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Definitions and Arguments. Extensions. If something is a cat, and I call it “a cat” then I have correctly applied the word “cat” to it. The extension of a word is all the things that the word correctly applies to. The extension of ‘cat’ is all of the cats. Definitions.
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Extensions If something is a cat, and I call it “a cat” then I have correctly applied the word “cat” to it. The extension of a word is all the things that the word correctly applies to. The extension of ‘cat’ is all of the cats.
Definitions A definition is an attempt to explain the meaning of a word by using a different word or phrase that has the same meaning. The word being defined is called the definiendum (Latin for “to be defined”). The word or phrase doing the defining is called the definiens (Latin for “defining”).
Extensional Adequacy Definitions should be extensionally adequate, meaning that the definiens and the definiendum should correctly apply to exactly the same things. Compare: “A bachelor is a man.” “A bachelor is an unmmaried man.”
Extensional Adequacy However, just because two things have the same extension does not mean that one of them is a good definition of the other. Compare: “A renate is an animal with kidneys.” “A renate is an animal with a heart.”
Reportative Definitions The most common type of definition is a “reportative definition.” This is a definition that gives the meaning of a word as it is actually used by speakers of the language.
Dictionaries You might think that dictionaries contain mostly reportative definitions, but this is not true: much of the time they do not actually present definitions. Example: ‘red is the color of ripe tomatoes’
Subtlety One reason that dictionaries don’t contain definitions is that their goal is not a great degree of accuracy, but instead informing you how to use a word. A dictionary might say, “religion is belief in a superhuman controlling power.” This works most of the time, except in unusual scenarios.
Jargon Another concern with using dictionaries to determine the meaning of a word is that sometimes words have special meanings to certain groups of people. If you’re in a conversation with a philosopher and they use the words “free will,” they will mean something different than what’s in the dictionary.
Stipulative Definition A stipulative definition does not report the meanings of words as they are actually used. Instead it introduces a new meaning, either for an already existing word, or for a new, made-up word.
Spotting Stipulative Definitions There are many ways people have of indicating that they are stipulating a meaning: • “Let us define X as…” • “In what follows, we will understand X to mean…” • “Suppose we say that a thing is X when…”
Purposes of Stipulative Definitions Sometimes there is not a word for what you want to talk about, so you have to invent one. Science and math are full of words with stipulative definitions. (“prime,” “composite,” “whole,” “continuous”…)
Precising Definitions Precising definitions are a combination of reportative and stipulative definitions. This is when you take the normal meaning of a word, and stipulate some aspects of its meaning. “Criminals cannot apply for this job.” “Students get a set lunch discount.”
Using Precising Definitions Precising definitions can often be used to resolve certain arguments. “If by ‘marriage’ you mean that gays can have a religious ceremony, live together, and call each other ‘spouse’ then yes, gays can get married in our country; but if you mean by ‘marriage’ a recognition by the government and society of the validity of such a relationship, then they cannot.”
Persuasive Definitions Persuasive definitions are definitions that get the correct meaning of a term, but not the correct emotional impact of it. The term is neutral, but the persuasive definition adds a positive (or negative) dimension to it.
Example Example from Hurley (2008): • definition supporting taxation: “the procedure by means of which our commonwealth is preserved and sustained” • definition opposing taxation: “the procedure used by bureaucrats to rip off the people who elected them”
Problems Persuasive definitions (as you would expect) can persuade people to change their minds or to support a particular view. But they do not do this with a good argument– instead they convince with emotional impact. Having a strong emotional reaction to something is not a reason for supporting it or being against it.
Evaluating Definitions As we’ve seen, definitions can play an important role in understanding arguments, resolving arguments, and misleading people. It is thus important to understand how they can go wrong, and how they can get things right.
Example: Too Wide Some definitions are “too wide.” This is a metaphor about the definition’s extension. A definition is “too wide” when it includes all the things in the word’s extension plus some other stuff. “A small business is a business with less than 25 workers.”
Example: Too Narrow A definition is “too narrow” when it includes only some of the things in the word’s extension. “A Christian is someone who believes that the Bible is the word of God. Therefore, allowing gay marriage discriminates against Christians, because the Bible says that homosexuality is wrong.”
Example: Neither (Both?) “A restaurant is a place where one can eat.” You can eat in your house, or in a park. So there are places where one can eat that are not restaurants. There are restaurants one cannot eat at, for example takeaway restaurants.
The Law and Definitions Definitions are particularly important in legal contexts. Often laws are written in ways that don’t foresee certain strange events, and they either technically apply or don’t apply, when that’s not what we want or expect.
“Using” A Gun In the US, there are higher penalties for drug crimes when people involved in the crime “use” a gun. But what happens if you trade your gun for drugs? Is that a “use”? Smith v. US: person giving gun uses it. Watson v. US: person receiving gun does not.
“Occurrence” On 11 September 2001, hijackers flew two planes into the World Trade Center towers in New York City. The towers collapsed and almost 3,000 people died. The lessee of the towers, Larry Silverstein, had insurance up to $3.5 million USD ($27m HKD) for any “occurrence” that damaged the buildings.
“Person” Suppose the government wants more people per car, so that less pollution is emitted for every person transported. They open up a lane in the road for cars with 2 or more people in them. You’re not allowed to drive in the lane if you’re the only “person” in your car. Now suppose that you’re pregnant? Can you drive in the lane?
Verbal Disputes Some arguments are “purely verbal” and depend on the meanings of words. Some are “factual” and depend on what the facts are. William James gives an example of a purely verbal dispute involving a man chasing a squirrel around a tree.
James’ Squirrel “Which party is right depends on what you practically mean by ‘going round’ the squirrel. If you mean passing from the north of him to the east, then to the south, then to the west, and then to the north of him again, obviously the man does go round him, for he occupies these successive positions…”
James’ Squirrel “…But if on the contrary you mean being first in front of him, then on the right of him then behind him, then on his left, and finally in front again, it is quite as obvious that the man fails to go round him... Make the distinction, and there is no occasion for any farther dispute.”
Ambiguity An ambiguous word is a word with more than one meaning. ‘Bank’ in English can mean a financial institution or the side of a river. Sometimes sentences can be ambiguous even if none of their words are. “Flying planes can be dangerous.”
Vagueness A vague word is not ambiguous– it has only one meaning. But it can be unclear whether it applies in any particular circumstance: • Tall • Rich • Bald • Beautiful
Usefulness of Vagueness Vague words are useful for communication. It’s better to have a word ‘tall’ for describing people than a word that means ‘over 1.8 meters.’ First, we might not know whether someone is over 1.8 meters. Second, we might not care about information so specific. Finally, we might want to call children ‘tall’ if they are tall for their age.
When to Avoid Vagueness? Even though vagueness is useful, it sometimes causes trouble. Vague policy recommendations are often completely unhelpful. If student reviews say “the class is hard,” it’s difficult to tell how hard it is, or in what ways. If someone says we need “better hospitals” we don’t know what counts.
Difficulty of Confirming Vague Statements Furthermore, people can use vague statements to avoid responsibility for what they’re saying.
No TRUE Scotsman Teacher: You didn’t get an A because you didn’t work hard. Student: But I did work hard, I studied five hours every day, came to class and office hours… Teacher: But you didn’t REALLY work hard, because people who REALLY work hard get A’s.
Arguments An ‘argument’ in philosophy is not a quarrel or dispute, instead it is a number of premises that are given in support of a conclusion.
Indicating Premises • since • firstly, secondly, ... • for, as, after all, • assuming that, in view of the fact that • follows from, as shown / indicated by • may be inferred / deduced / derived from
Indicating Conclusions • therefore, so, it follows that • hence, consequently • suggests / proves / demonstrates that • entails, implies
Hidden Assumptions Unlike arguments written in logic and proved using our formal logical systems SL and PL, arguments in ordinary language don’t always state all their assumptions.
Example #1 Assumption: If people make fun of religious beliefs, then religious people will have their feelings hurt. Hidden Assumption: It should be illegal to hurt people’s feelings. Conclusion: It should be illegal to make fun of religious beliefs.
Example #2 Assumption: My opponent wants to increase social welfare programs. Assumption: Social welfare programs help minorities more than other people. Conclusion: His agenda is to help minorities at the expense of the rest of us.
Example #3 Assumption: Lots of students talk with one another very loudly in class. Assumption: If lots of students do something, then it’s OK to do. Conclusion: It’s OK if I talk to my friends loudly in class.
Analogies An analogy is when you take two different things and compare them in some respect. “Life is like a box of chocolates: you never know what you’re going to get.”
Analogical Arguments An analogy is often used as the premise in an argument. “X is like Y; Y is Z; therefore X is Z.”
Analogical Arguments The universe is a complex system of interacting parts that serve a purpose. A watch is a complex system of interacting parts that serve a purpose. If we found a watch by itself in the wilderness we’d assume that some intelligent designer had made it. Therefore we should assume that an intelligent designer made the universe.
Analogies as Insults Analogies are sometimes used solely as smear tactics, with no real intellectual purpose. American musician Hank Williams Jr. said that John Boehner playing golf with Barack Obama was “like Netanyahu playing golf with Hitler.” All this analogy does is suggest that Obama is like Hitler.
Analogy to Arguments Analogies provide an important way of showing that arguments are bad: Person #1: The Iraq invasion was good; many Iraqis (e.g. Kurds) supported it. Person #2: That argument is like this one: Hitler’s invasion of Czechoslovakia was good; many Czechs supported it.
