. “Red” can be ostensively defined simply by pointing at a red object, and “blue” by pointing to a cloudless sky. And simply by listening to a dog barking, one can ostensively define the sound concept “barking”. Same with motions: “walking”, “running” etc. are ostensively defined simply by observing someone walking or running (do I need to repeat the “etcetera”?). Same with relationships: one can ostensively define what is meant by “above”, “below”, “to the right/left of” and many others.

True, those concepts can also be given a formal, genus-differentia definition. For example, Ayn Rand herself writes:

An adult definition of “table” would be: “A man-made object consisting of a flat, level surface and support(s), intended to support other, smaller objects”. (ITOE, P. 12.)

But this adult definition is certainly not needed to understand what a table is! Furthermore, the definition contains a couple of concepts that cannot be first level: “object” and “man-made”.

The same is true of “red” and other color concepts. “Red” can be formally defined as:

Any of a group of colors that may vary in lightness and saturation whose hue resembles that of blood.

Or:

The hue of the long wave-end of the spectrum.

Or:

One of the psychological primary hues, evoked in the normal observer by the long-wave end of the spectrum. (The American Heritage Dictionary.)

But nobody needs those definitions to grasp the concept “red”! (Well, except if one is blind.) And you certainly do not need to study optics and learn what is meant by “the long-wave end of the spectrum” to form the concept “red”; quite the opposite: you have to know the colors before you can even begin to learn what a spectrum is and what it has to do with wave-lengths.

The same holds true for simple concepts of consciousness that have to be formed by a process of introspection. If you have ever been thinking about something, you know what a thought is. If you have ever experienced an emotion – anger, or joy, or even boredom – you know what anger, joy and boredom are. And if you have ever made a choice or a decision, you know what they are. (The same, of course, is true about sensations, like “pain” or “tooth-ache”. Or about sexual satisfaction. How would you know anything about this without having experienced it?)

All this is virtually self-evident. So why do I even have to write about it? Well, take it as an exercise in conceptual entertainment.

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It may sometimes be hard to determine whether a concept is first level or not. Take the concept “coin”. A child may observe two coins and see that they are similar: they are round, flat and fairly small objects. But how does he distinguish a coin from a button? Well, the coin has engravings on it; but how then can he distinguish a coin from a medal? To understand what a coin is, the child will also have to know its function: that it can be exchanged for an ice-cream or some other good. Is seeing an exchange take place also first level? I’m not sure. I think the child’s parents have to explain to him what “buying” and “exchange” are. And for that to take place, the child would have to already have advanced a bit in his conceptual development.

More on concept formation another time.

What did Ayn Rand Know About Adverbs?

The reason I ask this question is the following excerpt from Introduction to Objectivist Epistemology:

Adverbs are concepts of the characteristics of motion (or action); they are formed by specifying a characteristic and omitting the measurements of the motion and of the entities involved – e.g., “rapidly”, which may be applied to “walking” or “swimming” or “speaking”, etc., with the measurement of what is “rapid” left open and depending, in any given case, on the type of motion involved. (ITOE, p. 16f.)

If this is meant as a definition of “adverb”, it is far too narrow. Yes, it applies to the example of “walking (swimming, speaking) rapidly”; but the vast majority of adverbs in the language have nothing to do with the velocity of motion or any other characteristic of motion. Let me give some examples:

“Here” and “there”, “now” and “when” are adverbs; but they have very little to do with motion. Take the simple sentence “I sit here now (in front of my computer).” But “sitting” is not a motion, it is an absence of motion, a state of rest. Well, I sit here typing, and I can type slowly or rapidly, but the “here” and “now” still do not apply to my speed of typing, nor to how well or badly I type, or to any other imaginable characteristic of typing. They apply solely to my location in space and time: when and where do I type?.

In modern English, the words “here” and “there” signify either location (“I sit here”, “I was there yesterday”) or direction (“I came here”, “I will go there tomorrow”. – Incidentally, in Swedish we have different word for location and direction; we still make the distinction between “here” and “hither”, “there” and “thither”, which seems to have been lost in modern English.

Or take the sentence “I’m thinking about adverbs, therefore I write about adverbs”. “Therefore” is an adverb answering the question “why?”. But is it about motion? Well, maybe the motions inside my mind. – And I might as well say “I write this for a reason”. “For a reason” is not an adverb but an adverbial phrase and serves the same function as the single adverb “therefore”.

So what is an adverb? – I was taught in school many years ago that an adverb answers (or asks) certain questions, such as “where?”, “when?”, “how?”, “why?”, “to what degree?”, etc. (They don’t ask or answer the questions “who” or “what”; nouns or pronouns answer those questions.) A more precise definition (taken from a dictionary) is:

1. A part of speech, comprising a class of words that modify a verb, adjective or other adverb. 2. A word belonging to this class. (The Heritage Illustrated Dictionary of the English Language.)

Most often, an adverb modifies a verb (this is why it is called an “adverb”). It may modify an adjective, as in the phrase “she is very beautiful”, where the “very” tells you the degree of her beauty. (You may think of your own examples. If you think really hard, you will find that “hard” modifies “think”, telling you the degree of intensity of your thinking, and that “really” in its turn modifies “hard”, telling you more about how hard you think.)

“Yes” and “no” are also adverbs – at least they are classified as adverbs in the dictionaries. They answer such question as “Is this true or not” or “Do I agree with this or not.” But there connection to motion is tenuous, at the very least.

What measurements are omitted when we form a concept that is an adverb? That is fairly easy to answer. “Here” must be some place, but it could be any place. “Now” must be some point in time, but it could be any point in time. “Therefore” must be some cause or reason, but it could be any cause or reason. “Yes” and “no” must be the answer to some question, but it could be the answer to any question.

“Well” is an adverb that is often used as a preamble to a sentence (“Well, I don’t think so” or “Well, you may be right”) and may be said to modify the whole sentence rather than some single word. But here, I simply cannot put my finger on what is the exact meaning of “well”, much less then what measurements are omitted.; I have to confess it eludes me. (In Swedish we have a whole host of such adverbs – something that I think gives translators headaches.)

I hope this is enough to show that Ayn Rand’s definition is far too narrow (“far” and “too” being adverbs modifying the narrowness of the definition but having nothing to do with motion or any characteristic of notion).

The adverbs I have mentioned this far are adverbs “in their own right”, but there are also adverbs that are derived from adjectives, turning an adjective into an adverb. In English, this is done by adding a “-ly”; Romanic languages typically add a “-ment” or “mente”, and in Swedish we add a “-t”.  – Also, in those cases, it is easy to re-write the sentence and turn the adverb back to an adjective; e.g. “I think slowly”; “I am a slow thinker” or “Ayn Rand writes beautifully”: “Her writing is beautiful”. One cannot do this with “here” and “now” and those other adverbs I mentioned. – But his does not change anything in my reasoning; it is just an interesting observation.

Quibbling and nit-picking? Maybe – but I get frustrated when I discover a mistake in Ayn Rand’s writings, and I have to get if off my chest. And grammar is a subject I know fairly well.

I may return to other aspects of Ayn Rand’s theory of concept formation later, because I have some question marks that I would like to straighten out.

(For Scandinavian speaking readers, I write about this in Filosofiska smulor; you have to scroll down a bit to find it. Also, I take up some of those other question marks I have.)

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Update May 2015: Further examples:

“Yes” and “no” are adverbs (at least they are classified as adverbs in dictionaries). They perform the function of condensing information – like “I agree/don’t agree” or “It is so/not so”. But they say nothing about the speed with which one agrees or disagrees.

Even the simple “not” is an adverb; it qualifies the sentence in which it occurs.

Anyone can find further examples. Just mark all the adverbs you find in a text, look them up, if necessary, and check what they have to do with velocity. You will find that only a minuscule number of them do.

I hate to find fault with Ayn Rand, but sometimes (an adverb) I just (an adverb) have to.

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Update August 31, 2015: There is a group of adverbs that denote frequency: “always”, “often”, “sometimes”, “seldom”, “never”. (There are also adverbial phrases, such as “now and then” or “once in a blue moon”.)

What measurements are omitted when forming those questions? Well, things can happen more or less often, or more or less seldom. But there is no more or less regarding “always” and “never”.

Just a thought …

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Update October 29, 2015: I cannot get this issue out of my head. Whenever I see an adverb, I say to myself: “What on earth (or even in hell) does this have to do with speed or velocity?” (For example “whenever” in the preceding sentence.)

The issue is not important enough to occupy my mind like this. Ayn Rand makes a relatively minor mistake, and I cannot stop thinking about it.

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Update November 3, 2015: It is actually doubtful whether “yes” and “no” are adverbs. Some dictionaries in different languages that I have consulted call them “adverbs”, others call them “interjections”, and still others say they can be both, depending on context.

My own best definition of “adverbs” is that they are modifiers or qualifiers: they modify or qualify a word, a clause or a sentence. (Wikipedia agrees with me here.) But “yes” and “no” do not modify or qualify; they affirm or deny what somebody has said or written.

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Update September 19, 2016: If you do not believe me, then go through a text and underline each adverb you find. (If you are uncertain whether a particular word is an adverb or something else, then look it up in a dictionary.) I would be surprised if more than one in a thousand of them has anything to do with speed or velocity. Or underline every adverb you find that actually signifies speed or velocity; there would be very few words underlined (and leaves open what the rest of the adverbs are, if they are not adverbs).

A commenter suggested that Ayn Rand did not intend to give a definition of “adverb” but merely to illustrate the process of concept formation. Fine – but then, why didn’t she say so?

That “rapidly” or “slowly” are adverbs is undeniable. But it is equally undeniable that the vast majority of adverbs are not in this rapid/slow category.

And compare what she says about adverbs to what she says about adjectives and prepositions:

Adjectives are concepts of attributes or of characteristics.

Prepositions are concepts of relationships, predominantly [but not, I might add, exclusively] of spatial or temporal relationships, among existents. (P. 17.)

But this is true af all adjectives and of all prepositions. You would look in vain for an adjective that does not refer to an attribute or a characteristic, or for a preposition that does not refer to a relationship of one or another kind. The only mystery here is why we would need an Ayn Rand to point this out to us.

Nouns may also refer to attributes or characteristics, but almost exclusively they are formed from adjectives by adding a suffix to them – a “-ness” or a “-hood” or an “-ity”. (The only exception I can think of in English is “beauty”, where the adjective “beautiful” is formed from the noun. But if you look at the etymology, you will find that it was originally formed from the French “beau”, to which a “-ty” was added to make it a noun.)

One nit-picking objection one might raise is that a large number of prepositions are about other relationships than spatial or temporal ones – for example, “about” in this very sentence, or “from” in the paragraph above. But I do not have the space or time to go into this at length to find out what kind of prepositions are predominant; neither do I see the necessity of it.

Anyway: With regard to adjectives and prepositions Ayn Rand states something that it would be a contradiction in terms to deny; but with regard to adverbs she states something that is only true for a slight sliver of adverbs. With regard to adjectives and prepositions, she says something that everybody knows anyway; with regard to adverbs, she says something that nobody knows, for the simple reason that (in most cases) it isn’t true.

Why she did so remains a mystery to me. It is even more mysterious that none of her detractors have ever taken her to task for it.

But then, none of her detractors read her carefully. If they read her at all.