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Types of Definitions

Local Definitions

When we use words to communicate with people or AI, we depend on a shared understanding of their meaning. We depend on us sharing a standard definition of the words we use. The New Oxford American Dictionary is filled with these. If our understanding of the words is too different, our ability to communicate will be hindered.

There is, however, a second type of definition, which specifies the meaning of a word within a particular context—be it a particular conversation, document, or book. Since these definitions only apply to their local context, I will call them local definitions.

Local definitions have several uses. They can reduce repetition. For example, a legal contract may repeat the phrase “a natural person, partnership, corporation, estate, trust, or any legal entity” many times. By defining person to mean “a natural person, partnership, corporation, estate, trust, or any legal entity,” the contract is shortened. Unlike a standard definition, the contract’s definition makes no claim about how person is usually used. It only tells the reader to equate person with this phrase while reading the contract.

Local definitions are meant to simplify a contract without affecting its meaning. Whether a local definition accomplish this depends on how often it is used. Two uses likely isn’t enough to justify making the reader keep it in mind while reading. Ten uses likely is enough since you have shortened ten sentences. Furthermore, local definitions let the reader to separate the cognitive load of understanding a definition from understanding the sentences it occurs in. (Local definitions also help lawyers write and update contracts.)

Local definitions are also used in less formal contexts, although less explicitly. For example, an author may state, near the end of chapter two, their own definition of racism. As in a contract, the rest of the book must be read with this definition substituted for the standard one. But unlike contract lawyers, authors may hope their definitions become standard.

Local definitions, especially ones that redefine words, can cause confusion. Quotations are easily misunderstood if an unaware reader substitutes the standard definition for the author’s intended local one. This confusion can be avoided by using new words, or by using longer, more precise phrases, instead. But both alternatives have shortcomings. New words are hard to remember, and phrases get tiresome. The latter problem may be evident in my use of the phrases local definition and standard definition.

Right and Wrong Definitions

A local definition can’t be wrong. It can only be useless—too precise, too general, or too confusing. Words that are too specific to be useful for most of us, may be useful for specialists. Sailors will need nautical terms and botanists botanical ones.

A standard definition, on the other hand, can be wrong if it’s not what people usually mean by the word. Language purists may have other reasons why a definition is wrong, but I think they’re usually born out of frustration that standard definitions can shift over time.

These language shifts are one reason that Shakespeare is hard to understand. It is also one reason it is hard to know what people usually mean. Word use also varies geographically, which is why there are British dictionaries and American dictionaries. Even two same-aged Americans will use words differently.

Despite these complexities, whether a standard definition is correct is a question of averages. What does the average American mean when they use racism? This question is hard, but not impossible, to answer. To do so, dictionary writers collect billions of American sentences to analyze how, and how often, words are used in them. They also track how word use changes and update their definitions accordingly.

Sometimes words have competing definitions. This can occur for political reasons, but it is also common among academics. Ten out of fifteen of the professors in a niche prefer one definition and the other five another. When they publish, local definitions are given to avoid confusion. “I’m using Johnston’s definition of the word.” Nobody outside their niche needs such a specific word, so nobody else cares.

Circular Definitions and How We Learn

As we mentioned earlier, local definitions can usually be removed by substituting the words with their meanings. This is not true for standard definitions.

Standard definitions, and the dictionary, give speakers and authors a dependable bag of meanings to rely on. They can use these words without bothering to give definitions. This is convenient, since definitions are usually boring. Tell me what you want to say! But the standard definitions are more than just a convenience, they are unavoidable. It would not be possible to provide formal definitions for all words used, since how could one provide the first formal definition before any other words were written? This unavoidable recursion ties back to how we learn language—by example! Once we have learned the core of the language by examples as a child, we may learn new words by only definitions, but the core of our understanding of the language is not formally defined. Thus legal documents and technical standards that include formal definitions must define them with standard definitions.

Similarly, mathematical texts use words to provide meaning to their axiomatic symbols.

Words are like mathematical models used by engineers and scientists. The simplest model that accurately describes the portion of reality that is of interest is often the best. Analogously, we often use words in ways that are precise enough to accomplish the task we need them too. Everyday conversations tend to use simpler grammar and vocabulary because simpler tasks are being accomplished.

Words that are too broad or too narrow are not useful. When no common words provide detailed enough models for the area of interest, specialists develop lingo.

Precise Definitions

When two people converse, each assumes the other is using the same standard definitions; if they aren't, they may not understand each other. While true, every day communication works well most of the time despite people being unable to precisely define the words they use. Why is this?

It is difficult to define words. recursive, and only as precise as they need to be for their common uses.

The contextual nature of words is best illustrated with examples: When a veterinarian asks whether a recently sedated dog is conscious, we know they are asking if the dog is a awake. When a contemplative person asks whether a dog is conscious, we know they are asking if the dog's mind is somehow like a human's mind. When a botanist is told by their friend to “turn right after the fourth tree,” they know when to turn, despite the second and third plants being shrubs. Words can be used in several ways. We infer the appropriate use from context.

The more fundamental problem with definitions is that they are recursive. A dictionary contains these two definitions recursive definitions:

If words are defined with other words, where does meaning come from?

I think that the meaning of abstract words like consciousness is built up from more concrete words in a huge web of definitions.

At the lowest level, the meaning of words comes directly from association with our sensory inputs and motor outputs. Thus, meaning bubbles up from the concrete uses at the bottom, to their more abstract uses at the top.

The more abstract a word is—that is, the more separate from material reality a word is—the less likely a precise definition can be given for the word.

Recursive definitions are especially problematic during abstract philosophical discussions. I have had heated conversations resolve after someone defines their words and we realize we had been agreeing all along!

I think this is one of the reasons why many philosophical treatises begin by defining their terms. Philosophical definitions are different than the definitions we find in a dictionary. A formal definition is an intended equivalence between a word and other words.

Definitions and Politics

Words and their definitions do not exist in isolation; definitions can have ethical and political implications. When this is the case, people often will say a definition is wrong even though it may be what people usually mean by the word. For example, people say things like “we should change how we define beauty to be more inclusive.” This statement is not saying the definition of beauty is wrong because it is, empirically, not what people usually mean by the word beauty. Rather, they are saying the word is wrong because it leads to unethical behavior.

What makes a better understanding of words useful?

Shared definitions are only as precise as they need to be for how they are used
Most tasks in everyday life don't require much precision
Specialists (lawyers, scientists, etc.) often require more precision, hence lingo
Many traditional philosophical problems appear to be caused when definitions are pushed too far
Words are recursively defined
Concrete meaning stems from underlying reality

Does language dictate how we think, or does how we think dictate language? Are the categories defined by words as such because the categories exist in reality, or do we project the (arbitrary) categories in our words onto the world? Likely, dictation occurs in both directions in differing degrees for different words; more concrete words would seem to be more tied to reality, and our language thus more dictated by thought, while abstract ideas may be more dictated by our words.

For example, what is the distinction between a philosophy and a religion? Since I considered stoicism to be a philosophy, it took me a while to notice and comprehend the religious components of Marcus Aurelius' work. If the categories in my head, of philosophy and religion, were different, my understanding of stoicism may not have taken so long to acquire.