2.2: How does meaning work? Definition and Concepts

Let’s think a little bit about how meaning actually functions. How does a word like “pig” refer to actual objects in the world? What does it mean to get more or less specific? How do we determine which actions are “lying” or “cheating” and which actions are just somewhat similar but are ultimately innocent? What does it mean to put things into categories with words?

Understanding all of this a bit better can help us to understand the meaning behind the words we use a bit more clearly.

Intension and Extension

Intension

Intension is essentially the specific information that a word or phrase conveys. The more specific a word or phrase or concept, the more intension it has (the more information it gives you).

The intension of a word is basically the set of instructions it gives you for identifying what thing or things the word is referring to. So the more intension a concept or definition has, the more specific it is in that we have more information we can use to identify things that fall under the concept.

“Human Female” refers to all of the women by having meaning that applies to all and only women.

“Zebra” applies to all and only the zebras in the world, past, present, future (and maybe some zebras that are only possible, but this is complicated) by having all of the instructions contained in it necessary for us to identify which things are and are not zebras.

“Potato” has less intension than “fingerling potato” in that the group of potatoes contains the group of fingerling potatoes. There’s more information in the second one than in the first, so it’s more specific, and there’s more intension.

Extension

Extension is the set of things referred to by a word, phrase, or concept.

The extension of a word is an actual set of things in the world, past, present, and future.

“John Claude Van Damme” refers to one specific person, whereas “Mammal” refers to a great deal of things: all of the mammals. The more extension a term has, the bigger the set of things it refers to.

Zebra	has the extension:	(All of the actual zebras, past, present, and future) (and maybe all the merely possible zebras too)
Jackalope	has the extension:	(Only imaginary animals, but all of the jackalopes. Fred the imaginary Jackalope, Marisol the imaginary Jackalope, ...)

Increasing and Decreasing Intension

• Animal, mammal, feline, tiger
• Wolf, canine, mammal, animal

Mammal has more intension than animal, since you not only have to check if it’s an animal, but also have to check if it’s a mammal (if it has mammary glands and gives birth to live young, etc.) in order to see if it’s the animal you’re talking about. Still more feline is more specific and gives you more information about what specific individuals fall within the extension. Tiger is more specific still.

Wolf is very specific, canine less specific, mammal and animal are less specific still.

Decreasing and Increasing Extension

• Animal, mammal, canine, wolf
• Tiger, feline, mammal, animal

The group of things called ‘animal’ is pretty big. It’s a very small percentage of animals that are mammals, so the extension has gotten much smaller. Again a very small group of mammals are canines and even fewer are specifically wolves. So the extension is decreasing.

Tigers are a relatively small group compared with felines (house cats, leopards, panthers, etc). Mammals are a bigger group than felines and animals are a bigger group than mammals. So the extension is increasing here.

Intension and Extension are typically inversely related: the more specific you get, the fewer things you’ll be talking about. If you want to talk about more things, you’ll have to get less specific.

This makes sense, though, right?

Things you can do with Concepts

Synthesis and Analysis are words we hear all of the time, but very seldom do we get any sort of idea what they actually mean. With that in mind, during this discussion about meaning and concepts, it seems like a good idea to think about what these words mean. They are, in short, the two different things one can do with concepts. One can build up from simpler concepts to a complex concept—this is called Synthesis. One can alternatively break down a complex concept into relatively simple concepts—this is called analysis. Synthesis is bringing different elements together to form a complex. Analysis is breaking down a complex into its elements.

• Synthesis: building up to more complex concepts from simpler ones
  • If you have a state in which citizens elect officials, you have a Republic.
  • A saw that cuts using a chain blade is a chainsaw.
  • A dog that performs a service for someone with a disability is a service dog.
• Analysis: breaking down to simple concepts from complex ones
  • A Cup is: a thing, that holds liquid, for drinking.
  • A teacup is a cup used for tea.
  • A hammer is a tool used for pounding.

Who Cares?

What’s the upshot of all of this talk of extension, intension, synthesis, analysis?

This is a really basic and philosophically naïve picture of how meaning works: We have concepts that can be synthesized into more specific concepts or analyzed into less specific concepts. Concepts have two aspects to them: they refer to some set of things in the world (their extension), and they do so by having a particular meaning or sense which describes all of those things it picks out. The more specific they are, the fewer things they can refer to in the world. The less specific, the more things they can refer to. The ideal definition is one that is neither too broad nor too narrow and so has the right level of specificity.

Each problem with meaning (like vagueness and ambiguity) is a problem with the meaning of a word or phrase and so is most likely a problem with either extension or intension. Most of the time with ambiguity, a single word or phrase is linked to different intensions and so by virtue of that is linked to different extensions. With vagueness, the problem is by definition too little specificity and so a problematic lack of intensional information. It’s helpful to “look under the hood” of what is going on with vagueness and ambiguity so we can approach concepts carefully and with a bit of understanding of how they work.

Types of Definitions

Not all definitions are created equal. Some are better than others. These are just three of the questions you might ask yourself when encountering a new definition. Understanding what sort of definition it is you are dealing with can go a long way towards being able to evaluate that definition as a basically good or basically problematic definition.

Other textbooks offer a wide variety of distinctions between definitions: enumerative vs. genusspecies vs. subclass vs synonymous, and then again theoretical vs. precising vs. ... It goes on and on. It doesn’t seem strictly necessary, though, to understand each of these different kinds of definition in order to make basically good judgments about the quality of a definition. I’ve instead boiled the lot down to three basic distinctions that seem truly useful in evaluating whether you’re dealing with a useful definition or an inaccurate or useless definition.

Stipulative or Descriptive?

First, is this definition attempting to stipulate new meaning? That is, is it trying to invent a new word or use an old word in a very precise or perhaps artificial way? Or maybe it’s doing the same thing as a dictionary definition: just trying to describe the way the word is in fact used by speakers of the language.

Definition: Stipulative definitions

Stipulative definitions either define a new word or define a familiar word in an unnatural way for the purpose of an argument or theory.

• A “Hill House” is a house in the Hollywood hills.
• For the purposes of this study, when I say “justice” I’ll mean “equal distribution.”
• A “rave review” for the sake of this argument, is a review of 4 or more stars out of 5.

Definition: Descriptive definitions

Descriptive definitions are standard dictionary definitions, they attempt to describe the way a word is actually used.

• A brick is a solid rectangular object made by drying clay.
• A Bitcoin is a unit of cryptocurrency run by the Bitcoin blockchain network.
• A mother is a female primary caregiver or a bearer of children.

It would be pretty odd to open up the dictionary and find a definition like the following:

Tall: a measurement of height applying to objects the tops of which extend 6’4” or more higher than their bases.

Who put Merriam and Webster in charge of what makes a thing tall? It seems oddly specific to choose 6’4” as the objective meaning of the word “tall.” So this seems like a bad descriptive definition. What about, though, if someone said:

Okay, I want all the tall people in the back row. If you’re 6’4” or more, then you’re tall, please go to the back row so we can take our picture.

Doesn’t sound quite as unnatural to me. What do you think? In this case, it seems okay to stipulate that tall means 6’4” or more in a particular context, but it doesn’t seem okay to act as if that’s just the definition of ‘tall.’ So it seems okay when it’s stipulative, but wouldn’t be good if it was descriptive.

Too Broad or Too specific? Or Apt?

Some definitions are simply too broad. They cover too many things. For instance, consider the following definition:

Currency is anything of value.

Well, teapots have value, but I doubt very much that you would be comfortable calling a tea pot “currency” (think about calling it “money”, sounds weird, doesn’t it?). Horses have value, but they don’t count as currency, right? So the group of things with value is much larger than the group of currencies (Yen, Mark, Rupee, Dollar, etc.), and so the definition doesn’t work. And then there’s the other issue of trying to understand what “value” means here. Monetary value? Exchange value? Sentimental value? This definition is too broad.

Other definitions are simply too narrow. They don’t seem to cover the whole group of things they’re meant to. Here’s one such example:

Example \(\PageIndex{1}\)

A (American) liberal is anyone who spent the 60’s burning bras and draft cards.

That seems to maybe cover a subset of American liberals: hippies. Even then, this might still be too narrow of a definition for hippy. Certainly, there are liberals who weren’t even born yet in the 60’s. There will be some who aren’t even born right now, let alone in the 1960’s. There were also liberals before the 60’s. This definition is far too restrictive: many people in fact count as liberals that would, by this definition, be included amongst the non-liberals.

Or maybe a definition is apt, meaning it captures the right group of things (the right extension) by being not too narrow (not too much intension) and not too vague or broad (not too little intension).

Argumentative vs. Neutral

Some definitions, like those in the dictionary, are at least trying to define the term or concept in a way that doesn’t slant in one way or another. Others, though, are biased towards a particular attitude or judgment or perhaps towards a particular conclusion. This is why we call these argumentative definitions, since they often implicitly contain an argument.

Definition: Argumentative definitions

Argumentative definitions have a clear ideological bias behind them. They’re trying to get you to feel a certain way or make a certain moral judgment about the thing being defined. Alternatively, an argumentative definition might be simply biased in favor of a particular conclusion in an argument.

• A Libertarian is someone who doesn’t understand what a government is.
• A stool is a chair designed to be uncomfortable.
• A laptop is a posture-killing personal computer.

Definition: Neutral definitions

Neutral definitions are at least attempts at trying to define a word or phrase or concept without biasing the reader toward one or another stance toward the thing being defined. They are attempts at bias-free definition (which is probably impossible, but they’re at least attempts).

• A drawer is a container on fixed rollers or rails.
• A dog is a domesticated member of the canus genus.
• A computer is anything that is designed to perform computations.

We need to be able to ask the right questions of a definition. These three distinctions correspond to good questions we can ask when trying to evaluate a particular definition. Knowing each of these distinctions helps one make better evaluations of definitions and therefore helps one to understand concepts and arguments that rest of definitions more clearly.

Fallacy of Equivocation

From Matthew J. Van Cleave's Introduction to Logic and Critical Thinking, version 1.4, pp. 189-195. Creative Commons Attribution 4.0 International License.

Consider the following argument:

Example \(\PageIndex{1}\)

Children are a headache. Aspirin will make headaches go away. Therefore, aspirin will make children go away.

This is a silly argument, but it illustrates the fallacy of equivocation. The problem is that the word “headache” is used equivocally—that is, in two different senses. In the first premise, “headache” is used figuratively, whereas in the second premise “headache” is used literally. The argument is only successful if the meaning of “headache” is the same in both premises. But it isn’t and this is what makes this argument an instance of the fallacy of equivocation.

Here’s another example:

Example \(\PageIndex{2}\)

Taking a logic class helps you learn how to argue. But there is already too much hostility in the world today, and the fewer arguments the better. Therefore, you shouldn’t take a logic class.

In this example, the word “argue” and “argument” are used equivocally. Hopefully, at this point in the text, you recognize the difference. (If not, go back and reread section 1.1.)

The fallacy of equivocation is not always so easy to spot. Here is a trickier example:

Example \(\PageIndex{3}\)

The existence of laws depends on the existence of intelligent beings like humans who create the laws. However, some laws existed before there were any humans (e.g., laws of physics). Therefore, there must be some non-human, intelligent being that created these laws of nature.

The term “law” is used equivocally here. In the first premise it is used to refer to societal laws, such as criminal law; in the second premise it is used to refer to laws of nature. Although we use the term “law” to apply to both cases, they are importantly different. Societal laws, such as the criminal law of a society, are enforced by people and there are punishments for breaking the laws. Natural laws, such as laws of physics, cannot be broken and thus there are no punishments for breaking them. (Does it make sense to scold the electron for not doing what the law says it will do?)

As with every informal fallacy we have examined in this section, equivocation can only be identified by understanding the meanings of the words involved. In fact, the definition of the fallacy of equivocation refers to this very fact: the same word is being used in two different senses (i.e., with two different meanings). So, unlike formal fallacies, identifying the fallacy of equivocation requires that we draw on our understanding of the meaning of words and of our understanding of the world, generally.

The following is from: Knachel, Matthew, "Fundamental Methods of Logic" (2017).

Philosophy Faculty Books. 1. http://dc.uwm.edu/phil_facbooks/1

Creative Commons Attribution 4.0 International License

Typical of natural languages is the phenomenon of homonymy24: when words have the same spelling and pronunciation, but different meanings—like ‘bat’ (referring to the nocturnal flying mammal) and ‘bat’ (referring to the thing you hit a baseball with). This kind of natural-language messiness allows for potential fallacious exploitation: a sneaky debater can manipulate the subtleties of meaning to convince people of things that aren’t true—or at least not justified based on what they say. We call this kind of maneuver the fallacy of equivocation

Here’s an example. Consider a banker; let’s call him Fred. Fred is the president of a bank, a real big-shot. He’s married, but he’s not faithful: he’s carrying on an affair with one of the tellers at his bank, Linda. Fred and Linda have a favorite activity: they take long lunches away from their workplace, having romantic picnics at a beautiful spot they found a short walk away. They lay out their blanket underneath an old, magnificent oak tree, which is situated right next to a river, and enjoy champagne and strawberries while canoodling and watching the boats float by.

One day—let’s say it’s the anniversary of when they started their affair—Fred and Linda decide to celebrate by skipping out of work entirely, spending the whole day at their favorite picnic spot. (Remember, Fred’s the boss, so he can get away with this.) When Fred arrives home that night, his wife is waiting for him. She suspects that something is up: “What are you hiding, Fred? Are you having an affair? I called your office twice, and your secretary said you were ‘unavailable’ both times. Tell me this: Did you even go to work today?” Fred replies, “Scout’s honor, dear. I swear I spent all day at the bank today.”

See what he did there? ‘Bank’ can refer either to a financial institution or the side of a river—a river bank. Fred and Linda’s favorite picnic spot is on a river bank, and Fred did indeed spend the whole day at that bank. He’s trying to convince his wife he hasn’t been cheating on her, and he exploits this little quirk of language to do so. That’s equivocation.

A similar linguistic phenomenon can also be exploited to equivocate: polysemy (Greek word, meaning ‘many signs (or meanings)’). This is distinct from, but similar to, homonymy. The meanings of homonyms are typically unrelated. In polysemy, the same word or phrase has multiple, related meanings—different senses. Consider the word ‘law’. The meaning that comes immediately to mind is the statutory one: “A rule of conduct imposed by authority.” (From the Oxford English Dictionary) The state law prohibiting murder is an instance of a law in this sense. There is another sense of ‘law’, however; this is the sense operative when we speak of scientific laws. These are regularities in nature—Newton’s law of universal gravitation, for example. These meanings are similar, but distinct: statutes, human laws, are prescriptive; scientific laws are descriptive. Human laws tell us how we ought to behave; scientific laws describe how things actually do, and must, behave. Human laws can be violated: I could murder someone. Scientific laws cannot be violated: if two bodies have mass, they will be attracted to one another by a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them; there’s no getting around it.

A common argument for the existence of God relies on equivocation between these two senses of ‘law’:

\[\begin{align*} & \text{There are laws of nature.} \\ & \text{By definition, laws are rules imposed by an Authority.} \\ & \text{So the laws of nature were imposed by an Authority.} \\ & \underline{ \text{The only Authority who could impose such laws is an all-powerful} \textbf{ Creator—God.}} \\ & \therefore \text{ God exists.} \end{align*}\]

This argument relies on fallaciously equivocating between the two senses of ‘law’—human and natural. It’s true that human laws are by definition imposed by an authority; but that is not true of natural laws. Additional argument is needed to establish that those must be so imposed.

A famous instance of equivocation of this sort occurred in 1998, when President Bill Clinton denied having an affair with White House intern Monica Lewinsky by declaring forcefully in a press conference: “I did not have sexual relations with that woman—Ms. Lewinsky.” The president wanted to convince his audience that nothing sexually inappropriate had happened, even though, as was revealed later, lots of icky sex stuff had been going on. He does this by taking advantage of the polysemy of the phrase ‘sexual relations’. In the broadest sense, the phrase connotes sexual activity of any kind—including oral sex (which Bill and Monica engaged in). This is the sense the president wants his audience to have in mind, so that they’re convinced by his denial that nothing untoward happened. But a more restrictive sense of ‘sexual relations’—a bit more old-fashioned and Southern usage—refers specifically to intercourse (which Bill and Monica did not engage in). It’s this sense that the president can fall back on if anyone accuses him of having lied; he can claim that, strictly speaking, he was telling the truth: he and Monica didn’t have ‘relations’ in the intercourse sense. Clinton later admitted to “misleading” the American people—but, importantly, not to lying.

The distinction between lying and misleading is a hard one to draw precisely, but roughly speaking it’s the difference between trying to get someone to believe something false by saying something false (lying) and trying to get them to believe something false by saying something true but deceptive (misleading). Besides homonymy and polysemy, yet another common linguistic phenomenon can be exploited to this end. This phenomenon is implicature, identified and named by the philosopher Paul Grice in the 1960s (See his Studies in the Way of Words, 1989, Cambridge: Harvard University Press). Implicatures are contents that we communicate over and above the literal meaning of what we say—aspects of what we mean by our utterances that aren’t stated explicitly. People listening to us infer these additional meanings based on the assumption that the speaker is being cooperative, observing some unwritten rules of conversational practice. To use one of Grice’s examples, suppose your car has run out of gas on the side of the road, and you stop me as I walk by, explaining your plight, and I say, “There’s a gas station right around the corner.” Part of what I communicate by my utterance is that the station is open and selling gas right now—that you can go there and solve your problem. You can infer this content based on the assumption that I’m being a cooperative conversational partner; if the station is closed or out of gas—and I knew it—then I would be acting unhelpfully, uncooperatively. Notice, though, that this content is not part of what I literally said: all I told you is that there is a gas station around the corner, which would still be true even if it were closed and/or out of gas.

Implicatures are yet another subtle aspect of meaning in natural language that can be exploited. So a final technique that we might classify under the fallacy of equivocation is false implication—saying things that are strictly speaking true, but which communicate false implicatures. Grocery stores do this all the time. You know those signs posted under, say, cans of soup that say “10 for $10”? That’s the store’s way of telling us that soup’s on sale for a buck a can; that’s right, you don’t need to buy 10 cans to get the deal; if you buy one can, it’s $1; 2 cans are $2, and so on. So why not post a sign saying “$1 per can”? Because the 10-for-$10 sign conveys the false implicature that you need to buy 10 cans in order to get the sale price. The store’s trying to drive up sales.

A striking example of false implicature is featured in one of the most prominent U.S. Supreme Court rulings on perjury law. In the original criminal case, a defendant by the name of Bronston had the following exchange with the prosecuting attorney: “Q. Do you have any bank accounts in Swiss Banks, Mr. Bronston? A. No, sir. Q. Have you ever? A. The company had an account there for about six months, in Zurich.” (Bronston v. United States, 409 US 352 - Supreme Court 1973). As it turns out, Bronston did not have any Swiss bank accounts at the time of the questioning, so his first answer was strictly true. But he did have Swiss bank accounts in the past. However, his second answer does not deny this. All he says is that his company had Swiss bank accounts—an answer that implicates that he himself did not. Based on this exchange, Bronston was convicted of perjury, but the Supreme Court overturned that conviction, pointing out that Bronston had not made any false statements (a requirement of the perjury statute); the falsehood he conveyed was an implicature. (The court didn’t use the term ‘implicature’ in its ruling, but this was the thrust of their argument.)