Two Observations on Definitions

Adapted from a Swedish blog post.

The purpose of a definition is to distinguish a concept from all other concepts and thus to keep its units differentiated from all other existents. – Ayn Rand, Introduction to Objectivist Epistemology, the first page of the chapter “Definitions”.

There are cases where correct definitions are extremely important and wrong definitions create havoc. There is for example all the difference in the world whether one defines “capitalism” as “a social system based on the private ownership of the means of production” or “a social system based on exploitation of the working people”. Another example is the concepts “inflation” and “deflation”; if one defines those concepts as “rising/falling prices” rather than “expansion/contraction of the money supply”, one gets completely wrong. [1]

And if you define “selfishness” as “trampling on other people” rather than “concern with one’s own interests”, you of course get completely wrong (it implies that there is no other way of concerning yourself with your own interests than precisely trampling on other people, i.e. that “man is man’s wolf”[2]).

And if one introduces a new concept, it is of course important that one defines if, so that people know what one is talking about.

But does this mean we have to define every single word we use or every single concept they stand for? If so, we would never have time for anything else!

Words/concepts on the lowest level of abstraction – i.e. those that stand for concrete, observable things, attributes/properties and relationships – are formed ostensively: one simply point at a table or something blue or something standing on a table or under or beside a table (for special relationships), and that is enough. They can be defined (as Ayn Rand does with “table” in her book), but it is not necessary and would be a waste of time, if one does it for every word on this level of abstraction.

The moral of this is: Don’t belabor your brain with “definition exercises” – except when it is necessary!

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A definition consists of a genus and a species. What differentiates one species from others under the same genius is called “differentia”. A genus may be on a lower or a higher level of abstraction. Genus for “table”, for example, is “piece of furniture”, and then “man-made object”, and finally “object” or “entity” in general. Genus for “dog” is “animal” and then “living organism” (or just “organism”, since all organisms are alive until they die) and finally “entity” again. (One could put “mammal” between “dog” and “animal”, but this is a concept a child does not form until it has learned some biology in school.) Genus for “blue” is “color”, and genus for “color” is “attribute” or “property”.

Now observe one thing: Genus in a definition is always, grammatically, a noun. The species also is often a noun, but also often an adjective (e.g. “blue” and all the other colors, while “color” is a noun). No problems this far.

But what about other parts of speech?

Take interjections – such “oh!”, “ouch!”, “hooray!”, “damn it!”, etc. What is the genus of those words and expressions? There is no interjection that is more abstract than other interjections. And what do they actually mean? “Oh!” expresses surprise, “ouch!” expresses pain or displeasure, “”hooray!” expresses pleasure or approval. To that extent they perform the same function as all other concepts: they condense information. But a definition in terms of genus, species and differentia cannot be given. (And what measurements are omitted? Well, the degree of pain or pleasure/displeasure and approval/disapproval.)

Someone will of course object and say that one may define those words precisely as interjections. But the word “interjection” is not an interjection; it is a noun! So this “definition” is not a definition, but a description of the grammatical function of the word/concept.

Adverbs I have written about before, but let me say something about them again. An adverb does not have another adverb as its genus. Take those small words that we fill out our language with, both in speech and in writing, such as “well”(or “why” in certain expressions, such as “Why, this was odd”)[3]. What on earth[4] would be a more abstract adverb that subsumes them? And if one defines them as “adverbs”, this is merely a “grammatical definition”; one does not define them, but gives a description of their grammatical function.

The best definition of “adverbs” I can come up with is that they are modifiers of qualifiers: they modify or qualify another word, a clause or a sentence. (The same is true of adverbial phrases.)

The words “yes” and “no” are sometimes classified as adverbs, sometimes as interjections, and sometimes as either-or, depending on context. (This seems to depend on what dictionary one is consulting.) I personally would reject calling them adverbs, since they do not modify or qualify anything; they merely confirm or deny something someone has said or written. The best definition was given in a Swedish grammar book, which classifies them as a sub-group under interjections and calls them “answering words”. But the point here is that there is no “answering word” that is more abstract and may serve as genus; the definition “answering word” is merely a description of a grammatical function.

The same is true of other parts of speech. The is no more abstract preposition to subsume other prepositions, no more abstract conjunction to subsume other conjunctions; but their grammatical function is easy to describe.

Verbs can actually be defined in terms of more abstract verbs. The genus for “walk”, “stroll”, “jump”, “gallop”, etc. may be “move”: the genus of “stand”; “sit”, “lie”, etc. could be “be in a certain position” (although there seems to be no single word for this concept).

Bur then there are auxiliary verbs. Examples are “do/does/did”, “have/had/had” “will/would”, “shall/should”, “may/might” and many more. Those words/concepts again can only be “defined” by describing their grammatical function.

And there are such words as the infinitive marker “to” and the word “it” in phrases like “It is raining (or snowing or whatever). What is this “it” that is raining of snowing?

Don’t wreck your brains too much over this issue! It is enough that I have wrecked my own brain over it.

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PS November 15: There is a simpler way to explain all of this:

There is a difference between defining the thing and defining the word. The thing we call “table” is defined by giving the common, essential characteristics: a flat surface, one or more supports, the function (to put other, smaller objects on it) and omit non-essentials (such as whether the table is made of wood or some other material); and it is easy to state its genus, “furniture” or “piece of furniture”. But the word “table” is defined as a noun, and the wider concept subsuming nouns is “part of speech”. And a part of speech certainly isn’t a piece of furniture, nor vice versa. We may then subdivide “noun” into e.g. countable or uncountable and say that “table” is a countable noun, as opposed to e.g. “water” or “money” or, for that matter “furniture”. We may talk about its syntactic function; it may appear as either the subject or the object in a clause or sentence. Adjectives and pronouns can also be analyzed this way.

But with adverbs, conjunctions and interjections we cannot give a definition in terms of genus and differentia – for there is no thing¸ no object or entity, or any attribute, quality or property, to define. But the words can always be defined in terms of parts of speech.

What about prepositions? The simplest propositions (such as “in”, “on”, “over”, “under”, “above”, “below”, “before”, “after”) can be defined ostensively, i.e. by pointing to the relationships they stand for (like pointing to a book that is on the table, or an event that happens immediately before or after another event); but it is impossible to find another preposition that stands as the genus of those ostensive definitions. But it is very easy to define the words as “prepositions”.[5]

I have not mentioned numerals before. When we have learned the first numbers and grasped the principle of how they are formed (e.g., that “twenty one” stands for “20+1”), we understand all numbers. When we now that “a hundred” or “a thousand” stands for groups of 1000 or 1 000 of objects or other phenomena, we have no problem grasping what for example “one hundred and twenty million five hundred thousand two hundred and twenty three”. So there is no scarcity of referents in reality. But in grammar we define as “numerals”.

What I could add is that it is only the very first numerals that we can grasp and define ostensively. We can see, without having to count, that we have five fingers on each hand. If we had ten fingers on each hand, it would be much harder, maybe impossible, to see it without counting. And if we look at both hands, we do not see “ten”; we see “twice five”. (How many one can see without counting probably varies from person to person, but it can hardly be many more than five.) – Ayn Rand exemplifies this in ITOE:

… project the state of your consciousness, if I … proceed to give you [a] sum by means of perceptual units, thus: ||||||||| … etc.

Enough grammar for now!


[1]) In this case, the correct definitions go to the root cause of those phenomena, while the incorrect one only names one of the consequences of the expansion or contraction of the money supply. It is an example of “definition by non-essentials”.

To define “deflation” in terms of just “falling prices is actually even worse than defining “inflation” in terms of just “rising prices and wages”, since it leads one to confuse falling prices due to increased production (a god thing) with falling prices due to a sudden contraction in the money supply (a very bad thing). See on this this essay by George Reisman.

[2]) ”homo homini lupus” in Latin.

[3]) Those “small words” differ a lot from language to language. Some of the examples I gave in my Swedish blog post have no exact counterpart in English. And there are many such “small words” in ancient Greek (probably in modern Greek, as well). I took some ancient Greek in school, and we were advised to simply skip those words when translating.

[4]) This is another example of how different languages may differ. In my Swedish blog post, I wrote “what seventeen?” – which would be completely incomprehensible in English. We take the numeral 17 and make an adverb out of it.

[5] Possibly, one might use the prepositional phrase ”in relation to” as the genus of prepositions.

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